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22.7: Review Exercises

22.7: Review Exercises



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Chapter Review Exercises

Distance and Midpoint Formulas; Circles

Exercise (PageIndex{1}) Use the Distance Formula

In the following exercises, find the distance between the points. Round to the nearest tenth if needed.

  1. ((-5,1)) and ((-1,4))
  2. ((-2,5)) and ((1,5))
  3. ((8,2)) and ((-7,-3))
  4. ((1,-4)) and ((5,-5))
Answer

2. (d=3)

4. (d=sqrt{17}, d approx 4.1)

Exercise (PageIndex{2}) Use the Midpoint Formula

In the following exercises, find the midpoint of the line segments whose endpoints are given.

  1. ((-2,-6)) and ((-4,-2))
  2. ((3,7)) and ((5,1))
  3. ((-8,-10)) and ((9,5))
  4. ((-3,2)) and ((6,-9))
Answer

2. ((4,4))

4. (left(frac{3}{2},-frac{7}{2} ight))

Exercise (PageIndex{3}) Write the Equation of a Circle in Standard Form

In the following exercises, write the standard form of the equation of the circle with the given information.

  1. radius is (15) and center is ((0,0))
  2. radius is (sqrt{7}) and center is ((0,0))
  3. radius is (9) and center is ((-3,5))
  4. radius is (7) and center is ((-2,-5))
  5. center is ((3,6)) and a point on the circle is ((3,-2))
  6. center is ((2,2)) and a point on the circle is ((4,4))
Answer

2. (x^{2}+y^{2}=7)

4. ((x+2)^{2}+(y+5)^{2}=49)

6. ((x-2)^{2}+(y-2)^{2}=8)

Exercise (PageIndex{4}) Graph a Circle

In the following exercises,

  1. Find the center and radius, then
  2. Graph each circle.
  1. (2 x^{2}+2 y^{2}=450)
  2. (3 x^{2}+3 y^{2}=432)
  3. ((x+3)^{2}+(y-5)^{2}=81)
  4. ((x+2)^{2}+(y+5)^{2}=49)
  5. (x^{2}+y^{2}-6 x-12 y-19=0)
  6. (x^{2}+y^{2}-4 y-60=0)
Answer

2.

  1. radius: (12,) center: ((0,0))

4.

  1. radius: (7,) center: ((-2,-5))

6.

  1. radius: (8,) center: ((0,2))

Parabolas

Exercise (PageIndex{5}) Graph Vertical Parabolas

In the following exercises, graph each equation by using its properties.

  1. (y=x^{2}+4 x-3)
  2. (y=2 x^{2}+10 x+7)
  3. (y=-6 x^{2}+12 x-1)
  4. (y=-x^{2}+10 x)
Answer

2.

4.

Exercise (PageIndex{6}) Graph Vertical Parabolas

In the following exercises,

  1. Write the equation in standard form, then
  2. Use properties of the standard form to graph the equation.
  1. (y=x^{2}+4 x+7)
  2. (y=2 x^{2}-4 x-2)
  3. (y=-3 x^{2}-18 x-29)
  4. (y=-x^{2}+12 x-35)
Answer

2.

  1. (y=2(x-1)^{2}-4)

4.

  1. (y=-(x-6)^{2}+1)

Exercise (PageIndex{7}) Graph Horizontal Parabolas

In the following exercises, graph each equation by using its properties.

  1. (x=2 y^{2})
  2. (x=2 y^{2}+4 y+6)
  3. (x=-y^{2}+2 y-4)
  4. (x=-3 y^{2})
Answer

2.

4.

Exercise (PageIndex{8}) Graph Horizontal Parabolas

In the following exercises,

  1. Write the equation in standard form, then
  2. Use properties of the standard form to graph the equation.
  1. (x=4 y^{2}+8 y)
  2. (x=y^{2}+4 y+5)
  3. (x=-y^{2}-6 y-7)
  4. (x=-2 y^{2}+4 y)
Answer

2.

  1. (x=(y+2)^{2}+1)

4.

  1. (x=-2(y-1)^{2}+2)

Exercise (PageIndex{9}) Solve Applications with Parabolas

In the following exercises, create the equation of the parabolic arch formed in the foundation of the bridge shown. Give the answer in standard form.

1.

2.

Answer

2. (y=-frac{1}{9} x^{2}+frac{10}{3} x)

Ellipses

Exercise (PageIndex{10}) Graph an Ellipse with Center at the Origin

In the following exercises, graph each ellipse.

  1. (frac{x^{2}}{36}+frac{y^{2}}{25}=1)
  2. (frac{x^{2}}{4}+frac{y^{2}}{81}=1)
  3. (49 x^{2}+64 y^{2}=3136)
  4. (9 x^{2}+y^{2}=9)
Answer

2.

4.

Exercise (PageIndex{11}) Find the Equation of an Ellipse with Center at the Origin

In the following exercises, find the equation of the ellipse shown in the graph.

1.

2.

Answer

2. (frac{x^{2}}{36}+frac{y^{2}}{64}=1)

Exercise (PageIndex{12}) Graph an Ellipse with Center Not at the Origin

In the following exercises, graph each ellipse.

