Suppose the wholesale price of a certain brand of medium-sized eggs p (in dollars/carton) is related to the weekly supply x (in thousands of cartons) by the following equation.
$ 625p^2 - x^2 =100$

if 35000 cartons of eggs are available at the beginning of a certain week and the price is falling at the rate of 5¢/carton/week, at what rate is the supply changing? (round your answer to the nearest whole number.) (hint: to find the value of p when x = 35, solve the supply equation for p when x = 35.)

cartons per week?

1300

Step-by-step explanation:

We are given

x = 35

 [rate of change of price with time]

We want to find , which is the rate at which supply is changing.

First, we need to implicitly differentiate the equation given:

Here, we have what we need except for p. We find p when x = 35:

Now, find dx/dt:

In thousands, 1.30 * 1000 = 1300 cartons per week decrease

757764

step-by-step explanation:

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the final amount you will pay is $68.04.

the tip is determined by the pre-tax amount, so we calculate the tip based on the original bill, not after we've added sales tax.

to find the tip:

we can divide 54.00 by 100 to get 1% of 54. then we multiply that by 18.

54 / 100 = .54

.54 x 18 = 9.72

tip = 9.72$

to find the tax:

we can divide 54.00 by 100 to get 1% of 54. then we can multiply that by 8 to get 8%.

54 / 100 = .54

.54 x 8 = 4.32

tax= 4.32

now we can add the tip and tax to the bill to get our total.

54 + 9.72 + 4.32 = 68.04

total: $68.04

step-by-step explanation: