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3 years ago

1. Find the simple interest.

Mathematics

2 answers:

Mars2501 [29]3 years ago

5 0

Answer:

29303

Step-by-step explanation:

1084 shush

Juliette [100K]3 years ago

4 0

Answer:

The first one is 648 and the second one is 11,600

Step-by-step explanation:

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What is the fraction as a decimal?

Bess [88]

You just divide 3/8= 0.375

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3 years ago

Evaluate the surface integral:S

rjkz [21]

Assuming $S$ does not include the plane $z=0$ , we can parameterize the region in spherical coordinates using

$\mathbf r(u,v)=\left\langle3\cos u\sin v,3\sin u\sin v,3\cos v\right\rangle$

where $0\le u\le2\pi$ and $0\le v\le\dfrac\pi/2$ . We then have

$x^2+y^2=9\cos^2u\sin^2v+9\sin^2u\sin^2v=9\sin^2v$
$(x^2+y^2)=9\sin^2v(3\cos v)=27\sin^2v\cos v$

Then the surface integral is equivalent to

$\displaystyle\iint_S(x^2+y^2)z\,\mathrm dS=27\int_{u=0}^{u=2\pi}\int_{v=0}^{v=\pi/2}\sin^2v\cos v\left\|\frac{\partial\mathbf r(u,v)}{\partial u}\times \frac{\partial\mathbf r(u,v)}{\partial u}\right\|\,\mathrm dv\,\mathrm du$

We have

$\dfrac{\partial\mathbf r(u,v)}{\partial u}=\langle-3\sin u\sin v,3\cos u\sin v,0\rangle$
$\dfrac{\partial\mathbf r(u,v)}{\partial v}=\langle3\cos u\cos v,3\sin u\cos v,-3\sin v\rangle$
$\implies\dfrac{\partial\mathbf r(u,v)}{\partial u}\times\dfrac{\partial\mathbf r(u,v)}{\partial v}=\langle-9\cos u\sin^2v,-9\sin u\sin^2v,-9\cos v\sin v\rangle$
$\implies\left\|\dfrac{\partial\mathbf r(u,v)}{\partial u}\times\dfrac{\partial\mathbf r(u,v)}{\partial v}\|=9\sin v$

So the surface integral is equivalent to

$\displaystyle243\int_{u=0}^{u=2\pi}\int_{v=0}^{v=\pi/2}\sin^3v\cos v\,\mathrm dv\,\mathrm du$
$=\displaystyle486\pi\int_{v=0}^{v=\pi/2}\sin^3v\cos v\,\mathrm dv$
$=\displaystyle486\pi\int_{w=0}^{w=1}w^3\,\mathrm dw$

where $w=\sin v\implies\mathrm dw=\cos v\,\mathrm dv$ .

$=\dfrac{243}2\pi w^4\bigg|_{w=0}^{w=1}$
$=\dfrac{243}2\pi$

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2 years ago

Examples of parallel lines

viktelen [127]

Answer:

what idea and experience do you get after being lockdown for long three or four months due to corona virus. write your experience in the form of article that is published in school magazine on the topic lack of physical activity.

Step-by-step explanation:

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2 years ago

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Answer and explanation please

Gnom [1K]

For the triangle, the shaded part, both the height and base are 12, so the area of it is:

1/2 (12 x 12) = 72

And the area of the whole square is 144

But what we’re looking for is the area of the unshaded region. So to find it, we’ll need to subtract the shaded from the total. So:

144 - 72 = 72

Thus, the area of the unshaded region is 72

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3 years ago

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There is a list of seven numbers. The average of the first four numbers is 5, and the average of the last four numbers is 8. If

sammy [17]

Answer:

Step-by-step explanation:

Sum of first 4 numbers= 4*5= 20

This includes 3 + 4th number

Sum of last 4 numbers= 4*8= 32

This includes 4th number + 3

Sum of 7 numbers= 7*(6+4/7)= 46

This includes 3+4th number +3

Number common to both sets= (20+32)- 46 = 6

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2 years ago