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3 years ago

9

Audrey has some guppies in a fish tank. The ratio of the orange guppies to silver guppies is 3 : 5. She has 12y orange puppies.

Write the number of silver guppies she has in terms of y.

2 answers:

adelina 88 [10]3 years ago

5 0

Answer:

Should be y=20

Step-by-step explanation:

Margarita [4]3 years ago

4 0

We solve:
$\frac{3}{5} = \frac{12y}{number \: of \: silver \: guppies} \: or \\ \\ 3 \times (number \: of \: silver \: guppies) \: \\ = 60y \\ \\ this \: means \: the \: number \: of \: \\ silver \: guppies \: in \: terms \: of \: y \: is \: \\ \frac{60y}{3} = 20y$

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Can you please help me figure out this answer? Please and thank you

galben [10]

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The formula for P is P = 2W + 2L.

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P = 2(3 1/2 yds) + 2(4 2/3 yds)

= 7 yds + 9 1/3 yds = 16 1/3 yds, total.

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3 years ago

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Step-by-step explanation:

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2 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 $\boxed{4\sqrt3\pi}$ .

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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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3 years ago

Complete the table of values fory=2x^2+x

Semmy [17]

Complete question:

y = 2x² + 2x - 3

x = -2 -1 0 1 2

Answer:

<u>Complete table of values</u>

x: -2 -1 0 1 2

y: 1 -3 -3 1 9

Step-by-step explanation:

Given;

y = 2x² + 2x - 3

To complete the table of values of the equation above, we substitute the value of x into the given equation and solve for y.

when, x = -2

y = 2(-2)² + 2(-2) - 3

y = 8 - 4 - 3

y = 1

when x = -1

y = 2(-1)² + 2(-1) - 3

y = 2 - 2 - 3

y = -3

when x = 0

y = 2(0)² + 2(0) - 3

y = 0 - 0 - 3

y = -3

when x = 1

y = 2(1)² + 2(1) - 3

y = 2 + 2 - 3

y = 1

when x = 2

y = 2(2)² + 2(2) - 3

y = 8 + 4 - 3

y = 9

<u>Complete table</u>

x: -2 -1 0 1 2

y: 1 -3 -3 1 9

7 0

3 years ago

HELP!!! SOLVE USING SUBSTITUTION OR ELIMINATION.

Bezzdna [24]

Search it up on the internet <3

8 0

3 years ago