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Question 41571

posted 11 months ago

1. Using the Laplace transform pairs in the formula sheet (available in the Start Here module on the Additional Resources page), derive the Laplace transforms for the following time functions. For full credit, be sure to specify the theorem you will use and the function for which you will use the Laplace Transform.
\text { a. } e^{-a t} \cos (\omega t) u(t)

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Question 41572

posted 11 months ago

.Find the inverse Laplace transform of the problem below. For full credit all partial fractions and all three terms will be correct.
F(s)=\frac{18}{s\left(s^{2}+6 s+18\right)}

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Question 42008

posted 11 months ago

Convert the spherical point (p, q,0) into rectangular coordinates.

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Question 41995

posted 11 months ago

Evaluate the iterated integral by converting to polar coordinates. Enter an exact form, do not use decimal approximation.
\int_{-7}^{7} \int_{0}^{\sqrt{49-x^{2}}} \sin \left(x^{2}+y^{2}\right) d y d x

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Question 41998

posted 11 months ago

\text { Evaluate the triple integral } \iiint_{Q} 2 x e^{y} \sin z d V, \text { where } Q \text { is the rectangle defined by }
Q=[(x, y, z) \mid 0 \leq x \leq 4,0 \leq y \leq 2, \text { and } 0 \leq z \leq \pi] \text {. Enter an exact form, do not use decimal approximation. }

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Question 41999

posted 11 months ago

\text { Evaluate } \iint_{Q} \int 24 x y d V, \text { where } Q \text { is the tetrahedron bounded by the planes } x=0, y=0, z=0 \text { and }
2 x+y+z=4, \text { by integrating first with respect to } x \text {. Express your answer as a fraction. }

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Question 42003

posted 11 months ago

Write the given equation in Cylindrical coordinates.
(x-95)^{2}+y^{2}=9,025
r=95 \sin (\theta)
r=95 \cos (\theta)
r=190 \sin (\theta)
r=190 \cos (\theta)

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Question 42007

posted 11 months ago

Set up and evaluate the indicated triple integral in the appropriate coordinate system. Enter an exactanswer. Do not use a decimal approximation.
\iiint_{Q} z d V, \text { where } Q \text { is the region between } z=\sqrt{x^{2}+y^{2}} \text { and } z=\sqrt{16-x^{2}-y^{2}}
\iiint_{Q} z d V=

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Question 41992

posted 11 months ago

\text { If } R=\{(x, y) \mid 0 \leq x \leq 2 \text { and } 1 \leq y \leq 4\}, \text { evaluate }
\int_{R} \int\left(6 x^{2}+6 x y^{3}\right) d A

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Question 41997

posted 11 months ago

\text { Find the center of mass of a lamina in the shape of } x^{2}+(y-1)^{2}=1 \text {, with density }
\rho(x, y)=\frac{71}{\sqrt{x^{2}+y^{2}}} . \text { Enter an exact answer, do not use decimal approximation. }

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