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?

Answers

Answer 1

Answer:

Answer:

Please find below the complete question:

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.

Supply = 398

Instantaneous rate of change of supply $=3.96$

Step-by-step explanation:

$x=80√(p+27) -410$

Supply when price = $75

$x=80√(75+27) -410 = x=80√(102) -410\n\nx = 80(10.1) -410= 808-410\n\nx = 398$

Supply = 398 stereo speakers

To get the instantaneous rate of supply, we differentiate the supply, x, with respect to price, p

$(dx)/(dp) = (d)/(dp)(80√(p+27) -410)\n\n(dx)/(dp) = (d)/(dp)(80(p+27)^(1/2) -410)$

Using chain rule, we have

$(x)/(y) (dx)/(dp)=(d)/(dp)( 80(p+27)^(1/2)) - (d)/(dp)(410) \n\n(dx)/(dp)=80((1)/(2))(p+27)^(-1/2) - 0\n\n(dx)/(dp)=(40)/(√(p+27) ) \n$

At p = $75

$(dx)/(dp)=(40)/(√(75+27) )=(40)/(√(102) )\n\n(dx)/(dp)=(40)/(10.1) = 3.96\n\n(dx)/(dp)=3.96$

Answer 2

Answer:

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

Answer:

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

Related Questions

Let p ( n ) and s ( n ) denote the product and the sum, respectively, of the digits of the integer n . For example, p ( 23 ) = 6 and s ( 23 ) = 5 . Suppose N is a two-digit number such that n = p ( n ) + s ( n ) . What is the unit digit of n ?
Factor this trinomial. x2 + 2x - 3 A. (x + 3)(x + 1) B. (x - 3)(x - 1) C. (x + 3)(x - 1) D. (x - 3)(x + 1)
What does n + 4n- 22=5 k equal?
What’s the answer for b. Please help this is due in a couple hours!!
I can't figure this equation out, help!!!!!!!!!!!!!!!!!!!!!!!***The answer is 1 and -0.5, but I just can't figure out how to work it out.***

if you assume that the observations in the sample are independent, what is the smallest value the sample size could be to meet the conditions for this hypothesis test?

Answers

Final answer:

To meet the conditions for a hypothesistest assuming independent observations, the sample size should have at least five successes and failures, and the population should be at least 10 or 20 times the size of the sample.

Explanation:

In order to meet the conditions for a hypothesistest that assumes independentobservations in the sample, the sample size should be such that each sample has at least five successes and five failures. Additionally, the population must be at least 10 or 20 times the size of the sample to avoid over-sampling and incorrect results.

Learn more about Sample size for independent observations here:

brainly.com/question/31190836

#SPJ1

PLEASE HELP!!!!!! I WILL MARK YOU BRAINLIEST

Answers

Answer:

its C

Step-by-step explanation:

I think the answer to that question is C

The image of -4,6 reflected along the y axis is?

Answers

The image of the point is still a point. The reflection point across the y-axis is (4,6)

Which of these relations is a function?
I’m I correct??

Answers

Answer:

the first one on the bottom

Step-by-step explanation:

There is a little trick to find out if it is a function or not. This trick is called the vertical line test. if you can scan the figure with a virtual line and it does not touch more than one side of the figure at one time then it is a function. if it touches more than one side or line of the figure it is not a function.

The correlation coefficient r between a child’s age, x, and the number of minutes spent doing homework each day, y, is 0.694. What percent of the variation in the number of minutes doing homework cannot be explained by differences in the children’s ages?

Answers

So, they are looking for the percentage that is NOT explained... Well, given the r we can find the percentage that IS explained by it first. That's given by r^2.

Now - let's take the square of r it gives me .481636. That means that about 48% IS explained. Therefore, the part that cannot be explained must be the missing part (out of 100% so 100% - 48.1636% should be it :)

So 100% - 48.1636% = 0.518364 and we want to round that off to three decimal places which will give us 0.518... and then we could convert that to a percent for the final. So 0.518 as a percentage is 51.8%! s

Suppose you produce a camera that costs $50 to make. At a selling price of $45, you will _____.earn a profit
just cover your costs
lose money