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r-ruslan [8.4K]
3 years ago
7

Consider the following. x = t2 − 2t, y = t5, 1 ≤ t ≤ 4 Set up an integral that represents the length of the curve. 4 1 dt Use yo

ur calculator to find the length correct to four decimal places.
Mathematics
1 answer:
zavuch27 [327]3 years ago
5 0

Answer:

L ≈ 1023.0562

Step-by-step explanation:

We are given;

x = t² - 2t

dx/dt = 2t - 2

Also, y = t^(5)

dy/dt = 5t⁴

The arc length formula is;

L = (α,β)∫√[(dx/dt)² + (dy/dt)²]dt

Where α and β are the boundary points. Thus, applying this to our question, we have;

L = (1,4)∫√[(2t - 2)² + (5t⁴)²]dt

L = (1,4)∫√[4t² - 8t + 4 + 25t^(8)]dt

L = (1,4)∫√[25t^(8) + 4t² - 8t + 4]dt

Using online integral calculator, we have;

L ≈ 1023.0562

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Scale factor is defined as a number which multiplies or scales some quantity.

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If the scale factor is greater than one, then the image is enlarged.

If the scale factor is less than 1 but greater that 0, then the image becomes smaller.

In the above image,  AD = 2 units.

It's corresponding side PS =  3 units

Similarly AB = 1 unit and PQ = 1.5 units

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Hence, the scale factor of the given image is 1.5 ... Answer

7 0
3 years ago
Homework - Pure Year 1 - Chapter 11B
ycow [4]

Answer:

|F net| = 20.22 N

θ ≈ 19.8°

Step-by-step explanation:

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= 15N i + 4N i + 4√3N j

= 19N i + 4√3N j

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5 0
2 years ago
Which number line shows the solution set for StartAbsoluteValue 2 p minus 4 EndAbsoluteValue greater-than-or-equal-to 6?
maks197457 [2]

Answer:

can u add a picture?

Step-by-step explanation:

8 0
3 years ago
Please help I really need help because I have to turn it in soon and yeah so comment
BartSMP [9]

Answer:

hi

Step-by-step explanation:

4- 3*1=3

6*1/100= 0.06

3+0.06= 3.06

5- 7*1= 7

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7- 3.3, 3.30

8- 9.3000, 9.30

9- 9.6, 9.600

10- 4.4000, 4.40

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3 0
3 years ago
Jordan changed the dimensions of a rectangular picture measuring 20 cm wide by 25 cm high by a scale factor of 5/2.
iVinArrow [24]

Answer:

I believe it's an enlargement, because 5/2 is more than one whole.

Step-by-step explanation:

7 0
3 years ago
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