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Questions and Answers
What is the point on the parabola 𝑦 = 9 − 𝑥^2 closest to the point 𝐴(3,9)?
What is the point on the parabola 𝑦 = 9 − 𝑥^2 closest to the point 𝐴(3,9)?
- (5,2)
- (2,5)
- (1,8) (correct)
- (4,3)
You are inflating a spherical balloon at the rate of 32 cm³/sec. How fast, in cm/sec, is its radius increasing when the radius is 4 cm?
You are inflating a spherical balloon at the rate of 32 cm³/sec. How fast, in cm/sec, is its radius increasing when the radius is 4 cm?
- 2 cm/sec
- 4 cm/sec (correct)
- 6 cm/sec
- 8 cm/sec
An airplane is flying away from a radar station at a constant height of 8 miles above the ground. If the distance s between the airplane and the station is increasing at a rate of 300 miles per hour when s = 10 miles, what is the horizontal speed, in miles per hour, of the plane?
An airplane is flying away from a radar station at a constant height of 8 miles above the ground. If the distance s between the airplane and the station is increasing at a rate of 300 miles per hour when s = 10 miles, what is the horizontal speed, in miles per hour, of the plane?
- 375 mph (correct)
- 500 mph
- 300 mph
- 250 mph
Suppose a forest fire spreads in a circle with radius changing at a rate of 8 ft/min. When the radius reaches 200 feet, at what rate is the area of the burning region increasing?
Suppose a forest fire spreads in a circle with radius changing at a rate of 8 ft/min. When the radius reaches 200 feet, at what rate is the area of the burning region increasing?
A gas is poured into a spherical balloon at a constant rate of 15 cm³/sec. At what rate is the radius of the balloon increasing when the radius is 8 cm?
A gas is poured into a spherical balloon at a constant rate of 15 cm³/sec. At what rate is the radius of the balloon increasing when the radius is 8 cm?
A cylindrical tank with radius 5 m is being filled with water at a rate of 3 m³/min. How fast is the height of the water increasing?
A cylindrical tank with radius 5 m is being filled with water at a rate of 3 m³/min. How fast is the height of the water increasing?
The length of a rectangle is increasing at a rate of 6 cm/sec and its width is increasing at a rate of 2 cm/sec. When the length is 18 cm and the width is 10 cm, how fast is the area of the rectangle increasing?
The length of a rectangle is increasing at a rate of 6 cm/sec and its width is increasing at a rate of 2 cm/sec. When the length is 18 cm and the width is 10 cm, how fast is the area of the rectangle increasing?
If the volume of a sphere is decreasing at the rate of 20 cm³/sec, find the rate at which the radius of the sphere is decreasing when the volume is 8 cm³.
If the volume of a sphere is decreasing at the rate of 20 cm³/sec, find the rate at which the radius of the sphere is decreasing when the volume is 8 cm³.
What are the critical points of the function $f(x) = -16x$?
What are the critical points of the function $f(x) = -16x$?
At which value(s) of $x$ does the function $g(x) = 2x^3 - 4x$ have critical point(s)?
At which value(s) of $x$ does the function $g(x) = 2x^3 - 4x$ have critical point(s)?
What is the absolute maximum value of the function $y = -x^2 + 5x + 6$ on the interval $[2, 15]$?
What is the absolute maximum value of the function $y = -x^2 + 5x + 6$ on the interval $[2, 15]$?
What is the absolute minimum value of the function $y = 2 \sin x$ on the interval $[0, 6.2]$?
What is the absolute minimum value of the function $y = 2 \sin x$ on the interval $[0, 6.2]$?
