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charle [14.2K]
3 years ago
12

Plz help!

Mathematics
1 answer:
GuDViN [60]3 years ago
5 0

Answer:

5x - y = 27

Step-by-step explanation:

Slope is the direction of line and it is calculated as,

Slope = \frac{y-y_{1}}{x-x_{1}}


where (x₁, y₁) is any two points on the line.

Here, we have given that

Slope = 5  and (x₁, y₁) = (5, -2)

∴  5 = \frac{y-(-2)}{x-5}


⇒ 5(x - 5) = y + 2

⇒ 5x - 25 = y + 2

⇒ 5x - y = 27

Hence, the equation of a line is: 5x - y = 27

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April lost 5 pounds in her first week of college. Over the next three weeks she lost 3 pounds, gained 2 pounds, and then lost 1
Doss [256]

Change in April's weight is -7

<em><u>Solution:</u></em>

Let the initial weight be "x"

April lost 5 pounds in her first week of college

First week = lost 5 pounds

Therefore, x - 5

Over the next three weeks she lost 3 pounds, gained 2 pounds, and then lost 1 pound

<em><u>Next three week:</u></em>

Lost 3 pound

Gained 2 pound

Lost 1 pound

<em><u>Therefore, weight after 4 weeks is given as:</u></em>

x - 5 - 3 + 2 - 1 = x -7

After 4 week, the weight is x - 7

<em><u>The change in April weight is given as:</u></em>

Weight after 4 week - initial weight = x - 7 - x = -7

Thus change in April's weight is -7 (Negative sign represents loss in weight )

4 0
3 years ago
Use the divergence theorem to calculate the surface integral s f · ds; that is, calculate the flux of f across s. f(x, y, z) = x
valkas [14]
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\mathrm{div}(\mathbf f)=\dfrac{\partial(x^4)}{\partial x}+\dfrac{\partial(-x^3z^2)}{\partial y}+\dfrac{\partial(4xy^2z)}{\partial z}=4x^3+0+4xy^2=4x(x^2+y^2)


Let \mathcal D be the region whose boundary is \mathcal S. Then by the divergence theorem,

\displaystyle\iint_{\mathcal S}\mathbf f\cdot\mathrm d\mathbf S=\iiint_{\mathcal D}4x(x^2+y^2)\,\mathrm dV

Convert to cylindrical coordinates, setting

x=r\cos\theta
y=r\sin\theta

and keeping z as is. Then the volume element becomes


\mathrm dV=r\,\mathrm dr\,\mathrm d\theta\,\mathrm dz

and the integral is

\displaystyle\iiint_{\mathcal D}4x(x^2+y^2)\,\mathrm dV=\int_{\theta=0}^{\theta=2\pi}\int_{r=0}^{r=1}\int_{z=0}^{z=r\cos\theta+7}4r\cos\theta\cdot r^2\cdot r\,\mathrm dz\,\mathrm dr\,\mathrm d\theta
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3 years ago
Use a reference angle to write sec255∘ in terms of the secant of a positive acute angle. Do not include the degree symbol in you
jarptica [38.1K]

Answer: sec (75) or csc (15)

Step-by-step explanation:

255 is in the 3rd quadrant where the secant is. Here, the tangent and cotangent is positive.

Reference angle for 255 is,

255 - 180 = 75 degrees.

Therefore, sec (255) = sec (75)

= csc (90 - 75) = csc (15)

6 0
3 years ago
Y varies directly as x. Y=42 when x=6. Find the value of y when x =15.
pentagon [3]

Answer:

y=120

Step-by-step explanation:

Y varies directly as x is written as

y \alpha x

introducing a constant

y=kx

<em>from</em><em> </em><em>the</em><em> </em><em>ques</em><em>tion</em><em>,</em><em> </em><em>whe</em><em>n</em><em> </em><em>y</em><em>=</em><em>4</em><em>8</em><em>,</em><em> </em><em> </em><em>x</em><em>=</em><em>6</em>

<em>sub</em><em>stitute</em><em> </em><em>it</em><em> </em><em>in</em><em> </em><em>the</em><em> </em><em>form</em><em>ula</em>

<em>4</em><em>8</em><em>=</em><em>6</em><em>k</em>

<em>making</em><em> </em><em>k</em><em> </em><em>the</em><em> subject</em><em> </em><em>by </em><em>divi</em><em>ding</em><em> </em><em>thr</em><em>ough</em><em> </em><em>by</em><em> </em><em>6</em>

<em>\frac{48}{6}  =  \frac{6k}{6}</em>

k=48/6

k=8

<em>put</em><em> </em><em>the</em><em> </em><em>va</em><em>lue</em><em> </em><em>of</em><em> </em><em>k</em><em> </em><em>in</em><em> </em><em>the </em><em>expression</em><em> </em><em>y</em><em>=</em><em>kx</em>

<em>y</em><em>=</em><em>8</em><em>x</em>

from the question,the value of y when x=15 is given by

y=8×15

y=120.

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3 years ago
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mrs_skeptik [129]

Answer:

1/16

Step-by-step explanation:

This means 1/2x2x2x2  = 1/16

7 0
2 years ago
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