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Mashcka [7]
3 years ago
12

What curve passes through the point ​(1 ​,2​) and has an arc length on the interval​ [2,6] given by Integral from 2 to 6 StartRo

ot 1 plus 64 x Superscript negative 6 EndRoot dx ​? What is the​ curve?
Mathematics
1 answer:
Georgia [21]3 years ago
3 0

Answer:

Step-by-step explanation:

Given

Length of curve

L=\int_{2}^{6}\sqrt{1+64x^{-6}}dx

Length of curve is given by

L=\int_{a}^{b}\sqrt{1+\left ( \frac{\mathrm{d} y}{\mathrm{d} x}\right )^2}dx over interval a to b

comparing two we get

\frac{\mathrm{d} y}{\mathrm{d} x}=8x^{-3}

dy=8x^{-3}dx

integrating

\int dy=\int 8x^{-3}dx

y=-4x^{-2}+C

Curve Passes through (1,2)

1=-4+C

C=5

curve is

y+\frac{4}{x^2}=5

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Let line A be the graph of 5x + 8y = -9. Line B is perpendicular to line A and passes through the point (10,10). If line B is th
frozen [14]
Find slope of line A:
Move into slope-intercept form y = mx+b

<span>5x + 8y = -9
8y = -5x - 9
y = (-5/8)x - 9/8

The slope of line A is -5/8.

If </span><span>Line B is perpendicular to line A, then

slope Line B = negative reciprocal of slope Line A</span>
<span>slope Line B = 8/5

So like B has the equation

y = (8/5)x + b

If it passes through (10,10), we know that when x = 10, y = 10. Use those values to solve for b:
</span>
<span>y = (8/5)x + b
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<span>10 = (8)·2 + b
10 = 16 + b
b = -6

So line B has equation </span>
<span>y = (8/5)x - 6

m = 8/5 and b = -6

so

m + b = 8/5 - 6 = 8/5 - 30/5 = -22/5

So m+b = -22/5 or -4.4 in decimal form
</span>
6 0
3 years ago
Can you make the area of your shape go up but the perimeter go down?
Virty [35]
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-- If it's a rectangle, make it more square ... make the length and width
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3 0
3 years ago
Read 2 more answers
Find the slope of the equation
andreyandreev [35.5K]

Answer:

In my guess I'll go for Slope = -\frac{4}{5}  y-intercept = 10

7 0
3 years ago
The length of a swimming pool is 10 ft shorter than twice the width. the length is 35 ft. what is the width
Hatshy [7]
Okay so we need to figure out the width of the swimming pool using the length, and we know the width is 10 ft shorter than twice the width. I believe the easiest way to do this would be to first do 35-10, and then divide it in half. That gives us 12.5. To check our work I'll do the problem 12.5+12.5+10=35.

The width of the swimming pool is 12.5 ft.
8 0
3 years ago
Answers for both boxes please ​
sleet_krkn [62]

Answer:

x = -5  y = -3

Step-by-step explanation:

-3x + 2y = 9

multiply the 2nd equation by 3 to set it up for elimination

3(x - 3y)= 3(4)

3x-9y = 12

so now combine both to add

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7 0
2 years ago
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