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Artemon [7]
3 years ago
11

Use the arc length formula to find the length of the curve y = 5x − 4, −1 ≤ x ≤ 3. check your answer by noting that the curve is

a line segment and calculating its length by the distance formula
Mathematics
1 answer:
AnnZ [28]3 years ago
6 0
The given curve is y = 5x -4,  -1 ≤ x ≤ 3.

The length of the arc is computed from the formula
S= \int_{-1}^{3} \,\sqrt{1+ (\frac{dy}{dx} )^{2}} \, dx

The derivative is 
y' = 5

Therefore
S = \int_{-1}^{3} \sqrt{1+25} \, dx =\sqrt{26}*(3-(-1))=20.396

Note that 
x = -1 +> y = 5(-1) - 4 = -9
x = 3 => y = 5(3) - 4 = 11
The distance between the points (-1, -9) and (3, 11) from the distance formula is
D = √[(3-(-1))² + (11-(-9))²] = √(16+400) = 20.396
This answer agrees with that obtained by integration.

Answer: 20.396
Obtained by integration and verified by the distance formula.

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Anuta_ua [19.1K]

Answer:

84 feet of ribbon is needed

Step-by-step explanation:

Given : Ribbon is sold by the foot. If Heather is making 84 bows, ​how many feet​ of ribbon must she buy?

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7 0
3 years ago
-(y-7)=14 solve the following equation
enyata [817]

First, distribute the negative sign and get -y + 7 = 14

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Hope this helps :)

3 0
2 years ago
Louis little brother is sick with a fever his temperature is 104​
valentina_108 [34]

Answer:

40

Step-by-step explanation:

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4 0
3 years ago
Read 2 more answers
Rewrite the formula to find the width of the base of the prism if the volume, length of the base, and height of the prism are al
notsponge [240]

Answer:

w = V/lh

Step-by-step explanation:

The volume of a rectangular prism is calculated using the formula V = lwh, where V is the volume of the prism, l and w are the length and width of the base of the prism, respectively, and h is the height of the prism.

Rewrite the formula to find the width of the base of the prism if the volume, length of the base, and height of the prism are already known.

volume of a rectangular prism,V = lwh

Where,

l = length of the base of the prism

w = width of the base of the prism

h = height of the prism

Rewrite the formula to find w

V = lwh

w = V/lh

That is,

width of the base of the prism = volume of the prism divided by length of the base of the prism multiplied by height of the prism

5 0
2 years ago
Need help show work??????
o-na [289]

Answer:

The t-shirt cost $10.70

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12.25 + T = 22.95

-12.25          -12.25

T=10.70

8 0
2 years ago
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