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Calculus Linear Algebra

09/15/24

Gauss-Jordan Elimination Question

Problem: Suppose that a matrix A satisfies Arref [-9 -43 * -133 *] [1 0 5 0 1] [3 16 * 48 *] [0 1 -3 0 -2] ... more

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Calculus Linear Algebra

09/15/24

Gauss-Jordan Elimination Problem

Hello,I am struggling to understand Gauss-Jordan Elimination. This question I believe is asking for me to apply the Rouche-Capelli Theorem. I would greatly appreciate your guidance on how to... more

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Calculus

09/15/24

Find integral of yArctan(2y)dy (having a hard time breaking it down and really understanding the integration.

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Calculus

09/13/24

A tank has a shape of a cone with a radius at the top of 3 m and a height of 5 m. The tank also has a 1 m spout at the top of the tank.

The tank is filled with water up to a height of 2 m. Find the work needed to pump all the water out the top of the spout. (Use 9.8 m/s2 for g and the fact that the density of water is1000 kg/m3.)

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Calculus

09/13/24

Define a piece-wise function f(x) that has a removable discontinuity at x=6, is only left continuous at x=2, and has no continuity at x=-3

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Calculus

09/13/24

A kite 50 ft above the ground moves horizontally at a speed of 6 ft/s. At what rate is the angle (in radians) between the string and the horizontal decreasing when 200 ft of string have been let out?

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Calculus

09/13/24

spherical tank with radius 4 m is half full of a liquid that has a density of 900 kg/m3. The tank has a 2 m spout at the top. Find the work W required to pump the liquid out of the spout.

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Calculus

09/12/24

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.

A water tank shaped like a triangular prism is given. The base of the prism is at the top and a spout is located at the top of the tank. The dimensions of the tank are 9 meters long, 4 meters wide,... more

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Calculus

09/12/24

A cylindrical tank has a radius of 3 m and a height of 7 m. The tank is filled with water. Find the work needed to pump the top 3 m of water out the top of the tank.

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Calculus

09/12/24

An aquarium 2 m long, 1 m wide, and 1 m deep is half-filled with water. Find the work needed to pump the water out of the aquarium. (

Use 9.8 m/s2 for g and the fact that the density of water is 1000 kg/m3.

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Calculus

09/12/24

How to compute left, right, & midpoint Riemann sums when n value is large (n=25, n=100)

f(x)= x2+1 on the interval [1,4]Compute the Riemann sums for L25, R25, M25, L100, R100, M100What is the exact area of the curve?I managed to get L5, R5, & M5, but am very confused on how to... more

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Calculus Math Linear Algebra

09/09/24

Linear Algebra: Vector Geometry Question

Problem 1: Suppose ∥v∥ = 4 and ∥w∥ = 7. Use inner products to determine the largest and smallest possible values of ∥6 v − 5w∥. Hint. Start by expanding ∥6 v − 5 w∥ ^2. Hi. I would really... more

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Calculus

09/09/24

Plsssssssssss help, so sorry for the trouble

Link to image of the problem

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Calculus

09/09/24

Determine the volume of the solid obtained by rotating the region bounded (using shell method)

Determine the volume of the solid obtained by rotating the region bounded by x=(y−2)^2 and y=x about the line y=−1. (Use cylindrical shell method)

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Calculus

09/09/24

Determine the volume of the solid obtained by rotating the region bounded

2) Determine the volume of the solid obtained by rotating the region bounded by y=x^2−2x and y=x about the line y=4.

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Calculus

09/09/24

Determine the volume of the solid obtained by rotating the portion of the region bounded.

1) Determine the volume of the solid obtained by rotating the portion of the region bounded by y= \root(3)(x) and y=x/4 lies in the first quadrant about the y-axis

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Calculus Math

09/08/24

Derivatives Help

Determine the derivative of f(x)=cos(x+1/x).

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Calculus Math

09/08/24

Derivatives Question

Find the derivative of f(x)=sinx/√x

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Calculus Math

09/08/24

Limits Question

i) Using the graph of the function f, evaluate the limit of f(x) as x approaches 1+.ii) Using the graph of the function f, evaluate the limit of f(x) as x approaches 2.

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Calculus

09/07/24

Reduce the equation 16x^2+y^2+16z^2-8y-160z+400=0 to one of the standard forms for Calculus III forms in a 3D plane.

This represents a ellipsoid figure. Please put this equation into the standard form for the ellipsoid.

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Calculus

09/06/24

What is the integral of inverse sine?

This is a difficult integration problem that will use BOTH integration by parts AND u-substitution.

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Calculus

09/05/24

The base of S is the triangular region with vertices (0, 0), (4, 0), and (0, 8). Cross-sections perpendicular to the x−axis are squares.

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Calculus

09/05/24

The base of a solid S is the region enclosed by the parabola y = 4 − x2 and the x-axis. Cross-sections perpendicular to the y-axis are squares.

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Calculus

09/05/24

The base of S is the region enclosed by the parabola y = 4 − 4x2 and the x-axis. Cross-sections perpendicular to the x-axis are isosceles triangles with height equal to the base.

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Calculus

09/05/24

Set up the integral that uses the method of disks/washers to find the volume V of the solid obtained by rotating the region bounded by the given curves about the specified lines.

Y=5√x , y=5, x=0a)about the y=5b)about the line x=5

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Gauss-Jordan Elimination Question

Gauss-Jordan Elimination Problem

Find integral of yArctan(2y)dy (having a hard time breaking it down and really understanding the integration.

A tank has a shape of a cone with a radius at the top of 3 m and a height of 5 m. The tank also has a 1 m spout at the top of the tank.

Define a piece-wise function f(x) that has a removable discontinuity at x=6, is only left continuous at x=2, and has no continuity at x=-3

A kite 50 ft above the ground moves horizontally at a speed of 6 ft/s. At what rate is the angle (in radians) between the string and the horizontal decreasing when 200 ft of string have been let out?

spherical tank with radius 4 m is half full of a liquid that has a density of 900 kg/m3. The tank has a 2 m spout at the top. Find the work W required to pump the liquid 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.

A cylindrical tank has a radius of 3 m and a height of 7 m. The tank is filled with water. Find the work needed to pump the top 3 m of water out the top of the tank.

An aquarium 2 m long, 1 m wide, and 1 m deep is half-filled with water. Find the work needed to pump the water out of the aquarium. (

How to compute left, right, & midpoint Riemann sums when n value is large (n=25, n=100)

Linear Algebra: Vector Geometry Question

Plsssssssssss help, so sorry for the trouble

Determine the volume of the solid obtained by rotating the region bounded (using shell method)

Determine the volume of the solid obtained by rotating the region bounded

Determine the volume of the solid obtained by rotating the portion of the region bounded.

Derivatives Help

Derivatives Question

Limits Question

Reduce the equation 16x^2+y^2+16z^2-8y-160z+400=0 to one of the standard forms for Calculus III forms in a 3D plane.

What is the integral of inverse sine?

The base of S is the triangular region with vertices (0, 0), (4, 0), and (0, 8). Cross-sections perpendicular to the x−axis are squares.

The base of a solid S is the region enclosed by the parabola y = 4 − x2 and the x-axis. Cross-sections perpendicular to the y-axis are squares.

The base of S is the region enclosed by the parabola y = 4 − 4x2 and the x-axis. Cross-sections perpendicular to the x-axis are isosceles triangles with height equal to the base.

Set up the integral that uses the method of disks/washers to find the volume V of the solid obtained by rotating the region bounded by the given curves about the specified lines.

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