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3 years ago

What is the solution to the equation 3x+7=-x+3

Mathematics

1 answer:

TiliK225 [7]3 years ago

7 0

Answer:

x = -1

Step-by-step explanation:

3x + 7 = -x + 3

4x + 7 = 3

4x + 4 = 0

x + 1 = 0

x = -1

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Find the area of the helicoid (or spiral ramp) with vector equation r(u, v) = ucos(v) i + usin(v) j + v k, 0 ≤ u ≤ 1, 0 ≤ v ≤ 9π

Natasha2012 [34]

Let $H$ denote the helicoid parameterized by

$\mathbb r(u,v)=u\cos v\,\mathbf i+u\sin v\,\mathbf j+v\,\mathbf k$

for $0\le u\le1$ and $0\le v\le9\pi$ . The surface area is given by the surface integral,

$\displaystyle\iint_H\mathrm dS=\iint_H\|\mathbf r_u\times\mathbf r_v\|\,\mathrm du\,\mathrm dv$

We have

$\mathbf r_u=\dfrac{\partial\mathbf r(u,v)}{\partial u}=\cos v\,\mathbf i+\sin v\,\mathbf j$
$\mathbf r_v=\dfrac{\partial\mathbf r(u,v)}{\partial v}=-u\sin v\,\mathbf i+u\cos v\,\mathbf j+\mathbf k$
$\implies\mathbf r_u\times\mathbf r_v=\sin v\,\mathbf i-\cos v\,\mathbf j+u\,\mathbf k$
$\implies\|\mathbf r_u\times\mathbf r_v\|=\sqrt{1+u^2}$

So the area of $H$ is

$\displaystyle\iint_H\mathrm dS=\int_{v=0}^{v=9\pi}\int_{u=0}^{u=1}\sqrt{1+u^2}\,\mathrm du\,\mathrm dv$
$=\dfrac{9(\sqrt2+\sinh^{-1}(1))\pi}2$

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3 years ago

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Anna35 [415]

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4 years ago

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A factory worker can pagage 150 in 15 minutes. how many games can he page per minute?

meriva

He can package 10 games in one minute because I divided 150 by 15.

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4 years ago

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Kamila [148]

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Step-by-step explanation:

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3 years ago

Find the equation of the line that goes through the point ( 6, 5) and has a slope of 1/3

PSYCHO15rus [73]

Answer (<u>assuming it can be slope-intercept form)</u>:

$y = \frac{1}{3} x +3$

Step-by-step explanation:

Since we already know a point the line intersects and its slope, we can use the point-slope formula $y-y_1 = m (x-x_1)$ to write an equation, then convert it to slope-intercept form.

Substitute values for $m$ , $x_1$ , and $y_1$ . Since $m$ represents the slope, substitute $\frac{1}{3}$ in its place. Since $x_1$ and $y_1$ represent the x and y values of one point the line intersects, use the x and y values of (6,5) and substitute them into the equation. Substitute 6 for $x_1$ and 5 for $y_1$ . Then, isolate y to put it into slope-intercept form and find an answer:

$y -5 = \frac{1}{3} (x-6)\\y-5 = \frac{1}{3}x-2\\y = \frac{1}{3} x+3$

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3 years ago