A spherical balloon is inflated with helium at the rate of 100π ft³/min. How fast is the balloon's radius increasing at the instant the radius is 5 ft? How fast is the surface area increasing?

A spherical balloon is inflated with helium at the rate of 100pi ft^3/min. How fast is the balloon's radius increasing at the instant the radius is 5 ft?

When a metal plate is heated, it expands. If the shape of the plate is circular and its radius is increasing at the rate of 0.02 cm/s, at what rate is the area of the top surface increasing when the radius is 3 cm?

A spherical balloon is inflating with helium at a rate of 144 pi(ft^3/min). How fast is the balloon's radius increasing at the instant the radius is 3 ft?

The length l of a rectangle is decreasing at the rate of 2 cm/sec while the width w is increasing at the rate of 2 cm/sec. When l = 12 cm and w = 5 cm, find the rates of change of (a) the area, (b) the perimeter, and (c) the lengths of the diagonals of the rectangle. Which of these quantities are decreasing, and which are increasing?

Fill in the blank with a word to introduce each noun clause. Address your complaints to _____ is responsible for the problem.

The voltage V (volts), current I (amperes), and resistance R (ohms) of an electric circuit like the one shown here are related by the equation V = IR. Suppose that V is increasing at the rate of 1 volt>sec while I is decreasing at the rate of 1/3 amp/sec. Let t denote time in seconds. a. What is the value of dV/dt? b. What is the value of dI/dt? c. What equation relates dR/dt to dV/dt and dI/dt? d. Find the rate at which R is changing when V = 12 volts and I = 2 amps. Is R increasing, or decreasing?

The radius r, height h, and volume V of a right circular cylinder are related by the equation V = πr²h. (a) How is dV/dt related to dh/dt if r is constant? (b) How is dV/dt related to dr/dt if h is constant? (c) How is dV/dt related to dr/dt and dh/dt if neither r nor h is constant?

Use implicit differentiation to find ∂z / ∂x and ∂z / ∂y. yz + x In y = z2

An object is dropped from a height of 1700 ft above the ground. The function $h=-16 t^{2}+1700$ gives the object's height h in feet during free fall at t seconds. When will the object be 1000 ft above the ground?

The volume V = (4/3)pi r^3 of a spherical balloon changes with the radius. a. At what rate (ft^3/ft) does the volume change with respect to the radius when r = 2 ft? b. By approximately how much does the volume increase when the radius changes from 2 to 2.2 ft?

Check the blank before each sentence that contains a subordinate clause. _____ Over the next few months, Pizarro plotted his escape from his employer.

The volume V - (4/3)πr3 of a spherical balloon changes with the radius. (a) At what rate does the volume change with respect to the radius when r = 2 ft? (b) By approximately how much does the volume increase when the radius changes from 2 to 2.2 ft?

Chavez writes that the “idea of modifying birthright citizenship has been around for decades but was previously relegated to the fringes of the immigration restriction movement” (2). What does the word fringes mean in this context? What connotations does it have? Why are these connotations important for her overall argument?