Y is inversely proportional to d^2 When d=10 y=4 D is directly proportional to x^2 When x=2, d=24 Find a formula for y in terms of x?

y = 1.44x⁴

Step-by-step explanation:

From the question,

Y∝d²

To remove the proportionality sign we introduce a constant.

Y = kd² Equation 1

make k the subject of the equation

k = Y/d² Equation 2

Given: Y = 4, d = 10

Substitute these values into equation 2

k = 4/10²

k = 4/100

k = 0.04

Substitute these value of k in equation 1

Y = 0.04d² Equation 3

Similarly,

d∝x²,

d = Cx²

make C the subject of the equation

C = d/x² Equation 4

Given:  d = 24, x = 2

Substitute into equation 4

C = 24/2²

C = 24/4

C = 6

Hence,

d = 6x² Equation 5

Substitute the value of d in equation 5 into equation 3

y = 0.04(6x²)²

y = 0.04(36x⁴)

y = 1.44x⁴

Hence the formula for y in terms of x is y = 1.44x⁴

$2416.6

step-by-step explanation:

per hour = $ 25

total work time = 35

commission = 15%

total she has to make = $ 4,500

let she sold x dollar products

so her commission will be 15 % of x

now

total = weekly basic pay + commission

4500= (25*35) + 15 % of x

4500=875 + * x

4500-875 =   * x

3625= * x

multiplying wwith 100 on both sides gives

36250 = 15 x

now

x =  

x= $2416.6