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Serga [27]
3 years ago
10

The American flag is customarily made with its width and length in the ratio of 10 to 19. Which of the following dimensions is i

n the correct ratio for the flag?
Mathematics
1 answer:
saul85 [17]3 years ago
3 0
You have not provided the options, therefore, I cannot give an exact answer. However, I can help you with the procedures.

We are given that the ratio between the width and the length of the flag is 10 to 19.
This means that:
\frac{width}{length} =  \frac{10}{19}

Therefore, to get the correct choice, all you have to do is divide the width by the length, if the result is 10/19, then the dimensions given are correct.

Examples:
For length = 190 and width = 100,
width / length = 100 / 190 = 10 / 19 .........> correct choice

For length = 1.9 and width = 1,
width / length = 1 / 1.9 = 10 / 19 .......> correct choice

Hope this helps :)
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ExtremeBDS [4]
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6 0
3 years ago
The expression (8-3)^2-(5-2)^2 is equivalent to what numerical expression
Tresset [83]
(8-3)²-(5-2)²
Follow the PEMDAS
P-Parenthesis
E-Exponents
M/D-Multiplication/Division
A/S-Addition/Subtraction
clear the numerals in the parenthesis:
(5)²-(3)²
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3 years ago
How to write 532÷4 in place valve
storchak [24]
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Problem 4: Let F = (2z + 2)k be the flow field. Answer the following to verify the divergence theorem: a) Use definition to find
Viktor [21]

Given that you mention the divergence theorem, and that part (b) is asking you to find the downward flux through the disk x^2+y^2\le3, I think it's same to assume that the hemisphere referred to in part (a) is the upper half of the sphere x^2+y^2+z^2=3.

a. Let C denote the hemispherical <u>c</u>ap z=\sqrt{3-x^2-y^2}, parameterized by

\vec r(u,v)=\sqrt3\cos u\sin v\,\vec\imath+\sqrt3\sin u\sin v\,\vec\jmath+\sqrt3\cos v\,\vec k

with 0\le u\le2\pi and 0\le v\le\frac\pi2. Take the normal vector to C to be

\vec r_v\times\vec r_u=3\cos u\sin^2v\,\vec\imath+3\sin u\sin^2v\,\vec\jmath+3\sin v\cos v\,\vec k

Then the upward flux of \vec F=(2z+2)\,\vec k through C is

\displaystyle\iint_C\vec F\cdot\mathrm d\vec S=\int_0^{2\pi}\int_0^{\pi/2}((2\sqrt3\cos v+2)\,\vec k)\cdot(\vec r_v\times\vec r_u)\,\mathrm dv\,\mathrm du

\displaystyle=3\int_0^{2\pi}\int_0^{\pi/2}\sin2v(\sqrt3\cos v+1)\,\mathrm dv\,\mathrm du

=\boxed{2(3+2\sqrt3)\pi}

b. Let D be the disk that closes off the hemisphere C, parameterized by

\vec s(u,v)=u\cos v\,\vec\imath+u\sin v\,\vec\jmath

with 0\le u\le\sqrt3 and 0\le v\le2\pi. Take the normal to D to be

\vec s_v\times\vec s_u=-u\,\vec k

Then the downward flux of \vec F through D is

\displaystyle\int_0^{2\pi}\int_0^{\sqrt3}(2\,\vec k)\cdot(\vec s_v\times\vec s_u)\,\mathrm du\,\mathrm dv=-2\int_0^{2\pi}\int_0^{\sqrt3}u\,\mathrm du\,\mathrm dv

=\boxed{-6\pi}

c. The net flux is then \boxed{4\sqrt3\pi}.

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\displaystyle\iint_{C\cup D}\vec F\cdot\mathrm d\vec S=\iiint_H\mathrm{div}\vec F\,\mathrm dV

We have

\mathrm{div}\vec F=\dfrac{\partial(2z+2)}{\partial z}=2

so the volume integral is

2\displaystyle\iiint_H\mathrm dV

which is 2 times the volume of the hemisphere H, so that the net flux is \boxed{4\sqrt3\pi}. Just to confirm, we could compute the integral in spherical coordinates:

\displaystyle2\int_0^{\pi/2}\int_0^{2\pi}\int_0^{\sqrt3}\rho^2\sin\varphi\,\mathrm d\rho\,\mathrm d\theta\,\mathrm d\varphi=4\sqrt3\pi

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STatiana [176]
Hello,


1   .65 + 0.20(65) = 65 + 13 = 78
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2.  I posted a file to help you on this question!

3. <span>Find principal by using the formula </span><span>I=P⋅i⋅t</span><span>, where </span>I<span> is interest, </span>P<span> is total principal, </span>i<span> is rate of interest per year, and </span>t<span> is total time in years.
</span>
So basically your answer is 600.


I truley hope this helps.

Have a good day!


-Jurgen

4 0
3 years ago
Read 2 more answers
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