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svlad2 [7]
3 years ago
14

Write an equation for the relation.

Mathematics
1 answer:
NeX [460]3 years ago
8 0

Answer:

the answer is f(x)= x-2

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Bella bought and candies ?
kondor19780726 [428]

Hmm I’ve done this before but I can’t remember sorry but I will try and think
6 0
3 years ago
Let f(x,y,z) = ztan-1(y2) i + z3ln(x2 + 1) j + z k. find the flux of f across the part of the paraboloid x2 + y2 + z = 3 that li
Sophie [7]
Consider the closed region V bounded simultaneously by the paraboloid and plane, jointly denoted S. By the divergence theorem,

\displaystyle\iint_S\mathbf f(x,y,z)\cdot\mathrm dS=\iiint_V\nabla\cdot\mathbf f(x,y,z)\,\mathrm dV

And since we have

\nabla\cdot\mathbf f(x,y,z)=1

the volume integral will be much easier to compute. Converting to cylindrical coordinates, we have

\displaystyle\iiint_V\nabla\cdot\mathbf f(x,y,z)\,\mathrm dV=\iiint_V\mathrm dV
=\displaystyle\int_{\theta=0}^{\theta=2\pi}\int_{r=0}^{r=1}\int_{z=2}^{z=3-r^2}r\,\mathrm dz\,\mathrm dr\,\mathrm d\theta
=\displaystyle2\pi\int_{r=0}^{r=1}r(3-r^2-2)\,\mathrm dr
=\dfrac\pi2

Then the integral over the paraboloid would be the difference of the integral over the total surface and the integral over the disk. Denoting the disk by D, we have

\displaystyle\iint_{S-D}\mathbf f\cdot\mathrm dS=\frac\pi2-\iint_D\mathbf f\cdot\mathrm dS

Parameterize D by

\mathbf s(u,v)=u\cos v\,\mathbf i+u\sin v\,\mathbf j+2\,\mathbf k
\implies\mathbf s_u\times\mathbf s_v=u\,\mathbf k

which would give a unit normal vector of \mathbf k. However, the divergence theorem requires that the closed surface S be oriented with outward-pointing normal vectors, which means we should instead use \mathbf s_v\times\mathbf s_u=-u\,\mathbf k.

Now,

\displaystyle\iint_D\mathbf f\cdot\mathrm dS=\int_{u=0}^{u=1}\int_{v=0}^{v=2\pi}\mathbf f(x(u,v),y(u,v),z(u,v))\cdot(-u\,\mathbf k)\,\mathrm dv\,\mathrm du
=\displaystyle-4\pi\int_{u=0}^{u=1}u\,\mathrm du
=-2\pi

So, the flux over the paraboloid alone is

\displaystyle\iint_{S-D}\mathbf f\cdot\mathrm dS=\frac\pi2-(-2\pi)=\dfrac{5\pi}2
6 0
3 years ago
Three friends went apple picking and then counted the apples they picked.Who had the largest red to green apple ratio? Use compl
antoniya [11.8K]

Answer:

Carmen had the largest red to green apple ratio of 5 : 3

Step-by-step explanation:

Red apples : Green apples

Carmen = 20 red apples : 12 green apples

= 20 / 12

= 5 / 3 = 1.67

= 5 : 3

Dylan = 12 red apples : 10 green apples

= 12 / 10

= 6 / 5 = 1.2

= 6 : 5

Eli = 16 red apples : 20 green apples

= 16 / 20

= 4 / 5 = 0.8

= 4 : 5

Carmen had the largest red to green apple ratio of 5 : 3

7 0
3 years ago
Please solve with explanation
OverLord2011 [107]

Real life scenarios of acute angles are:

  • Sighting a ball from the top of a building at an angle of 55 degrees.
  • The angle between two adjacent vanes of a fan that has 6 vanes

<h3>What are acute angles?</h3>

As a general rule, an acute angle, x is represented as: x < 90

This means that acute angles are less than 90 degrees.

<h3>The real life scenarios</h3>

The real life scenarios that involve acute angles are scenarios that whose measure of angle is less than 90 degrees.

Sample of the real life scenarios that satisfy the above definition are:

  • Sighting a ball from the top of a building at an angle of 55 degrees.
  • The angle between two adjacent vanes of a fan that has 6 vanes

Read more about acute angles at:

brainly.com/question/3217512

#SPJ1

8 0
1 year ago
Find the values of &lt; and y.<br> (8x + 7)<br> 5yº<br> (7y -- 34)<br> = (2x - 4)^
Lilit [14]

Answer:

x = 11

y = 17

Step-by-step explanation:

We know that opposite angles (or vertical angles) are equal.

So

8x + 7 = 9x - 4

Subtract 8x from both sides of the equation

8x - 8x + 7 = 9x - 8x - 4

7 = x - 4

Add 4 to both sides of the equation

7 + 4 = x - 4 + 4

11 = x

Looking at the other 2 angles,

5y = 7y - 34

Subtract 7 y from both sides of the equation

5y - 7y = 7y - 7y - 34

-2y = -34

Divide both sides by -2

-2y/-2 = -34/-2

y = 17

6 0
3 years ago
Read 2 more answers
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