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2 years ago

The following pentagon, ABCDE is rotated about the origin 90 counterclockwise. Select the new coordinates of C and E after the

Mathematics

1 answer:

katrin2010 [14]2 years ago

8 0

Answer:

its 10

Step-by-step explanation:

10 times 1 is 10

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Evaluate the surface integral. s x2 + y2 + z2 ds s is the part of the cylinder x2 + y2 = 4 that lies between the planes z = 0 an

Leya [2.2K]

Parameterize the lateral face $T_1$ of the cylinder by

$\mathbf r_1(u,v)=(x(u,v),y(u,v),z(u,v))=(2\cos u,2\sin u,v$

where $0\le u\le2\pi$ and $0\le v\le3$ , and parameterize the disks $T_2,T_3$ as

$\mathbf r_2(r,\theta)=(x(r,\theta),y(r,\theta),z(r,\theta))=(r\cos\theta,r\sin\theta,0)$
$\mathbf r_3(r,\theta)=(r\cos\theta,r\sin\theta,3)$

where $0\le r\le2$ and $0\le\theta\le2\pi$ .

The integral along the surface of the cylinder (with outward/positive orientation) is then

$\displaystyle\iint_S(x^2+y^2+z^2)\,\mathrm dS=\left\{\iint_{T_1}+\iint_{T_2}+\iint_{T_3}\right\}(x^2+y^2+z^2)\,\mathrm dS$
$=\displaystyle\int_{u=0}^{u=2\pi}\int_{v=0}^{v=3}((2\cos u)^2+(2\sin u)^2+v^2)\left\|{{\mathbf r}_1}_u\times{{\mathbf r}_2}_v\right\|\,\mathrm dv\,\mathrm du+\int_{r=0}^{r=2}\int_{\theta=0}^{\theta=2\pi}((r\cos\theta)^2+(r\sin\theta)^2+0^2)\left\|{{\mathbf r}_2}_r\times{{\mathbf r}_2}_\theta\right\|\,\mathrm d\theta\,\mathrm dr+\int_{r=0}^{r=2}\int_{\theta=0}^{\theta=2\pi}((r\cos\theta)^2+(r\sin\theta)^2+3^2)\left\|{{\mathbf r}_3}_r\times{{\mathbf r}_3}_\theta\right\|\,\mathrm d\theta\,\mathrm dr$
$=\displaystyle2\int_{u=0}^{u=2\pi}\int_{v=0}^{v=3}(v^2+4)\,\mathrm dv\,\mathrm du+\int_{r=0}^{r=2}\int_{\theta=0}^{\theta=2\pi}r^3\,\mathrm d\theta\,\mathrm dr+\int_{r=0}^{r=2}\int_{\theta=0}^{\theta=2\pi}r(r^2+9)\,\mathrm d\theta\,\mathrm dr$
$=\displaystyle4\pi\int_{v=0}^{v=3}(v^2+4)\,\mathrm dv+2\pi\int_{r=0}^{r=2}r^3\,\mathrm dr+2\pi\int_{r=0}^{r=2}r(r^2+9)\,\mathrm dr$
$=136\pi$

7 0

3 years ago

a customer buys a diiferent book that has an original selling price of $38 the books is discounted 25% the customer must pay a 6

Nimfa-mama [501]

Answer: 30.21$
Explanation:
1. 38• 0.25(25%)=28.50
2. 28.50•0.06(6)=1.71 ( the sales taxes)
3. 28.50+1.71=30.21$
Hope this helps. If it’s correct please tell me.

7 0

2 years ago

Could the equation. For the graph of the function have degree 4?explain

aivan3 [116]

The graphed polynomial seems to have a degree of 2, so the degree can be 4 and not 5.

<h3>Could the graphed function have a degree 4?</h3>

For a polynomial of degree N, we have (N - 1) changes of curvature.

This means that a quadratic function (degree 2) has only one change (like in the graph).

Then for a cubic function (degree 3) there are two, and so on.

So. a polynomial of degree 4 should have 3 changes. Naturally, if the coefficients of the powers 4 and 3 are really small, the function will behave like a quadratic for smaller values of x, but for larger values of x the terms of higher power will affect more, while here we only see that as x grows, the arms of the graph only go upwards (we don't know what happens after).

Then we can write:

y = a*x^4 + c*x^2 + d

That is a polynomial of degree 4, but if we choose x^2 = u

y = a*u^2 + c*u + d

So it is equivalent to a quadratic polynomial.

Then the graph can represent a function of degree 4 (but not 5, as we can't perform the same trick with an odd power).

If you want to learn more about polynomials:

brainly.com/question/4142886

#SPJ1

5 0

2 years ago

Which statement describes the value of the expression 15*(8+45)?

Degger [83]

What are the choices so that we Can help you appropriately

4 0

3 years ago

Read 2 more answers

MN bisects OP at point Q . Which statement is true <br> OQ=QP <br> MQ=QN<br> MQ=QP<br> OQ=QN

barxatty [35]

OQ is equal to QP so the first option is correct

7 0

2 years ago