25,270 Answered Questions for the topic calculus

10/12/23

What is the smallest positive integer which is divisible by 225 and uses only the digits 0, 1 and 2?

Show work please
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Calculus

10/12/23

Calculus 3 Implicit Differentiation
Calculate the derivative using implicit differentiation:x4w + w8 + wz2 + 9yz = 0dw/dz = 
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Calculus

10/12/23

estimate the amount of solid
Let f(t) be the weight (in grams) of a solid sitting in a beaker of water. Suppose that the solid dissolves in such a way that the rate of change (in grams/minute) of the weight of the solid at... more
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Calculus

10/12/23

Approximate sin56
Use differentials (or equivalently, a linear approximation) to approximate sin(56∘) as follows: Let 𝑓(𝑥)=sin(𝑥) and find the equation of the tangent line to 𝑓(𝑥) at a "nice" point near 56∘. Then... more
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Calculus

10/12/23

AP Calculus - Graph
State the intervals of the function f(x) = sqrt(x2-9) + sqrt(16-x2) is decreasing.
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Calculus

10/11/23

AP Calculus BC - Linearization

Find the linearization of the given function centered at x = a, use it to estimate f(b).f(x) = sqrt(17 sin(x)), a = π/6, b = 0.5
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Calculus

10/11/23

Find the time(s) when the ball's height is 48 feet.
Dana is going to throw a ball from the top floor of her middle school. The function h(t)= -16t2+32t+48 models the height, h, of the ball above the ground as a function of time t.Find the time(s)... more
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Calculus

10/11/23

A large explosion causes wood and metal debris to rise vertically into the air with an initial velocity of 112 feet per second.

A large explosion causes wood and metal debris to rise vertically into the air with an initial velocity of 112 feet per second. The function h(t)=112t -16t2gives the height of the falling debris... more
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Calculus

10/11/23

A ball is thrown upward in the air, and its height above the ground after t seconds is
A ball is thrown upward in the air, and its height above the ground after t seconds is H(t) = 97⋅t - 16t2 feetFind the time t when the ball will be traveling downward at 48.5 feet per second.Give... more
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Calculus

10/11/23

A ball is thrown upward in the air, and its height above the ground after seconds is...
A ball is thrown upward in the air, and its height above the ground after t seconds is H(t) = 85 ⋅ t - 16t2 feetFind the time t when the ball will be traveling upward at 42.5 feet per second.Give... more
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Calculus

10/11/23

Find an equation for θ in terms of x
A boat is sailing towards a cliff that rises 272 meters above water level. Let θ be the angle of elevation from the boat to the top of the cliff, and let x be the distance from the boat to the... more
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Calculus

10/11/23

Find the velocity at time t.

Suppose that the position of a particle is given by s = f(t) = 2t3+4t+9 (a) Find the velocity at time t. v(t)= ___ m/s (b) Find the velocity at time t = 3 seconds. ____ m/s (c) Find the... more
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Calculus

10/11/23

Find a function for the velocity.
Let s(t) = 4t3 +12t2 -180t be the equation of motion for a particle. Find a function for the velocity. v(t)Where does the velocity equal zero? [Hint: factor out the GCF.] t = and t = Find a... more
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Calculus

10/11/23

Find the growth rate after 3 hours.
The population of a slowly growing bacterial colony after t hours is given by p(t) = 4t2+29t +200. Find the growth rate after 3 hours.
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Calculus

10/11/23

Approximate the population of the bacteria 20 minutes from now.
The current population of a certain bacteria is 6,416 organisms. It is believed that the bacteria's population is tripling every 10 minutes. Approximate the population of the bacteria 20 minutes... more
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Calculus

10/11/23

busn calc revenue
a manufacturer estimates that when x units of a certain commodity are produced and sold, the revenue derived will be R(x)=0.5x^2+3x-2 thousand dollars. at what rate is the revenue changing with... more
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Calculus

10/11/23

In this question you will use integration by parts twice. Consider the integral
In this question, you will use integration by parts twice. Consider the integralI = ∫sin(4x)cosh(3x)dxThink of this as s ∫uv′ dx Let u= cosh(3 x) .Now apply integration by parts to this second... more
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Calculus

10/11/23

In this question, you will solve a definite integral problem using the method of substitution.
In this question, you will solve a definite integral problem using the method of substitution.∫ sin(4x)cos6(4x)dx from pi to pi/3(a) Make the substitution u= cos4x], and write the integrand as a... more
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Calculus

10/11/23

Find the work required to pump the water out of the spout.
A tank is full of water. Find the work required to pump the water out of the spout. Use the fact that water weighs 62.5 lb/ft3. (Assume r = 4 ft, R = 8 ft, and h = 12 ft.)
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Calculus

10/11/23

Find the work required to pump the water out of the spout.
A tank is full of water. Find the work required to pump the water out of the spout. (Use 9.8 m/s2 for g. Use 1000 kg/m3 as the density of water. Assume r = 3 m and h = 1 m.)
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Calculus

10/11/23

Find the work W required to pump the water out of the spout.
A tank is full of water. Find the work W required to pump the water out of the spout. (Use 9.8 m/s2 for g. Use 1000 kg/m3 as the weight density of water. Assume... more
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Calculus

10/11/23

If the work required to stretch a spring 1 ft beyond its natural length is 6 ft-lb, how much work is needed to stretch it 9 in. beyond its natural length?
If the work required to stretch a spring 1 ft beyond its natural length is 6 ft-lb, how much work is needed to stretch it 9 in. beyond its natural length?
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Calculus

10/10/23

the question is below
The height of a triangle is increasing at 3 cm/min while the area of the triangle is increasing at 4cm2/min. at what rate is the triangle's base changing when the triangle's height is 10 cm and its... more
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Calculus

10/10/23

A circular arc of length 17 feet subtends a central angle of 25 degrees. Find the radius of the circle in feet.

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Calculus

10/10/23

Mat 270: Calc 3.10
I want to preface this by asking for an example with the same structure as the problem I provide so I can solve it. Such as giving an example of 8x+3=15 instead of my given 4x+12=32The question I... more
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