  1. (frac{(x-1)^{2}}{25}+frac{(y-6)^{2}}{4}=1)
  2. (frac{(x+4)^{2}}{16}+frac{(y+1)^{2}}{9}=1)
  3. (frac{(x-5)^{2}}{16}+frac{(y+3)^{2}}{36}=1)
  4. (frac{(x+3)^{2}}{9}+frac{(y-2)^{2}}{25}=1)
Answer

2.

4.

Exercise (PageIndex{13}) Graph an Ellipse with Center Not at the Origin

In the following exercises,

  1. Write the equation in standard form and
  2. Graph.
  1. (x^{2}+y^{2}+12 x+40 y+120=0)
  2. (25 x^{2}+4 y^{2}-150 x-56 y+321=0)
  3. (25 x^{2}+4 y^{2}+150 x+125=0)
  4. (4 x^{2}+9 y^{2}-126 x+405=0)
Answer

2.

  1. (frac{(x-3)^{2}}{4}+frac{(y-7)^{2}}{25}=1)

4.

  1. (frac{x^{2}}{9}+frac{(y-7)^{2}}{4}=1)

Exercise (PageIndex{14}) Solve Applications with Ellipses

In the following exercises, write the equation of the ellipse described.

  1. A comet moves in an elliptical orbit around a sun. The closest the comet gets to the sun is approximately (10) AU and the furthest is approximately (90) AU. The sun is one of the foci of the elliptical orbit. Letting the ellipse center at the origin and labeling the axes in AU, the orbit will look like the figure below. Use the graph to write an equation for the elliptical orbit of the comet.
Answer

1. Solve

Hyperbolas

Exercise (PageIndex{15}) Graph a Hyperbola with Center at ((0,0))

In the following exercises, graph.

  1. (frac{x^{2}}{25}-frac{y^{2}}{9}=1)
  2. (frac{y^{2}}{49}-frac{x^{2}}{16}=1)
  3. (9 y^{2}-16 x^{2}=144)
  4. (16 x^{2}-4 y^{2}=64)
Answer

1.

3.

Exercise (PageIndex{16}) Graph a Hyperbola with Center at ((h,k))

In the following exercises, graph.

  1. (frac{(x+1)^{2}}{4}-frac{(y+1)^{2}}{9}=1)
  2. (frac{(x-2)^{2}}{4}-frac{(y-3)^{2}}{16}=1)
  3. (frac{(y+2)^{2}}{9}-frac{(x+1)^{2}}{9}=1)
  4. (frac{(y-1)^{2}}{25}-frac{(x-2)^{2}}{9}=1)
Answer

1.

3.

Exercise (PageIndex{17}) Graph a Hyperbola with Center at ((h,k))

In the following exercises,

  1. Write the equation in standard form and
  2. Graph.
  1. (4 x^{2}-16 y^{2}+8 x+96 y-204=0)
  2. (16 x^{2}-4 y^{2}-64 x-24 y-36=0)
  3. (4 y^{2}-16 x^{2}+32 x-8 y-76=0)
  4. (36 y^{2}-16 x^{2}-96 x+216 y-396=0)
Answer

1.

  1. (frac{(x+1)^{2}}{16}-frac{(y-3)^{2}}{4}=1)

3.

  1. (frac{(y-1)^{2}}{16}-frac{(x-1)^{2}}{4}=1)

Exercise (PageIndex{18}) Identify the Graph of Each Equation as a Circle, Parabola, Ellipse, or Hyperbola

In the following exercises, identify the type of graph.

    1. (16 y^{2}-9 x^{2}-36 x-96 y-36=0)
    2. (x^{2}+y^{2}-4 x+10 y-7=0)
    3. (y=x^{2}-2 x+3)
    4. (25 x^{2}+9 y^{2}=225)
    1. (x^{2}+y^{2}+4 x-10 y+25=0)
    2. (y^{2}-x^{2}-4 y+2 x-6=0)
    3. (x=-y^{2}-2 y+3)
    4. (16 x^{2}+9 y^{2}=144)
Answer

1.

  1. Hyperbola
  2. Circle
  3. Parabola
  4. Ellipse

Solve Systems of Nonlinear Equations

Exercise (PageIndex{19}) Solve a System of Nonlinear Equations Using Graphing

In the following exercises, solve the system of equations by using graphing.

  1. (left{egin{array}{l}{3 x^{2}-y=0} {y=2 x-1}end{array} ight.)
  2. (left{egin{array}{l}{y=x^{2}-4} {y=x-4}end{array} ight.)
  3. (left{egin{array}{l}{x^{2}+y^{2}=169} {x=12}end{array} ight.)
  4. (left{egin{array}{l}{x^{2}+y^{2}=25} {y=-5}end{array} ight.)
Answer

1.

3.

Exercise (PageIndex{20}) Solve a System of Nonlinear Equations Using Substitution

In the following exercises, solve the system of equations by using substitution.

  1. (left{egin{array}{l}{y=x^{2}+3} {y=-2 x+2}end{array} ight.)
  2. (left{egin{array}{l}{x^{2}+y^{2}=4} {x-y=4}end{array} ight.)
  3. (left{egin{array}{l}{9 x^{2}+4 y^{2}=36} {y-x=5}end{array} ight.)
  4. (left{egin{array}{l}{x^{2}+4 y^{2}=4} {2 x-y=1}end{array} ight.)
Answer

1. ((-1,4))

3. No solution

Exercise (PageIndex{21}) Solve a System of Nonlinear Equations Using Elimination

In the following exercises, solve the system of equations by using elimination.

