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Aleks [24]
3 years ago
13

The table below shows the number of Japanese yen that could be exchanged for U.S. dollars on the day

Mathematics
1 answer:
olga55 [171]3 years ago
7 0

Answer:

The Answer is B.

Step-by-step explanation:

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Put these fractions and decimals in least to greatest<br><br> 8 1/9,8.117,8.28,163/20
suter [353]
Turn them all into decimals so you can clearly see the difference between them

8 1/9 = 8.11
8.117
8.28
163/20 = 8.15

8 1/9, 8.117, 163/20, 8.28 is your answer
8 0
3 years ago
Am I correct? I added them all.
max2010maxim [7]
Yes you are correct.
6 0
3 years ago
Read 2 more answers
PART A. A fruit juice recipe uses three ingredients. Two of the ingredients use a ratio of 2 ounces of pineapple juice to 5 ounc
Rashid [163]

Answer:

(B) The equation of line is 5 X = 2 Y.

Step-by-step explanation:

2 ounces of pineapple juice

5 ounces of fruit punch

Other is 4 ounces pineapple juice and 10 ounces fruit punch

(A) Graph is shown below:

(B) Let X is the pineapple juice and Y is the fruit punch

(2, 5)  and (4, 10)

So, the equation of line is

Y - 5 = \frac{10-5}{4-2}\times (x -2)\\\\Y-5=2.5 (X-2)\\\\Y - 5 = 2.5 X - 5 \\\\2.5 X = Y\\\\ 5 X = 2 Y

8 0
2 years ago
Integral <br><img src="https://tex.z-dn.net/?f=x%5E%7B3%7D%20%20-%207x%5E%7B2%7D%20%2B%205x%20%2B%2040%20%5Cdiv%20x%5E%7B2%7D%20
solong [7]

Answer:

ext^{4}-7x^{2}+3x+401dvx^{2}i-8ext

Step-by-step explanation:

6 0
3 years ago
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}.

d. By the divergence theorem, the flux of \vec F across the closed hemisphere H with boundary C\cup D is equal to the integral of \mathrm{div}\vec F over its interior:

\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

4 0
3 years ago
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