Since raindrops grow as they fall, their surface area increases and therefore the resistance to their falling increases. A raindrop has an initial downward velocity of 10 m/s and its downward acceleration...
Since raindrops grow as they fall, their surface area increases and therefore the resistance to their falling increases. A raindrop has an initial downward velocity of 10 m/s and its downward acceleration...
The circumference of a sphere was measured to be 80 cm with a possible error of 0.5 cm. (a) Use differentials to estimate the maximum error in the calculated surface area. What...
Find f. f ''(t) = 3e^t + 8sin(t), f(0) = 0, f(π) = 0
A high-speed bullet train accelerates and decelerates at the rate of 10 ft/s^2. Its maximum cruising speed is 90 mi/h. (a) What is the maximum distance the train can travel if...
Find f. f ''(x) = 20x^3 + 12x^2 + 6, f(0) = 3, f(1) = −1
Find equations of both the tangent lines to the ellipse x^2 + 9y^2 = 81 that pass through the point (27, 3).
1) A number (g) less y 2) Twice the sum of a and b
When a foreign object lodged in the trachea (windpipe) forces a person to cough, the diaphragm thrusts upward causing an increase in pressure in the lungs. This is accompanied by a contraction of...
In the viewing rectangle [-4, 4] by [-20, 20], graph the function f(x) = x^3 - 3x and its secant line through the points (-3, -18) and (3, 18). Find the values of the numbers c that satisfy...
Verify that the function satisfies the three hypotheses of Rolle's Theorem on the given interval. Then find all numbers c that satisfy the conclusion of Rolle's Theorem. f(x) = cos 2x, [π/8,...
Find the number c that satisfies the conclusion of Rolle's Theorem. f(x) = x^1/2 - x/7 [0, 49]
Find an equation of the tangent line to the astraoid at the (3(3)^1/2, 1) x2/3 + y2/3 = 4
A particle moves according to a law of motion below 0 <= t < 12, where t is measured in seconds and s in feet. s= f(t) = cos(tpi/6) (a) Find the total...
(a) The volume V of a growing spherical cell is V = 4/3 pi r^, where the radius is measured in micrometers (1 µm = 10^-6m). Find the average rate of change of V with respect to r when r changes...
What is the area of the garden in square feet, NOT including the walkway?
Use logarithmic differentiation: (x2 + 2)2 * (x4 + 4)4 ANSWER: (x2 + 2)2 * (x 4+ 4)4 * [4x / (x2 + 2) + 16x3 / (x4 +...
Two sides of a parallelogram are 14 feet and 15 feet. The measure of the angle between these sides is 95°. Find the area of the parallelogram to the nearest square foot.
Two sides of a parallelogram are 1.2 feet and 2.3 feet. The measure of the angle between these sides is 29°. Find the area of the parallelogram to the nearest 10th of a square foot.
Find dy/dx by implicit differentiation (9x + y)1/2 = 3 +x2y2
A particle moves according to a law of motion below, 0 ≤ t < 12, where t is measured in seconds and s in feet. s = f(t) =cos(tpi/6) (a) Find the total distance...