  1. (left{egin{array}{l}{x^{2}+y^{2}=16} {x^{2}-2 y-1=0}end{array} ight.)
  2. (left{egin{array}{l}{x^{2}-y^{2}=5} {-2 x^{2}-3 y^{2}=-30}end{array} ight.)
  3. (left{egin{array}{l}{4 x^{2}+9 y^{2}=36} {3 y^{2}-4 x=12}end{array} ight.)
  4. (left{egin{array}{l}{x^{2}+y^{2}=14} {x^{2}-y^{2}=16}end{array} ight.)
Answer

1. ((-sqrt{7}, 3),(sqrt{7}, 3))

3. ((-3,0),(0,-2),(0,2))

Exercise (PageIndex{22}) Use a System of Nonlinear Equations to Solve Applications

In the following exercises, solve the problem using a system of equations.

  1. The sum of the squares of two numbers is (25). The difference of the numbers is (1). Find the numbers.
  2. The difference of the squares of two numbers is (45). The difference of the square of the first number and twice the square of the second number is (9). Find the numbers.
  3. The perimeter of a rectangle is (58) meters and its area is (210) square meters. Find the length and width of the rectangle.
  4. Colton purchased a larger microwave for his kitchen. The diagonal of the front of the microwave measures (34) inches. The front also has an area of (480) square inches. What are the length and width of the microwave?
Answer

1. (-3) and (-4) or (4) and (3)

3. If the length is (14) inches, the width is (15) inches. If the length is (15) inches, the width is (14) inches.

Practice Test

Exercise (PageIndex{23})

In the following exercises, find the distance between the points and the midpoint of the line segment with the given endpoints. Round to the nearest tenth as needed.

  1. ((-4,-3)) and ((-10,-11))
  2. ((6,8)) and ((-5,-3))
Answer

1. distance: (10,) midpoint: ((-7,-7))

Exercise (PageIndex{24})

In the following exercises, write the standard form of the equation of the circle with the given information.

  1. radius is (11) and center is ((0,0))
  2. radius is (12) and center is ((10,-2))
  3. center is ((-2,3)) and a point on the circle is ((2,-3))
  4. Find the equation of the ellipse shown in the graph.
Answer

1. (x^{2}+y^{2}=121)

3. ((x+2)^{2}+(y-3)^{2}=52)

Exercise (PageIndex{25})

In the following exercises,

  1. Identify the type of graph of each equation as a circle, parabola, ellipse, or hyperbola, and
  2. Graph the equation.
  1. (4 x^{2}+49 y^{2}=196)
  2. (y=3(x-2)^{2}-2)
  3. (3 x^{2}+3 y^{2}=27)
  4. (frac{y^{2}}{100}-frac{x^{2}}{36}=1)
  5. (frac{x^{2}}{16}+frac{y^{2}}{81}=1)
  6. (x=2 y^{2}+10 y+7)
  7. (64 x^{2}-9 y^{2}=576)
Answer

1.

  1. Ellipse

3.

  1. Circle

5.

  1. Ellipse

7.

  1. Hyperbola

Exercise (PageIndex{26})

In the following exercises,

  1. Identify the type of graph of each equation as a circle, parabola, ellipse, or hyperbola,
  2. Write the equation in standard form, and
  3. Graph the equation.
  1. (25 x^{2}+64 y^{2}+200 x-256 y-944=0)
  2. (x^{2}+y^{2}+10 x+6 y+30=0)
  3. (x=-y^{2}+2 y-4)
  4. (9 x^{2}-25 y^{2}-36 x-50 y-214=0)
  5. (y=x^{2}+6 x+8)
  6. Solve the nonlinear system of equations by graphing: (left{egin{array}{l}{3 y^{2}-x=0} {y=-2 x-1}end{array} ight.).
  7. Solve the nonlinear system of equations using substitution: (left{egin{array}{l}{x^{2}+y^{2}=8} {y=-x-4}end{array} ight.).
  8. Solve the nonlinear system of equations using elimination: (left{egin{array}{l}{x^{2}+9 y^{2}=9} {2 x^{2}-9 y^{2}=18}end{array} ight.)
  9. Create the equation of the parabolic arch formed in the foundation of the bridge shown. Give the answer in (y=a x^{2}+b x+c) form.

10. A comet moves in an elliptical orbit around a sun. The closest the comet gets to the sun is approximately (20) AU and the furthest is approximately (70) AU. Use the graph to write an equation for the elliptical orbit of the comet.

11. The sum of two numbers is (22) and the product is (−240). Find the numbers.

12. For her birthday, Olive’s grandparents bought her a new widescreen TV. Before opening it she wants to make sure it will fit her entertainment center. The TV is (55)”. The size of a TV is measured on the diagonal of the screen and a widescreen has a length that is larger than the width. The screen also has an area of (1452) square inches. Her entertainment center has an insert for the TV with a length of (50) inches and width of (40) inches. What are the length and width of the TV screen and will it fit Olive’s entertainment center?

Answer

2.

  1. Circle
  2. ((x+5)^{2}+(y+3)^{2}=4)

4.

