if 16 y varies directly to X and zip varies directly to the square of y and (x, y, z) =(10,20,4) then find y and z when x =20

Question

if 16 y varies directly to X and zip varies directly to the square of y and (x, y, z) =(10,20,4) then find y and z when x =20

Answer 1

When x=20 the y=40 and z=16.

 

x=16ky where k is a constant. So 10=16*k*20, Therefore k=1/32. So x=20 y=40.

 

z=qy.y, when y=20, z=4. So 4=q.20.20 Therefor q=1/100 and when y=40, z=40.40/100 that is z=16

 

(x,y,z)=(20,40,16)

 

Shashikant K

Answer 2

Hi, Issamar!

 

Step 1: Set up your equations based on the descriptions in the question. (Note: "varies directly" means that the first part is equal to the second part multiplied by some constant, k.)

16y = k₁ * x

z = k₂ * y²

 

Step 2: Use the point given to you to solve for k₁ and k₂. (This is the (x, y, z) = (10, 20, 4) part.)

16y = k₁ * x

16(20) = k₁ * (10)

320 = k₁ * 10

k₁ = 32

 

z = k₂ * y²

(4) = k₂ * (20)²

4 = k₂ * 400

k₂ = 0.01

 

Updated equations:

16y = 32x

z = 0.01y²

 

Step 3: Use the constants and updated equations to find y and z when x = 20.

16y = 32x

16y = 32(20)

16y = 640

y = 40

 

z = 0.01y²

z = 0.01*(40)²

z = 16

 

Hope this helps!