1answer.
Ask question
Login Signup
Ask question
All categories
  • English
  • Mathematics
  • Social Studies
  • Business
  • History
  • Health
  • Geography
  • Biology
  • Physics
  • Chemistry
  • Computers and Technology
  • Arts
  • World Languages
  • Spanish
  • French
  • German
  • Advanced Placement (AP)
  • SAT
  • Medicine
  • Law
  • Engineering
Romashka-Z-Leto [24]
3 years ago
8

Find the simplified form of each expression

Mathematics
1 answer:
astraxan [27]3 years ago
7 0

11.(y^6)² = y^12

12.(x^-3)^-5 x^6 = x^21

13.(6q^6)^–4 = 1/1296q^24

You might be interested in
hurry! You are monitoring a stock investment for a client, for which positive numbers indicate an increase in value, and negativ
dusya [7]
-23.94??? are you sure
7 0
3 years ago
Evaluate the surface integral S F · dS for the given vector field F and the oriented surface S. In other words, find the flux of
tresset_1 [31]

Because I've gone ahead with trying to parameterize S directly and learned the hard way that the resulting integral is large and annoying to work with, I'll propose a less direct approach.

Rather than compute the surface integral over S straight away, let's close off the hemisphere with the disk D of radius 9 centered at the origin and coincident with the plane y=0. Then by the divergence theorem, since the region S\cup D is closed, we have

\displaystyle\iint_{S\cup D}\vec F\cdot\mathrm d\vec S=\iiint_R(\nabla\cdot\vec F)\,\mathrm dV

where R is the interior of S\cup D. \vec F has divergence

\nabla\cdot\vec F(x,y,z)=\dfrac{\partial(xz)}{\partial x}+\dfrac{\partial(x)}{\partial y}+\dfrac{\partial(y)}{\partial z}=z

so the flux over the closed region is

\displaystyle\iiint_Rz\,\mathrm dV=\int_0^\pi\int_0^\pi\int_0^9\rho^3\cos\varphi\sin\varphi\,\mathrm d\rho\,\mathrm d\theta\,\mathrm d\varphi=0

The total flux over the closed surface is equal to the flux over its component surfaces, so we have

\displaystyle\iint_{S\cup D}\vec F\cdot\mathrm d\vec S=\iint_S\vec F\cdot\mathrm d\vec S+\iint_D\vec F\cdot\mathrm d\vec S=0

\implies\boxed{\displaystyle\iint_S\vec F\cdot\mathrm d\vec S=-\iint_D\vec F\cdot\mathrm d\vec S}

Parameterize D by

\vec s(u,v)=u\cos v\,\vec\imath+u\sin v\,\vec k

with 0\le u\le9 and 0\le v\le2\pi. Take the normal vector to D to be

\vec s_u\times\vec s_v=-u\,\vec\jmath

Then the flux of \vec F across S is

\displaystyle\iint_D\vec F\cdot\mathrm d\vec S=\int_0^{2\pi}\int_0^9\vec F(x(u,v),y(u,v),z(u,v))\cdot(\vec s_u\times\vec s_v)\,\mathrm du\,\mathrm dv

=\displaystyle\int_0^{2\pi}\int_0^9(u^2\cos v\sin v\,\vec\imath+u\cos v\,\vec\jmath)\cdot(-u\,\vec\jmath)\,\mathrm du\,\mathrm dv

=\displaystyle-\int_0^{2\pi}\int_0^9u^2\cos v\,\mathrm du\,\mathrm dv=0

\implies\displaystyle\iint_S\vec F\cdot\mathrm d\vec S=\boxed{0}

8 0
3 years ago
Find the width of a cereal box that has a volume of 2,112 cm^3 and is 22 cm long and 24 cm high.
allochka39001 [22]
Divide 2112 by 24 and 22 to find your answer.

the answer is 4.

brainlisest please.
3 0
3 years ago
Which best describes the error in finding the simple interest earned on $500 at 6% for 18 months?
valentinak56 [21]
$540.00 is the interest
Hope I helped
Let me know if you need me to help you with anything else

My Username: Ashlynnicole02
7 0
3 years ago
What is the missing number?<br><br> Question 4 options:
Semenov [28]

Answer:

i dont see it

Step-by-step explanation:

6 0
2 years ago
Other questions:
  • The linear equation graphed above gives the height in feet above the ground of Shelly t seconds after she opened her parachute w
    8·1 answer
  • Help please
    5·2 answers
  • What is 675 divided by 12 long division...lol I’m TIRED.help...
    6·1 answer
  • 3
    11·1 answer
  • At a football game there are 4 children for every 14 adults. If there are 1584 total people at the game, how many of them are ch
    8·1 answer
  • Consider the system of linear equations 2x + 3y = 8 and 3x+y=-2. Which statement is correct
    5·2 answers
  • Solve the equation by factoring: x2 − 7x + 12 = 0
    5·1 answer
  • 14n + p – 6n = 16p solve for and please explain
    10·2 answers
  • Which of the following is equal to 2 -5 ?
    6·1 answer
  • Brittany irons 1/8 of her shirt in 4 1/2 minutes. How much of her shirt does she iron each minute?
    12·2 answers
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!