  1. Hyperbola
  2. (frac{(x-2)^{2}}{25}-frac{(y+1)^{2}}{9}=1)

6. No solution

8. ((0,-3),(0,3))

10. (frac{x^{2}}{2025}+frac{y^{2}}{1400}=1)

12. The length is (44) inches and the width is (33) inches. The TV will fit Olive’s entertainment center.

Glossary

system of nonlinear equations
A system of nonlinear equations is a system where at least one of the equations is not linear.

22.7: Review Exercises

Find the first 5 terms of the sequence as well as the 30 th term.

Find the first 5 terms of the sequence.

a n = a n − 1 + 5 where a 1 = 0

a n = 4 a n − 1 + 1 where a 1 = − 2

a n = a n − 2 − 3 a n − 1 where a 1 = 0 and a 2 = − 3

a n = 5 a n − 2 − a n − 1 where a 1 = − 1 and a 2 = 0

Find the indicated partial sum.

Arithmetic Sequences and Series

Write the first 5 terms of the arithmetic sequence given its first term and common difference. Find a formula for its general term.

Given the terms of an arithmetic sequence, find a formula for the general term.

Calculate the indicated sum given the formula for the general term of an arithmetic sequence.

Find the sum of the first 175 positive odd integers.

Find the sum of the first 175 positive even integers.

Find all arithmetic means between a 1 = 2 3 and a 5 = − 2 3

Find all arithmetic means between a 3 = − 7 and a 7 = 13 .

A 5-year salary contract offers $58,200 for the first year with a $4,200 increase each additional year. Determine the total salary obligation over the 5-year period.

The first row of seating in a theater consists of 10 seats. Each successive row consists of four more seats than the previous row. If there are 14 rows, how many total seats are there in the theater?

Geometric Sequences and Series

Write the first 5 terms of the geometric sequence given its first term and common ratio. Find a formula for its general term.

Given the terms of a geometric sequence, find a formula for the general term.

a 2 = − 5 2 and a 5 = − 625 16

Find all geometric means between a 1 = − 1 and a 4 = 64 .

Find all geometric means between a 3 = 6 and a 6 = 162 .

Calculate the indicated sum given the formula for the general term of a geometric sequence.

After the first year of operation, the value of a company van was reported to be $40,000. Because of depreciation, after the second year of operation the van was reported to have a value of $32,000 and then $25,600 after the third year of operation. Write a formula that gives the value of the van after the nth year of operation. Use it to determine the value of the van after 10 years of operation.

The number of cells in a culture of bacteria doubles every 6 hours. If 250 cells are initially present, write a sequence that shows the number of cells present after every 6-hour period for one day. Write a formula that gives the number of cells after the nth 6-hour period.

A ball bounces back to one-half of the height that it fell from. If dropped from 32 feet, approximate the total distance the ball travels.

A structured settlement yields an amount in dollars each year n according to the formula p n = 12,500 ( 0.75 ) n − 1 . What is the total value of a 10-year settlement?

Classify the sequence as arithmetic, geometric, or neither.


7 Reasons You Hit a Workout or Weight Loss Plateau & 5 Fixes

So you’ve hit a workout or weight loss plateau the size of a…well, an actual plateau, eh?

Have no fear, our step-by-step guide will get you back on track! (Plus, the most badass Bruce Lee quote you’ll ever read).

Whether you’ve stalled in your weight loss journey, strength training, or some other fitness benchmark, today we’ll tell you exactly how to keep progressing by sharing with you the exact tools we use with our coaching clients.

A Nerd Fitness Coach can design you a program to keep progressing! Learn more here.

Don’t lose morale. Together we got this!

I know how demoralizing plateaus can be, especially when it comes to strength training and weight loss – they can be a total momentum killer!

It’s actually why we built our newest app, Nerd Fitness Journey! It’s designed so when you wake up in the morning, you know the exact next step to help you reach your goals.

You can try it for free right here, so this plateau can be a thing of the past:

A plateau occurs when you stall out on progress despite continuing to do “all of the right things,” usually including:

Our bodies go from losing weight consistently to getting stuck at a certain number….


What exercises to do after knee replacement surgery?

1. Isometrics Exercise

Isometrics apply zero pressure to your joints. More technically, the maneuvers increase muscle strength without affecting muscle length or joint angle. They can be done anywhere, at any time. All you do is tighten your muscle, hold the tension for a few seconds, and release. Isometrics will be the first maneuvers you do after your total knee replacement.

Do this Easy Calf Strengthener: Your calf muscles are actually two muscles. The larger of the two is closer to your knee. It is known as the gastrocnemius. The smaller of the two is closer to your ankle. This one is known as the soleus. Strong calves reduce your risks of falling, tripping, and/or stumbling.

Sit in a comfortable chair. Place your feet firmly on the floor. Tighten your right calf muscle. Hold this tension for eight seconds. Release the tension. Repeat this maneuver five times. Does it again with your left calf muscle.

2. Chair Yoga Exercise

This form of yoga is becoming more popular for a variety of reasons. It is ideal for those with health issues. Poses are gentle, slow-moving, and thorough. This is NOT EASY yoga, though. You will get a thorough workout that both strengthens and flexes your body.

You utilize the chair in a variety of ways with this relaxing, yet effective, yoga form. Poses involve sitting in a chair, standing behind the chair, or leaning in front of the chair.

