The number x of stereo speakers a retail chain is willing to sell per week at a price of p dollars is given by. Find the supply and instantaneous rate of change of supply when the price is 75 dollars?

The question is not complete and the complete question says:

The number  x  of stereo speakers a retail chain is willing to sell per week at a price of  p  dollars is given by x=80√(p+27) − 410 Find the supply and instantaneous rate of change of supply when the price is  75  dollars

A) Approximately 398 stereo speakers

B) Instantaneous rate of change = 3.961

Step-by-step explanation:

From the question, the number of speakers is given as;

x=80√(p+27) − 410

A) Thus at a price of $75,

The amount supplied will be;

x = 80√(75+27) − 410

x = 80√(102) - 410

x = (80 x 10.0995) - 410

x = 807.96 - 410 = 397.96 ≈ 398 stereo speakers

B) The instantaneous rate of change is given as;

dx/dp of the supply equation.

Thus, let's rearrange the supply equation first before differentiating.

So, x = 80√(p+27) − 410

x = 80[(p +27)^(1/2)] - 410

So, dx/dp = [(80 x 1/2) (p + 27)^(-1/2)]

dx/dp = 40/√(p+27)

So, at price of $75,

dx/dp = 40/√(75+27) = 40/√102

= 40/10.0995 = 3.961

step-by-step explanation:

abc

c. y = 1/4 x + 5

step-by-step explanation:

first, put the equation of the line on the graph into slope-intercept form

(y = mx + b):   y = -4x + 8

second, a perpendicular line has to have "an opposite/reciprocal slope" to the original slope. so, find the "m" value in your original equation (it's -4, right? )

original slope: m = -4   perpendicular slope: change the sign to its opposite and find the reciprocal ("flip" the number)

new slope is now positive (b/c the original slope was negative 4), and it's 1/4 (not the original slope of 4 or 4/1)