A body of mass m fell from a vertical plane. Find the velocity of the object as a function of time t. Assume that the air resistance is proportional to the velocity of the object

Q: If a person's temperature after x hours of strenuous exercise is  T(x) = x3(7 − x2) + 98.6  degrees…

A: given,                If a person's temperature after x hours of strenuous…

Q: Given the function h(x) = –x² – 6x + 17, determine the average rate of change of the function over…

A:

Q: The function f(x) = x3 describes the volume of a cube, f(x), in cubic inches, whose length, width,…

A: Given function is fx=x3

Q: The volume V of a right circular cylinder of height h and radius r is V = πr 2 h. If the height is…

A: Given: The volume of a right circular cylinder is, V=πr2h . Here, h is the height of the cylinder…

Q: One yardstick for measuring how steadily-if slowly-athletic performance has improved is the mile…

A: (a).       The function that express the record time for the mile run, M, in terms of number of…

Q: The velocity graph of a car accelerating from rest to a speed of 120 km/h over a period of 30…

A: The velocity graph of a car accelerating from rest to a speed of 120 km/h over a period of 30…

Q: The graph shows the depth of water W in a reservoir over a one-year period as a function of the…

A:

Q: A jogger ran 4 miles and then walked 2 miles. The average velocity running was 3 miles per hour…

A: Given  A jogger ran 4 miles and then walked 2 miles. Total time is T  The average velocity of…

Q: The function f(x) = x2 describes the area of a square, f(x),in square inches, whose sides each…

A: Given: fx=x2. Here, fx describes the area of a square in square in inches

Q: The function f(x) = x3 describes the volume of a cube, f(x), in cubic inches, whose length, width,…

A: Given volume function fx=x3 to find instantaneous rate of change of the volume x=4 in

Q: Find the average rate of change of the function f (x)

A:

Q: Given the function g(x) = -x² + 6x + 15, determine the average rate of change of the function over…

A: The average of a function over an interval is given by . The given function is and the interval…

Q: Two cars start at the same time and travel in the same direction along a straight road.  The…

A: Given velocity of car A and car B as a function of time t is,

Q: A pebble is embedded in the tread of a rotating bicycle  wheel of diameter 60cm. If the wheel…

A:

Q: As a cold front moved through a midwestern city, the temperature dropped at the rate of 3F per hour…

A: Given: Rate of change in temperature between noon and 8 p.m. = -3∘F. At 1 p.m. the temperature was…

Q: One company buys a new bulldozer for $126400. The company depreciates the bulldozer linearly over…

A:

Q: A stock analyst plots the price per share of a certain common stock as a function of time and finds…

A: Given, Stock price as a function of time S(t) = 40+9e-0.03t We have to find the average price of…

Q: The function f(x) = x3 describes the volume of a cube, f(x), in cubic inches, whose length, width,…

A: Given: fx=x3,  x=5 inches

Q: Calculate the average rate of change for the function g(x) = 412 - 5x + 1 over each interval.

A: Given query is to find the average rate of change.

Q: The volume V of a right circular cylinder of height h and radius r is V= π r 2h. If the height is…

A: Volume of a right circular cylinder = V = π r2 h where r is radius of cylinder  and h is height of…

Q: Given the function h(x) = x² – 8x+8, determine the average rate of change of the function over the…

A:

Q: The cost, in dollars, of water consumed by a factory is given by the function C(w) = 15 +0.1vw,…

A:

Q: The function f(x) = x describes the area of a circle, f(x), in square inches, whose radius measures…

A: It is given that fx=πx2 is the area of circle with radius x inches. (a) The radius changes from 7…

Q: Find the maximum rate of change of f at the given point and the direction in which it occurs.

A:

Q: considering that the rate of decay is proportional to the cube of the material

A: When a proportionality sign is removed the constant is applied with the equal sign.

Q: If an object moves along a line so that it is at y = f(x) = 9x² – 7x at time x (in seconds), find…

A: Given : fx = 9x2-7x

Q: Suppose that Nolan throws a baseball to Ryan and that the baseball leaves Nolan's hand at the same…

A:

Q: Determine the average rate of change of f(x)=3(2)" on the interval 0<x<2. a) 4. Ax b) Ax d) = 45 c)…

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Q: hamster wheel has a point on the wheel with height modelled by the equation, where h is in cm and t…

A: In this question, the concept of the average rate of change is applied. The average rate of change…

Q: Use the given graph to estimate the value of each derivative.  (a) f ′(−3) (b) f ′(−2) (c) f ′(−1)…

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Q: If an object moves along a line so that it is at y=f(x)=3x2−2x at time x​ (in seconds), find the…

A:

Q: determine the most general function M(x, y) or N(x, y) so that equation is exact.

A: We have to find M(x, y) Or N(x, y).

Q: The function f(x) = x3 describes the volume of a cube, f(x), in cubic inches, whose length, width,…

A: From given the volume function is fx=x3.

Q: The function f(x) = ᴫx2 describes the area of a circle, f(x), in square inches, whose radius…

A: Consider the function that describes the area of a circle  fx=πx2

Q: Use the given graph to estimate the value of each derivative.Then sketch the graph of f'. (a) f' (0)…

A:

Q: Find the linearization of the function at a . f(x) = sqrt  x    , a = 4

A: Consider the provided function, fx=x,    a=4 Find the linearization of the function at a. Apply the…

Q: Use the position function below to solve the following problem. A projectile is fired vertically…

A:

Q: According to the U.S. Census Bureau, in 2011, the median (middle of the range) annual income of a…

A: Since multiple subparts are posted, we will solve the first three subparts only. To get the…

Q: If an object moves along a line so that it is at y = f(x) = 9x-2x at time x (in seconds), find the…

A: Given query is to find the instantaneous velocity of the object using derivative.

Q: The rate of change in the number of miles s of road cleared per hour by a snowplow is inversely…

A:

Q: Write the equation of the line tangent to f(x)=\x at x=4 and from that line approximate V3.98 a)…

A:

Q: The graph shows the depth of water W in a reservoir over a one-year period as a function of the…

A:

Q: Find the average rate of change of the function f(x) = as x changes from x= -2 to x=5. %3D X-6

A:

Q: Let f (x) = Vx. Find the slope m and the point-slope equation of the line tangent to the graph of f…

A: Consider the given function fx=x Suppose m be the slope of the line tangent to the graph of the…

Q: Find the relative rate of change, f'(t) of the function f(t) = 3e2t. f(t)’ f'(t)

A: ft=3e2tTo find f'tft

Q: If an object moves along a line so that it is at y = f(x) = 7x-6x at time x (in seconds), find the…

A: Given  y=f(x)=7x2-6xInstantaneous velocity V=f'(x)∵f'(x)=ddx(7x2-6x)f'(x)=14x-6∵V=f'(x)=14x-6ft/sec…

Q: A ball is thrown into the air with an initial upward velocity of 48 ft/s. The height () of the ball…

A: Given, initial upward velocity = 48 ft/s h(t)=-16t2+48t+4

Q: The distance, s, of a moving body from a fixed point is given as 24ei. Find the velocity, v, of the…

A: We will find out the required solution.