3. Balance Builder Exercise

Building your balance back up after a total knee replacement is crucial for your overall health. Good balance decreases your risks of falling. Here is an easy balance exercise you can do any time of the day:

Stand on the right side of your chair. Place your feet shoulder-width apart. Gently place your hands in a prayer pose in front of your chest. Slowly lift your right leg from the surface.

Gently and slowly move your leg away from your body. Place your body weight onto your left leg. Hold this position for 10 seconds. Slowly return to the original position. Do the exercise again with your left leg.

Use the chair as your anchor whenever you need it.

4. Quad Strengthener Exercise

Sit in the chair. Move your body towards the front of the chair. Place your feet firmly on the floor. Slowly straighten your right knee (as much as possible) to lift your lower leg toward the ceiling. This will be very difficult in the beginning. Hold this position for eight seconds. Slowly lower to the original position. Repeat this movement five times. Perform this maneuver with your left leg.

5. Walking

If you were like me, your health care provider has you up and walking down the hospital corridors the day after a total knee replacement. There is a reason for this. Walking improves your balance, flexibility, and strength.

Be sure to walk only on flat surfaces. Start indoors at your own home. Then, progress to a physical therapy or fitness center. During this time, you may wish to use an indoor track. These walking gems not only keep you protected from the outdoor elements, they provide a cushioning effect which your joints love.

Avoid walking on gravel, stones, and uneven surfaces. Uneven surfaces include pothole fillings, elevated hiking trails, buckled pavements, and hills. Even mild hills can detrimentally affect your balance.

Remember the importance of good walking shoes. Nothing can hinder your walking health more than painful feet. When first recuperating from your total knee replacement, you will probably use your slippers in the comfort of your home.

Always start out walking at a comfortable, gentle pace for only a few minutes. You may need to use a cane or walker, depending on your individual situation. Do not concern yourself with speed.

Gradually increase your speed and time. Your ultimate goal is to walk at a pace that allows you to speak without becoming breathless.

6. Water Aerobics Exercise

Water aerobics provide a wonderful workout for those of us with a total knee replacement or other joint concern. Many people fear to fall during workouts. Water to the rescue! Water’s natural buoyancy properties prevent falling. It provides a safe environment that everyone – at any age – can enjoy.

You know how painful exercising can be after a tkr? Water provides a joint-friendly medium that reduces pain. There is no pressure applied to the joints. That is why this exercise medium is so popular with individuals having joint concerns.

Water also provides a natural resistance that strengthens muscles. Every movement is met with a counteractive movement. Though the weight strengthening may be less than land-based weight lifting, you will receive benefits.

Moving is easier in water. This increased fluidity is a blessing for getting stiff, injured, or painful joints moving.

Consider joining a water aerobics class conducted by a trained professional. A good workout program will help your entire body. Your arms, abdomen, legs, and heart will all thank you!

7. Flexor Exercise in Your Routine

Your hips support your body weight, also. Your hip flexors play an important role in optimizing your total knee replacement. Strong, flexible hips make for a healthier, happier person! Keep your hips lubricated and flexible by doing the following water-based maneuver:

Get into waist-deep water. Place your right side against the pool’s wall. Hold onto the side, if needed. Slowly lift your left leg sideways, away from you. Do not bend your knee. Return to the original position. Repeat this maneuver five times.

Turn your body around so your left side is against the pool’s wall. Repeat this exercise with your right leg.

8. Try Some Weights

Weights take all forms. Whether it is a fitness machine with weights, sandbags, free-standing barbells/dumbbells, and/or pulleys – there is something for everyone here. You can even make your own weights.

9. Straightening Your Knee

Many people need to straighten out their total knee replacement leg during recuperation. You can work on this with sandbags.

Sit on the sofa. Stretch out your tkr leg. Prop your ankle onto a pillow. Allow space underneath your knee. Place the sandbag on your knee. It will be painful. Do this for two minutes. Remove the bag. Repeat exercise throughout the day.

Never stop exercising after a total knee replacement. Make physical activity a part of your everyday living. You won’t regret it!


Birth

Prior to birth, the lungs are filled with amniotic fluid, mucus, and surfactant. As the fetus is squeezed through the birth canal, the fetal thoracic cavity is compressed, expelling much of this fluid. Some fluid remains, however, but is rapidly absorbed by the body shortly after birth. The first inhalation occurs within 10 seconds after birth and not only serves as the first inspiration, but also acts to inflate the lungs. Pulmonary surfactant is critical for inflation to occur, as it reduces the surface tension of the alveoli. Preterm birth around 26 weeks frequently results in severe respiratory distress, although with current medical advancements, some babies may survive. Prior to 26 weeks, sufficient pulmonary surfactant is not produced, and the surfaces for gas exchange have not formed adequately therefore, survival is low.

Respiratory distress syndrome (RDS) primarily occurs in infants born prematurely. Up to 50 percent of infants born between 26 and 28 weeks and fewer than 30 percent of infants born between 30 and 31 weeks develop RDS. RDS results from insufficient production of pulmonary surfactant, thereby preventing the lungs from properly inflating at birth. A small amount of pulmonary surfactant is produced beginning at around 20 weeks however, this is not sufficient for inflation of the lungs. As a result, dyspnea occurs and gas exchange cannot be performed properly. Blood oxygen levels are low, whereas blood carbon dioxide levels and pH are high.

