91Ó°ÊÓ

Translate the following sentence into a mathematical equation: The area \(A\) of a circle equals the product of the square of its radius \(r\) and the constant \(\pi\).

Solve the inequality \(-3 x-2<7\). (pp. \(123-126\) )

Find the intercepts of the equation $y=x^{2}-9 .

Use a graphing utility to find the line of best fit for the following data: $$ \begin{array}{|c|rrrrrr|} \hline x & 3 & 5 & 5 & 6 & 7 & 8 \\ \hline y & 10 & 13 & 12 & 15 & 16 & 19 \\ \hline \end{array} $$

The price \(p\) (in dollars) and the quantity \(x\) sold of a certain product satisfy the demand equation $$ x=-6 p+600 $$ (a) Find a model that expresses the revenue \(R\) as a function of \(p .(\) Remember \(, R=x p .)\) (b) What is the domain of \(R ?\) Assume \(R\) is nonnegative. (c) What price \(p\) maximizes the revenue? (d) What is the maximum revenue? (e) How many units are sold at this price? (f) Graph \(\underline{R}\). (g) What price should the company charge to earn at least \(\$ 12,600\) in revenue?

True or False The correlation coefficient is a measure of the strength of a linear relation between two variables and must lie between -1 and 1 , inclusive.

The price \(p\) (in dollars) and the quantity \(x\) sold of a certain product satisfy the demand equation $$ x=-3 p+360 $$ (a) Find a model that expresses the revenue \(R\) as a function of \(p\). (b) What is the domain of \(R ?\) Assume \(R\) is nonnegative. (c) What price \(p\) maximizes the revenue? (d) What is the maximum revenue? (e) How many units are sold at this price? (f) Graph \(R\). (g) What price should the company charge to earn at least \(\$ 9600\) in revenue?

The price \(p\) (in dollars) and the quantity \(x\) sold of a certain product satisfy the demand equation $$ x=-5 p+100 $$ (a) Find a model that expresses the revenue \(R\) as a function of \(p\). (b) What is the domain of \(R\) ? Assume \(R\) is nonnegative. (c) What price \(p\) maximizes the revenue? (d) What is the maximum revenue? (e) How many units are sold at this price? (f) Graph \(R\). (g) What price should the company charge to earn at least \(\$ 480\) in revenue?

The graph of a quadratic function is called a(n) _____________.

David has 400 yards of fencing and wishes to enclose a rectangular area. (a) Express the area \(A\) of the rectangle as a function of the width \(w\) of the rectangle. (b) For what value of \(w\) is the area largest? (c) What is the maximum area?