25,270 Answered Questions for the topic calculus

Calculus

03/15/24

An open-top box is made from a 24in x 36in cardboard piece by taking a square from each corner of the box and folding up all 4 side flaps. What size squares should be cut to get a box with max volume?
If you can, please show all work and write a detailed explanation-- I would really like to understand this problem!An open-top box is to be made from a 24 inch by 36 inch piece of cardboard by... more
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Calculus

03/15/24

Evaluate the double integral integral ∫∫ y dxdy. The plane region is (x-1)^2+(y-1)^2 <=8.
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Calculus

03/14/24

Find the equation of the sphere if one of its diameters has endpoints (-4,-5,8) and (-1,1,17).
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03/14/24

Which of the following integrals represents the volume of the solid obtained by rotating the region bounded by the curves 𝑦=sin(𝑥) and 𝑦=0, with 0≤𝑥≤𝜋 about the line 𝑦=1?
I keep getting it wrong. Here's the link to the question: https://ibb.co/BNDJS8J
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Calculus

03/14/24

An inverted pyramid is being filled with water at a rate of 45 cubic cm/sec. The pyramid top is square with sides 5 cm and the height is 11 cm. Find the rate of the water level rising when it's 5 cm.
An inverted pyramid is being filled with water at a constant rate of 45 cubic centimeters per second. The pyramid, at the top, has the shape of a square with sides of length 5 cm, and the height is... more
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Calculus

03/14/24

Related Rates: Fill in the Blank
A circle is inside a square.The radius of the circle is decreasing at a rate of 5 meters per hour and the sides of the square are increasing at a rate of 5 meters per hour.When the radius is 2... more
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Calculus

03/14/24

Related Rates: Inverted Pyramid filled with water at 55cc's/sec. Top is a square with sides 2cm long, and the height is 10cm. Find the rate of water level rise when the water level is 7 cm.
An inverted pyramid is being filled with water at a constant rate of 55 cubic centimeters per second. The pyramid, at the top, has the shape of a square with sides of length 2 cm, and the height is... more
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Calculus

03/14/24

A street light is on top of a 12 ft tall pole. A woman 6 ft tall walks away from the pole at speed 4 ft/sec on a straight path. How fast is the tip of her shadow moving from 40 ft from the pole?
A street light is at the top of a 12 ft tall pole. A woman 6 ft tall walks away from the pole with a speed of 4 ft/sec along a straight path. How fast is the tip of her shadow moving when she is 40... more
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Calculus

03/14/24

Related Rates: The altitude of a triangle is increasing while the area of the triangle is increasing. At what rate is the base of the triangle changing?
The altitude of a triangle is increasing at a rate of 1 centimeters/minute while the area of the triangle is increasing at a rate of 2 square centimeters/minute. At what rate is the base of the... more
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Calculus

03/14/24

Evaluate the double integral integral ∫∫ y dxdy. The plane region is (x-1)^2+(y-1)^2 <=8.

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Calculus

03/14/24

error and relative error
For a car with standard tires stopping on dry asphalt, its speed S (in mph) can be found from the length of its skid marks according toS = 9.4L0.37where L is the length (in feet) of the skid marks.... more
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Calculus Math

03/14/24

Evaluate the Integral
Evaluate the Integral. Please show all steps. If possible please attach a video going through the problem.
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Calculus Math

03/14/24

Write out the general form of the partial fraction decomposition of the function. Do not determine the numerical values of the constants.
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Calculus

03/13/24

Differential Equations
A 100 L tank contains 1 L of a brine solution with 2 kg of salt dissolved in it. At time t = 0, another brine solution flows into the tank at a rate of 6 L/min, however, this brine solution... more
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Calculus

03/13/24

A conical water tank with vertex down has a radius of 11 feet at the top and is 21 feet high. If water flows into the tank at a rate of 20ft^3/min,
A conical water tank with vertex down has a radius of 11 feet at the top and is 21 feet high. If water flows into the tank at a rate of 20ft^3/min, how fast is the depth of the water increasing... more
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Calculus

03/12/24

Consider the function 𝑓(𝑥)=2𝑥2+4𝑥−1. Which of the following statements is FALSE?
Select one:This function is concave up everywhereThis function is increasing at x=1This function has a horizontal tangent line at x=0This function is increasing at a faster rate at x=3 than x=2.
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Calculus

03/12/24

Arc Length Integral Questions
Let R be the region in the first quadrant bounded by y=x2 and y=√x. Write down a single integral that represents the perimeter of R.
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Calculus

03/12/24

Work to empty trough
 trough is 4 meters long, 1 meters wide, and 1 meters deep.The vertical cross-section of the trough parallel to an end is shaped like an isosceles triangle (with height 1 meters, and base, on top,... more
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03/12/24

Calculus Help!!
A farmer wants to fence in a rectangular field. The farmer must use a different type of fencing for each pair of parallel sides of the field. One type costs $10 per metre, and the other type costs... more
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03/12/24

calculus Help!!!
Consider the function defined by f(x)= ln( sqrt(|1−x^2|)). •a) State the domain of this function.b) Determine the derivative of ln(sqrt(|1−x^2|)).Be careful to show your work.
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03/12/24

Urgent calculus help
I need help finding some contour lines for the following function:
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Calculus

03/12/24

Differential Equations
Find the general solution to the differential equation dy/dx = yln(y).
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Calculus

03/12/24

AP Calculus BC - Series Convergent/ Divergent
1 to infinity, sin(1/x^2) 1 to infinity, 1/n(n+2)(n+5) 1 to infinity, ((-1)^n n^8 + 15)/ n^8 + 14
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03/12/24

Differentiable function of two variables
                                                                 A differentiable function of two variables reaches its maximum value at (0,0) being the value of the function 5. A student... more
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Calculus Math Precalculus

03/12/24

Determining the maximum and minimum values of function
Determine the maximum and minimum values of the function f(x,y)=x^2+y^2-2x-4y+5 in the set D = {( x ,y )∈R^2 / x^2 + y^2 ≤ 45}.
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