The primary cause of RDS is premature birth, which may be due to a variety of known or unknown causes. Other risk factors include gestational diabetes, cesarean delivery, second-born twins, and family history of RDS. The presence of RDS can lead to other serious disorders, such as septicemia (infection of the blood) or pulmonary hemorrhage. Therefore, it is important that RDS is immediately recognized and treated to prevent death and reduce the risk of developing other disorders.

Medical advances have resulted in an improved ability to treat RDS and support the infant until proper lung development can occur. At the time of delivery, treatment may include resuscitation and intubation if the infant does not breathe on his or her own. These infants would need to be placed on a ventilator to mechanically assist with the breathing process. If spontaneous breathing occurs, application of nasal continuous positive airway pressure (CPAP) may be required. In addition, pulmonary surfactant is typically administered. Death due to RDS has been reduced by 50 percent due to the introduction of pulmonary surfactant therapy. Other therapies may include corticosteroids, supplemental oxygen, and assisted ventilation. Supportive therapies, such as temperature regulation, nutritional support, and antibiotics, may be administered to the premature infant as well.

Chapter Review

The development of the respiratory system in the fetus begins at about 4 weeks and continues into childhood. Ectodermal tissue in the anterior portion of the head region invaginates posteriorly, forming olfactory pits, which ultimately fuse with endodermal tissue of the early pharynx. At about this same time, an protrusion of endodermal tissue extends anteriorly from the foregut, producing a lung bud, which continues to elongate until it forms the laryngotracheal bud. The proximal portion of this structure will mature into the trachea, whereas the bulbous end will branch to form two bronchial buds. These buds then branch repeatedly, so that at about week 16, all major airway structures are present. Development progresses after week 16 as respiratory bronchioles and alveolar ducts form, and extensive vascularization occurs. Alveolar type I cells also begin to take shape. Type II pulmonary cells develop and begin to produce small amounts of surfactant. As the fetus grows, the respiratory system continues to expand as more alveoli develop and more surfactant is produced. Beginning at about week 36 and lasting into childhood, alveolar precursors mature to become fully functional alveoli. At birth, compression of the thoracic cavity forces much of the fluid in the lungs to be expelled. The first inhalation inflates the lungs. Fetal breathing movements begin around week 20 or 21, and occur when contractions of the respiratory muscles cause the fetus to inhale and exhale amniotic fluid. These movements continue until birth and may help to tone the muscles in preparation for breathing after birth and are a sign of good health.


5 Examples Of Body Composition Exercises You Can Do At Home

Transforming your body shape is not as hard as it may sound. Whether you want to lose weight or lose fat but gain muscles, the fact is that such goals are achievable. The trick is discovering the key body composition exercise to perform in order to attain these goals.

Here is a sample of five effective workouts to try at home to transform your body shape. Remember to consult with your trainer and doctor before trying any of these exercises. They are:

Burpees

Burpees are among the best total body exercises. Performing them makes your heart pound faster, and your heart rate increases quickly. They are great workouts to train your muscle coordination, endurance, and power ( 3 ).

However, simply because they are effective does not mean they are a favorite. You may hate them, specifically, because they tend to incorporate other exercises. A burpee will incorporate a squat, a push-up, and a jump.

You may modify a burpee depending on your fitness abilities. Nonetheless, the basic protocol of performing a burpee is as follows:

  • Start in a standing position with your arms by your sides. When ready, drop into a squat.
  • Instead of coming back up, you will proceed to drop into the high plank position.
  • Perform one push-up, and then jump up into the standing position.
  • Repeat your set, take a break, and, if possible, do another set or two.

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Key Pointers

When you start your fitness journey, you will be classified into the beginner, intermediate, or advanced fitness levels. The fitness aspect determines the exercise variation or modification that you perform. Here are various key pointers to take note of when doing the burpee:

  • If you are new to these workouts, enroll a trainer to help you perform them correctly. Similarly, you can reduce the intensity of this workout by first skipping the jump ( 8 ).
  • If you have any hip or knee injuries, consult with your doctor before doing burpees. If they give you the go-ahead to perform them, skip the jumps at first. These entail the jumps back to the plank position from the squat and the jump from the squat up. Instead, walk it out.
  • If you want to add intensity, especially if you are in the advanced fitness level, don’t skip the jumps. Similarly, try doing one or two push-ups to make it more challenging.

Push-Ups

While exercises are indeed vital for general body fitness, it does not mean that they ought to be loved. In the list of the exercises, most people would rather not do the push-ups. It is not because they are not effective but instead because they can be quite complex at first.

Although they are certainly not the easiest, they are very effective in muscular development. The following all-body exercise will work your chest, legs, shoulder, arms, and core muscles. The other great thing about this body composition exercise is that you can do it anywhere and any time.

Experts advocate for this exercise and prefer it over the chest press machine exercise ( 2 ). It is because it is better in building muscular development and activating your total core. Here is how you do a push-up:

  • Start by kneeling on the floor with your head facing downward. Press your palms on the floor and directly beneath your shoulders. Make sure your arms are straight and fully extended.
  • Stretch your legs back and make sure your body weight rests on the balls of your feet. Keep your back straight, such that your entire body appears to form a straight line.
  • Slowly start to lower your body as if you want your nose or chest to touch the floor. Do not let your body lie on the floor. It should rest a few inches from it. Hold this position for some seconds, and then push yourself back up.
  • Do ten reps for one set and proceed to do another set after taking a break.

