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3 years ago

Find x (round to the nearest tenth)

Mathematics

1 answer:

never [62]3 years ago

5 0

9514 1404 393

Answer:

x = 8

Step-by-step explanation:

By AA similarity, ΔABD ~ ΔCDE. So, corresponding sides are proportional.

AB/BD = CD/DE

x/12 = 4/6

x = 12(4/6)

x = 8

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Use Stokes' Theorem to evaluate C F · dr F(x, y, z) = xyi + yzj + zxk, C is the boundary of the part of the paraboloid z = 1 − x

Serggg [28]

I assume $C$ has counterclockwise orientation when viewed from above.

By Stokes' theorem,

$\displaystyle\int_C\vec F\cdot\mathrm d\vec r=\iint_S(\nabla\times\vec F)\cdot\mathrm d\vec S$

so we first compute the curl:

$\vec F(x,y,z)=xy\,\vec\imath+yz\,\vec\jmath+xz\,\vec k$

$\implies\nabla\times\vec F(x,y,z)=-y\,\vec\imath-z\,\vec\jmath-x\,\vec k$

Then parameterize $S$ by

$\vec r(u,v)=\cos u\sin v\,\vec\imath+\sin u\sin v\,\vec\jmath+\cos^2v\,\vec k$

where the $z$ -component is obtained from

$1-(\cos u\sin v)^2-(\sin u\sin v)^2=1-\sin^2v=\cos^2v$

with $0\le u\le\dfrac\pi2$ and $0\le v\le\dfrac\pi2$ .

Take the normal vector to $S$ to be

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

Then the line integral is equal in value to the surface integral,

$\displaystyle\iint_S(\nabla\times\vec F)\cdot\mathrm d\vec S$

$=\displaystyle\int_0^{\pi/2}\int_0^{\pi/2}(-\sin u\sin v\,\vec\imath-\cos^2v\,\vec\jmath-\cos u\sin v\,\vec k)\cdot(\vec r_v\times\vec r_u)\,\mathrm du\,\mathrm dv$

$=\displaystyle-\int_0^{\pi/2}\int_0^{\pi/2}\cos v\sin^2v(\cos u+2\cos^2v\sin u+\sin(2u)\sin v)\,\mathrm du\,\mathrm dv=\boxed{-\frac{17}{20}}$

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3 years ago

I REALLY NEED HELP PLEASE!

zhuklara [117]

Answer:

The answer to that question is b

Step-by-step explanation:

6 0

3 years ago

A bee flies at 20 feet per second directly to a flower bed from its hive. The bee stays at the flower bed for 15 minutes, and th

oee [108]

Answer:

a. Speed of flight * ( total spent away from hive - time stayed on flower bed)

b. The flower bed is 2,400 ft from the hive

Step-by-step explanation:

a. Mathematically, the distance will be ;

the speed * time taken

Given that he stays a total of 17 minutes away from the hive and he stayed 15 minutes in the flower bed, the time it used on the flower bed will be 17 minutes - 15 minutes = 2 minutes

So the distance from the flower bed to the hive is;

Speed of flight * ( total spent away from hive - time stayed on flower bed)

b. We want to find the distance of the flower bed from the hive

That will be;

20 ft per second * 2 minutes (120 seconds)

= 20 * 120 = 2,400 ft

4 0

3 years ago