3 years ago

Tollowing: a) 3x + 4 = 9.5 7 + 2x = b) = 5

Mathematics

1 answer:

Vera_Pavlovna [14]3 years ago

8 0

See attachment for math work and answer.

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Evaluate the surface integral. s x ds, s is the triangular region with vertices (1, 0, 0), (0, −2, 0), and (0, 0, 12).

aniked [119]

Parameterize the surface by

$\mathbf r(s,t)=(1-s)(0,0,12)+s\bigg((1-t)(1,0,0)+t(0,-2,0)\bigg)$
$\implies\mathbf r(s,t)=(x(s,t),y(s,t),z(s,t))=(s-st,-2st,12-12s)$

where $(s,t)\in(0,1)\times(0,1)$ . We have

$\|\mathbf r_s\times\mathbf r_t\|=\|(1-t,-2t,-12)\times(-s,-2s,0)\|=2\sqrt{181}s$

The surface integral is then

$\displaystyle\iint_Sx\,\mathrm dS=2\sqrt{181}\int_{s=0}^{s=1}\int_{t=0}^{t=1}s(s-st)\,\mathrm dt\,\mathrm ds$
$=\displaystyle2\sqrt{181}\left(\int_{s=0}^{s=1}s^2\,\mathrm ds\right)\left(\int_{t=0}^{t=1}(1-t)\,\mathrm dt\right)$
$=\dfrac{\sqrt{181}}3$

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bija089 [108]

Answer:

0.25

Step-by-step explanation:

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A fitness club has two options, one for members and one for nonmembers. Members pay a one-time registration fee of $12 plus $8 p

Liula [17]

Answer:

See below.

Step-by-step explanation:

Let's look at the cost for members (C1) first. Let x be the number of visits.

C1(x) = 12 + 8x

For non-members (C2), we can do the same.

C2(x) = 10x

You can graph these two equations.

x C1 C2

0 12 0

1 20 10

2 28 20

3 36 30

4 44 40

5 52 50

6 60 60

7 68 70

Let's make the two equations equal, to find out where the benefit is the same.

12 + 8x = 10x

2x = 12

x = 6

Up to 5 visits, the non-member cost is better. At 6 visits, there's the same price. For more than 6 visits, the member cost is better.

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3 years ago

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Fynjy0 [20]

Answer:

$-\frac{26}{2}/ -\sqrt{9}/ 13.5(percent)/ 0/ 13.5$

Step-by-step explanation:

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Complete the comparison: 26 <

EastWind [94]

26< any number larger than 26 (whole numbers and fractions/decimals)

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