NOTE:

Your reps may vary depending on your trainer’s instructions or on your fitness level. If you are at the advanced phase, you may tend to do more reps before tiring. Again, this basic variation may be challenging for beginners. Here is an easier low-impact modification of the exercise that you can try at first:

  • Start in the same position and stretch your arms to allow your palms to rest underneath your shoulders.
  • Instead of extending your legs back, you will simply rest on your knees. You will continue to lower your body and lift it while in this position. Over time, this modification will become effortless and less challenging, and your trainer will recommend doing the standard push-up version.

Below are more expert-approved tips to help you perfect how you do this body composition exercise ( 4 ):

  • If you are a beginner, start doing push-ups in the presence of an instructor. If it is not possible, then do this full-body workout in front of your mirror. It will help you have a glimpse of your form. If you are doing the wrong push-up form, you will get to correct it before it leads to any injuries.
  • If you want to tone your muscles, focus on your reps and variations. Do not just do many reps of the standard push-up version. You can also do this exercise on your knees or while you stand at a wall.
  • For more muscle mass in your back and upper arms, do fewer reps but with a maximum weight load. Remember to keep your legs straight and lower your chest not less than two inches from the floor.

Squats

Squats are also great exercises to maintain body composition. They are particularly effective in helping you work out your lower body muscles. You might have seen or heard about it among the people obsessed with these exercises due to their impeccable results.

However, sometimes your obsession may not yield results. You may want to sculpt your lower body but end up injuring your back and knees in the process. It happens when you do the wrong form of this exercise.

Here is a guideline on how to do a proper regular squat ( 10 ):

  • Stand with your feet shoulder-width apart. You should be facing directly in front.
  • Stretch your arms in front of your body and slowly start to lower your butt as if you are seating. Try to lower it as much as possible without tripping or losing your balance. Again, remember to keep your back straight. Take note of your knees to make sure they are not in front of your toes. Hold this squatting position for a while before standing to the starting position.
  • Clench your glutes after you stand and repeat this as many times as possible.

Key Pointers

For more intensity, you can hold onto weights to make these squats more challenging. Remember to consult a fitness coach before you start incorporating weights into your workout plans.

Again, like any other exercise, you can also perform various modifications of the squat. If you want to lose butt fat and sculpt this region, then try the one leg squat. It will be challenging to perform but will yield results. Here is how you do it ( 10 ):

  • Stand upright with your feet shoulder-width apart. Extend your arms in front of your body.
  • Stand on your right leg and extend your left one in front of you. Try to lift it as high as you can.
  • Slowly start to descend into a squatting position. Be cautious as possible to avoid losing your stability and tripping over. Keep your back straight too, and your right knee in line with your right leg.
  • Return to the starting stance and do this severally before switching to the left leg.

You also need to note that various injuries may arise when you are doing this body composition exercise. You may squat incorrectly and end up spraining or with a knee injury. Such issues may result in pain and tenderness around your knee or ankle area.

Experts advise you follow the following tips to the latter to avoid any issues arising from squatting incorrectly ( 7 ):

  • Keep your feet shoulder-width apart while starting, and hold out your arms to help in improving balance.
  • As you drop into the squat position, breathe out and keep your heels firmly pressed on the floor.
  • Keep your thighs parallel to the floor.
  • Remember to keep your hips, toes, and knees pointing forward while in the squat stance.
  • Breathe in as you return to the standing position.

Planks

Planks are other exercises for body composition that you can do at home. The plank exercise is very effective in improving your posture by strengthening various muscles. It works the muscles in your core, shoulders, hamstrings, and glutes.

The exercise also helps in the proper alignment of your spine. Experts recommend doing planks instead of either sit-ups or the crunch machine workout ( 2 ). It is because planks are much better for your spin and neck.

Besides that, they also help in activating the (transverse) abdominal muscles that are often overlooked. So, you can also do planks to help in building mass in these muscles.

Whatever reason you choose as your goal of doing planks, remember to consult with your doctor and trainer. Otherwise, you might end up doing this exercise believing it is helping yet causing more problems.

To plank correctly, you need to follow these steps ( 5 ):

  • Get on the floor and onto your hands and knees. Find a comfortable mat if your floor is uncomfortable.
  • Align your hands with your shoulders as you stretch them towards the floor. Similarly, align your knees with your hips.
  • Start to slowly stretch your legs back until you come onto the balls of your feet. Straighten your legs and make sure that you are not bending either your knees or elbows. Also, keep your back straight such that your body forms a straight line.
  • Open your chest and lean your shoulders back. Stay in this position anywhere between 30 and 60 seconds.
  • Repeat as many times as you can.

NOTE:

As with the squats, there are also various plank variations. Perform the recommended variations by your instructor depending on your fitness abilities. Additionally, learn how to do each plank exercise correctly ( 9 ). It will help you transform into your desired body shape.

Similarly, take note of the instructed body forms while planking. It will help in avoiding injuries. For example, remember to keep your back straight. Remember to also breathe normally instead of holding your breath.

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Lunges

The last exercise in this body composition exercise list is the lunges. Whether or not you have done a lunge before, you might be familiar with the lunge position. It is because chances are you have knelt before to tie your shoelace. Such a position is quite similar to the lunge stance.

However, it does not imply that whenever you go on one knee you are doing a lunge. That is not the case. There are various forms of lunges that you can be asked to do. So, the form may tend to vary depending on the variation you are doing.

