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3 years ago

Regarding Linear questions

Mathematics

2 answers:

soldi70 [24.7K]3 years ago

8 0

See the attached pictures for the solutions:

viva [34]3 years ago

7 0

1.
2x + 10 = 30 - x
x = 20/3 = 6.67
y = 70/3 = 23.33333...
Both lines intersect at the 23.33... point

Blue Line: (0,10) , (20/3)(70/3)
Red Line: (0,30) , (12,17)

2.
Slope: (y2 - y1 ÷ x2 - x1)

= (-3 - 5) ÷ 3 - (-1)

= -6 ÷ 4

= -2

Slope = -2

Intercept:

y = mx + b

SLOPE = m

y = (-2x) + b

b = y1 + m

b = 5 + (-2) = 5 - 2 = 3

Intercept = 3

Hope This HELPS!

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Setler79 [48]

Answer:

x=19/4 , y=3/4

Step-by-step explanation:

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

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:

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

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Zolol [24]

Answer:

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Step-by-step explanation:

There are 4 quarts in a gallon so the cost of a gallon of oil currently is 1.85×4=$7.40

If the gallon price of oil goes up 50% then our answer is: 7.40× $\frac{3}{2}$ = $\frac{22.2}{2}$ =11.1

The price of oil in March will be $11.10 per gallon.

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3 years ago

A mason is forming a rectangular floor for a storage shed.

Dmitry [639]

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width=11

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Marta_Voda [28]

Hi!

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Divided by 5 is 1.13137085
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Divided by 7 is 0.767715934

The answer is <span>0.767715934

Hope this helps! :)
-Peredhel</span>

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3 years ago

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