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3 years ago

12

A publisher shipped 15 boxes of books to a bookstore each box contained 32 books how many books did the publisher ship to the bo

okstore?

2 answers:

Alenkinab [10]3 years ago

8 0

Answer:

Try This! 32 time 15 =480

Step-by-step explanation:

sukhopar [10]3 years ago

4 0

480 books!
32 x 15=480

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How many times larger is 3*10^8 than 5*10^6

Alex777 [14]

60 times larger.
Hope I helped!!!

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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:

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

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3 years ago

a sphere has a diameter of 7 centimeters what is the surface area is 3.14 to approximate Pi round to the nearest hundredth if ne

Over [174]

Good idea to look up the formula for "surface area of a sphere" and to write it down for later reference. It is A=4 pi r^2, where r is the radius of the sphere.
If the given sphere has a diameter of 7 cm, what is the radius of this sphere?

Write your answer inside the parentheses, below:

Sphere surface area = 4 pi (r)^2, or (in this case), A = 4(3.14)( )^2

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3 years ago

The following menu items were ordered at a pizza parlor on Friday. 3 salads, 8 pizzas, 4 sides of breadsticks, and 5 pepperoni c

den301095 [7]

Answer:

Using proportions, the pizza parlor should expect 20 breadsticks and 25 calzone orders if there were 100 total orders.

Step-by-step explanation:

Orders:

Salads 3

Pizzas 8

Sides of breadsticks 4

Pepperoni calzones 5

Total orders: 20

Proportion of sides breadsticks=4/20=0.2

Proportion of pepperoni calzones=5/20=0.25

For 100 total orders:

Sides of breadsticks=0.2(100)=20

Pepperoni calzones=0.25(100)=25

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3 years ago

Find the exact value of sin (13pi/8)

AnnZ [28]

Answer:

degree 0.089

radian -0.92

Step-by-step explanation:

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2 years ago