Here is how you correctly perform a regular standing lunge:

  • Stand with your feet hip-width apart and your arms on your hips. Your feet must be firmly pressed on the ground.
  • Take one huge step in front using your right leg. Start to slowly lower your body as if you want to kneel. Both of your knees will automatically bend. Remember to try to bend your knees not more than 90 degrees. Similarly, remember to keep the right knee aligned over your front ankle. Also, do not let your left knee touch the floor.
  • Hold this position for some seconds before returning to the starting standing position.
  • Do this severally for your right leg, and then alternate and do the same for your left leg.

NOTE: If done right, these exercises certainly help in transforming your body shape, especially your lower body. If not, it can put so much pressure on your knee joints and lower back, causing problems in these two regions ( 6 ).

Always take time to learn how to do an exercise before you start performing it. If this is not working, enroll a trainer to help you with your workouts. They will undoubtedly correct you whenever you do an exercise in the wrong form.


Sam Kramer, MS, RD, CSSGB, LDN, CISSN

Sam Kramer is a Registered Dietitian, Licensed Dietitian Nutritionist, Six Sigma Green Belt Certified, and Certified Sports Nutritionis Read Full Bio

By Sam Kramer, MS, RD, CSSGB, LDN, CISSN Reviewed by CHD Expert Team
Updated: 2021, May 26

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What are your alternatives?

Lifepro's FlexCycle Exercise Bike, the predecessor to the FlexStride, has been on the market since October 2020 and provides a similar function.

The difference — other than its pedal shape — is that it doesn't sit on a flat, solid plate and it features a mechanism that pushes down like a bike pedal. It also comes with extras like a stabilizer tether that attaches to your chair as opposed to chair stoppers.

Another differentiator is that it can be converted to an arm pedaler for greater variety, comes with resistance bands to incorporate upper body options, and costs less.

Other manufacturers with similar concepts include the DeskCycle Ellipse and the Cubii Pro Under Desk Elliptical.

The DeskCycle costs more and offers the same levels of magnetic resistance as the FlexStride. However, it lacks the high rims of the pedals and a carrying handle. The same can be said for the sleeker Cubii Pro, which boasts a burn of "up to 150 calories an hour," which is in line with the FlexStride's tested output. It does cost roughly $100 more, too.


Background

Bipolar disorder is a chronic condition characterized by elevated (manic) and depressive episodes often associated with difficulty functioning and poor quality of life. A diagnosis of bipolar disorder is also associated with an increased risk of cardiovascular disease leading to premature mortality (Roshanaei-Moghaddam and Katon, 2009 Dome et al., 2012 Crump et al., 2013). Further, obesity and a sedentary lifestyle are risk factors for diabetes, metabolic syndrome and cardiovascular disease, all of which disproportionally affect people with bipolar disorder (Elmslie et al., 2001 Morriss and Mohammed, 2005 Alsuwaidan et al., 2009 Cairney et al., 2009 Kilbourne et al., 2009). Thus, individuals with bipolar disorder face the dual struggle of needing to focus their attention and treatment on not only their mental health but also their physical health.

Exercise may be an excellent candidate to meet this need. Exercise unequivocally improves physical heath (e.g., obesity, cardiorespiratory fitness, blood pressure, cholesterol Cornelissen and Fagard, 2005 Church et al., 2007 Department of Health, 2011), but recent data also suggest that exercise is an effective treatment of depression and anxiety (Daley, 2008 Wipfli et al., 2008 Rethorst et al., 2009 Moylan et al., 2013 Rethorst and Trivedi, 2013). These data have prompted some to view exercise as a first line of treatment for mild to moderate depression (Carek et al., 2011). Given the promising data for depression and anxiety, exercise may also prove to be beneficial for the management of bipolar disorder. Specifically, evidence suggests that exercise is neuroprotective at least in part by increasing brain derived neurotrophic factor (BDNF Sylvia et al., 2010). Other mechanisms will be explored, including the genetic expression and endorphin hypothesis.

The aim of this review is to understand the amount of exercise and physical activity currently engaged in by individuals with bipolar disorder. For the purpose of this review, exercise is defined as a conscious, planned decision to move and be physically active, whereas physical activity refers to any movement, including leisure activity, occupational activity, or other activities of daily living (Caspersen et al., 1985 Thompson et al., 2003). A second aim is to evaluate the research on the role of exercise in improving physical (obesity, blood pressure) and mental (symptoms, quality of life) health outcomes in bipolar disorder. Finally, we will discuss the potential mechanisms of how exercise is suspected of improving mood and functioning in bipolar disorder.


J.F. is funded by an MRC Doctoral Training Grant. D.V. is funded by the Research Foundation – Flanders (FWO-Vlaanderen). S.R. is funded by a Society for Mental Health Research Early Career Fellowship (Australia). K.H.N. is funded by NIMH, Janssen, Stanley Medical Research Institute, and Posit Science. B.M. is funded by the German Federal Ministry of Education and Research (BMBF: 01EE1407AE).

We would like to acknowledge the assistance of Prof. David Kimhy (Columbia University) for kindly agreeing to share study data necessary for the meta-analysis. The authors have declared that there are no conflicts of interest in relation to the subject of this study.


Watch the video: Exercise helps the brain: BBC News Review (August 2022).