Question

Find the constant of variation for an inverse relationship when x=6 and y=3.
k=

The table below models inverse variation. Write an equation to represent the relationship between x and y.
x|3|5|7|10.5
y|14|8.4|6|4
Gear A drives Gear B. Gear A has teeth and speed rA in revolutions per minute (rpm). Gear B has b teeth and speed rB. The quantities are related by the formula arA=brB. Gear A has 60 teeth and speed 5400 rpm. Gear B has 45 teeth. Find the speed of Gear B in rpm.
Suppose x and y vary inversely. When x=20, y=5. Find y when x=10.
y=
Find the constant of variation of the ordered pair ( \sqrt{8} \sqrt{32} ) if the pair is from an inverse variation.
k= .
Describe the combined variation modeled by the equation l = πrα/180
The length of an arc varies inversely with the product of the radius and angle measurement.
The length of an arc varies directly with its radius and angle measurement.
The length of an arc varies directly with the square of the radius and inversely with the angle measurement.
The length of an arc varies directly with its radius and inversely with the angle measurement.

Suppose z varies inversely with the product of x and y. When x=2 and y=4, z=0.5. Find z when x=4 and y=9. Round your answer to the nearest hundredth.

Which equation shows that z varies directly with the square of x and inversely with the cube of y?

Health care professionals use the body mass index (BMI) to establish guidelines for determining any possible risks of their patients and for planning any useful preventative programs. The BMI varies directly with weight (in pounds) and inversely with the square of height (in inches), using the equation BMI=705wh2. Find the BMI of a person who is 5'8" and weights 185 lbs. Round your answer to the nearest tenth.

Describe the combined variation represented by the equation h=3A/πr2.

The height of a cone varies jointly with its area and radius.
The height of a cone varies directly with the square of the radius and inversely with its area.
The height of a cone varies directly with its area and inversely with the square of the radius.
The height of a cone varies directly with its area and inversely with the square-root of the radius.

Answer 1

1.) For inverse relationships, y = k/x
3 = k/6
k = 3 x 6 = 18

2.) y = k/x
14 = k/3
k = 14 x 3 = 42
Required equation is y = 42/x

3.) arA = brB
60 x 5400 = 45 x rB
rB = 60 x 5400 / 45 = 7,200
Therefore, the speed of Gear B is 7,200 rpm

4.) y = k/x
5 = k/20
k = 5 x 20 = 100
When x = 10, y = 100/10 = 10

5.) y = k/x
sqrt(32) = k/sqrt(8)
k = sqrt(32) x sqrt(8) = sqrt(32 x 8) = sqrt(256) = 16
Constant of variation is 16.

6.) The length of an arc varies directly with its radius and angle measurement.

7.) z = k/xy
k = xyz = 2 x 4 x 0.5 = 4
z = 4/xy
When x = 4 and y = 9,
z = 4/(4 x 9) = 4/36 = 1/9 = 0.11

8.) z varies directly with the square of x and inversely with the cube of y is given by the equation
z = kx^2 / y^3

9.) BMI = 705w/h^2 = 705 x 185 / 5'8" = 25,407.5

10.) The height of a cone varies directly with its area and inversely with the square of the radius.

Answer 2

Answer:

b: The height of a cone varies directly with the square of the radius and inversely with its area.

Step-by-step explanation: