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2 years ago

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Mathematics

2 answers:

Nadusha1986 [10]2 years ago

4 0

L only

i did this last week

Mademuasel [1]2 years ago

3 0

Answer:

I only

Step-by-step explanaition:

The domain (x) can not repeat in order for it to be a function.

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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

Use the following expression to answer the questions: g(to the second power) -4g+6. How many terms are in this expression? What

zmey [24]

G^2-4g+6
# Terms: 3, (g^2), (-4g), (6)
Variable: g
Constant: 6

4 0

3 years ago

fredy the frog was 18 feet down below ground in a well and is trying to climb out the first day he climbed up 7 feet but slid ba

lisov135 [29]

Writing this situation out in terms of operating with integers and indicating Fredy's position at the moment is as follows:

Fredy's position in the well = <u>13 feet in depth</u> or 5 feet from the bottom.

<h3>What is an integer?</h3>

An integer is a whole number, both positive and negative.

<h3>Data and Calculations:</h3>

Depth of well = 18 feet

Height climbed the first day = 7 feet

Height climbed the second day = 4 feet

Height of climb up the well = 11 feet

Depth of slid on the first day = 2 feet

Depth of slid on the second day = 4 feet

Total slid down the well = 6 feet (2 + 4)

The position of Fredy the Frog is at 13 feet (18 - 11 + 6) depth

Thus, based on integer operations, we can conclude that Fredy the Frog has only climbed <u>5 feet</u> (18 - 13) from the well's depth.

Learn more about integers at brainly.com/question/17695139

#SPJ1

<h3>Question Completion:</h3>

Fredy the frog was 18 feet down below ground in a well and is trying to climb out. The first day he climbed up 7 feet but slid back down <u>2 feet</u> the next day he climbed 3 feet but slid back down 4 feet.

7 0

2 years ago

Solutions to the quadratic question are -1/2 and 1/3. Figure out the original equation and write it in standard form.

OleMash [197]

Answer:

$6 {x}^{2} + 5x + 1 = 0$

7 0

3 years ago

Please help will give brainliest and good points

alina1380 [7]

7. (x-8)(x-7)

8. x=7 and x=8

9. (x-7)(x-8)=0 and solve

10. (x-8)(x-5)

11. x=8 and x=5

12. (x-8)(x-5)=0 and solve

hope this helps!!

5 0

3 years ago