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2 years ago

Please help me!!!!!!!!!!!!!!!!!!!!!!

Mathematics

1 answer:

Sloan [31]2 years ago

4 0

Answer:

Step-by-step explanation:

f(x)=3(2^x)+6 so

f(3)=3(2^3)+6

f(3)=3(8)+6

f(3)=24+6

f(3)=30

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Consider the following region R and the vector field F. a. Compute the two-dimensional curl of the vector field. b. Evaluate bo

Shalnov [3]

Looks like we're given

$\vec F(x,y)=\langle-x,-y\rangle$

which in three dimensions could be expressed as

$\vec F(x,y)=\langle-x,-y,0\rangle$

and this has curl

$\mathrm{curl}\vec F=\langle0_y-(-y)_z,-(0_x-(-x)_z),(-y)_x-(-x)_y\rangle=\langle0,0,0\rangle$

which confirms the two-dimensional curl is 0.

It also looks like the region $R$ is the disk $x^2+y^2\le5$ . Green's theorem says the integral of $\vec F$ along the boundary of $R$ is equal to the integral of the two-dimensional curl of $\vec F$ over the interior of $R$ :

$\displaystyle\int_{\partial R}\vec F\cdot\mathrm d\vec r=\iint_R\mathrm{curl}\vec F\,\mathrm dA$

which we know to be 0, since the curl itself is 0. To verify this, we can parameterize the boundary of $R$ by

$\vec r(t)=\langle\sqrt5\cos t,\sqrt5\sin t\rangle\implies\vec r'(t)=\langle-\sqrt5\sin t,\sqrt5\cos t\rangle$

$\implies\mathrm d\vec r=\vec r'(t)\,\mathrm dt=\sqrt5\langle-\sin t,\cos t\rangle\,\mathrm dt$

with $0\le t\le2\pi$ . Then

$\displaystyle\int_{\partial R}\vec F\cdot\mathrm d\vec r=\int_0^{2\pi}\langle-\sqrt5\cos t,-\sqrt5\sin t\rangle\cdot\langle-\sqrt5\sin t,\sqrt5\cos t\rangle\,\mathrm dt$

$=\displaystyle5\int_0^{2\pi}(\sin t\cos t-\sin t\cos t)\,\mathrm dt=0$

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3 years ago

Explain how to find simple interest

mr_godi [17]

Answer:

Simple interest is calculated by multiplying the daily interest rate by the principal, by the number of days that elapse between payments.

Step-by-step explanation:

Principal x rate x time = interest.

$100 x .05 x 1 = $5 simple interest for one year.

$100 x .05 x 3 = $15 simple interest for three years.

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kodGreya [7K]

Answer:

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Step-by-step explanation:

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Kruka [31]

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Ainat [17]

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3 years ago

Please help me!!!!!!!!!!!!!!!!!!!!!!​

Please help me!!!!!!!!!!!!!!!!!!!!!!