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Harlamova29_29 [7]
2 years ago
9

Math For test HELPPPP plz due in 45 mins

Mathematics
1 answer:
Klio2033 [76]2 years ago
3 0
It’s BD because it need to be the opposite ray and this one is the opposite ray so yes this is it
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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 3.4 metre ladder is leaning against a wall. The bottom of the ladder is 1.5m from the wall. Determine the angle formed between
xxTIMURxx [149]

Answer:

80 degree angle

Step-by-step explanation:

8 0
3 years ago
Which expressions are equivalent to 10a - 25 + 5b
sergey [27]

Answer:

<h2>(2a − 5 + b) · 5</h2><h2>10×(a − 2.5 + 0.5b)</h2><h2>(−2a + 5 − b) ⋅ (−5)</h2>

Step-by-step explanation:

10a-25+5b\\\\-2(-5a-25+5b)=(-2)(-5a)+(-2)(-25)+(-2)(5b)\\=10a+50-10b\qquad NOT\\\\(2a-5+b)(5)=(2a)(5)+(-5)(5)+(b)(5)=10a-25+5b\qquad YES\\\\10(a-2.5+0.5b)=(10)(a)+(10)(-2.5)+(10)(0.5b)\\=10a-25+5b\qquad YES\\\\(-2a+5-b)(-5)=(-2a)(-5)+(5)(-5)+(-b)(-5)\\=10a-25+5b\qquad YES\\\\-10(-a-2.5-0.5b)=(-10)(-a)+(-10)(-2.5)+(-10)(-0.5b)\\=10a+25+5b\qquad NOT

5 0
3 years ago
If 1/2 = 32/d what is d first answer gets brainerlist
Scilla [17]

Answer:

D would be equal to 64

You just need to multiply 32 by 2

4 0
3 years ago
Read 2 more answers
Find the value of a in the parallelogram shown to the right. Note that the figure is not drawn to scale.
AveGali [126]

Answer:

Step-by-step explanation:

3a + 26 = 86

3a = 86 - 26 = 60

a = 60/3 = 20

5 0
2 years ago
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