91Ó°ÊÓ

In the study of the response to acetylcholine by a frog's heart, the formula $$ R(x)=\frac{x}{c+d x} $$ arises, where \(x\) denotes the concentration of the drug and \(c\) and \(d\) are positive constants. a. Find \(R(0)\) and \(R\) (2). What is the physical significance of \(R(0)\) ? b. Find a formula that expresses the concentration \(x\) in terms of \(R(x)\).

a. Describe the region consisting of all \((x, y)\) for which $$ (x, y)=(x,-y) . $$ b. Describe the region consisting of all \((x, y)\) for which $$ (x, y)=(-x, y) . $$

The revenue function \(R\) for a certain product is given by $$ R(x)=5 x^{2}-\frac{x^{4}}{10} $$ The cost function \(C\) is given by $$ C(x)=4 x^{2}-24 x+38 $$ The profit function \(P\) is defined as the difference \(R-C\). Find the equation that describes \(P\). Then find \(P(1)\) and \(P(2)\), and show that it is possible to lose money and also possible to make a profit.

Solve the inequality. $$ |x+3| \geq 3 $$

Suppose two vertices of a rectangle \(R\) are \((2,5)\) and \((7,1)\), and the sides of \(R\) are parallel to the coordinate axes. Determine the other vertices of \(R\).

Solve the inequality. $$ |x-0.3|>1.5 $$

Recall that the volume \(V(r)\) of a spherical balloon of radius \(r\) is given by the formula $$ V(r)=\frac{4}{3} \pi r^{3} \quad \text { for } r \geq 0 $$ Suppose the radius is given by \(r(t)=3 \sqrt{t} .\) Write a formula for the volume in terms of \(t\).

Solve the inequality. $$ |2 x+1| \geq 1 $$

Suppose the sides of a square \(S\) are 4 units long and are parallel to the coordinate axes. If \((-3,3)\) is the vertex of \(S\) closest to the origin, find the other vertices of \(S\).

A sphere with surface area \(s\) has a radius \(r(s)\) given by $$ r(s)=\frac{1}{2} \sqrt{\frac{s}{\pi}} $$ a. Using the formula in Exercise 64 , find a formula for the volume of a sphere in terms of its surface area. b. Determine the volume corresponding to a surface area of 6 .