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Stella [2.4K]
3 years ago
14

How do you do this question?

Mathematics
1 answer:
r-ruslan [8.4K]3 years ago
5 0

Step-by-step explanation:

y = 3 + 8x^(³/₂), 0 ≤ x ≤ 1

dy/dx = 12√x

Arc length is:

s = ∫ ds

s = ∫₀¹ √(1 + (dy/dx)²) dx

s = ∫₀¹ √(1 + (12√x)²) dx

s = ∫₀¹ √(1 + 144x) dx

If u = 1 + 144x, then du = 144 dx.

s = 1/144 ∫ √u du

s = 1/144 (⅔ u^(³/₂))

s = 1/216 u^(³/₂)

Substitute back:

s = 1/216 (1 + 144x)^(³/₂)

Evaluate between x=0 and x=1.

s = [1/216 (1 + 144)^(³/₂)] − [1/216 (1 + 0)^(³/₂)]

s = 1/216 (145)^(³/₂) − 1/216

s = (145√145 − 1) / 216

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Answer:

Given equation is y = 6x + 8.

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Hence slope is 6 and y-intercept is 8.

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Question: (b) What are the rate of change and the initial amount? Explain the meaning of the rate of change and the initial amount for the situation.

Answer:

Rate of change means slope so answer is 6.

Initial amount means y-intercept so that is 8.

rate of change of 6 means six baskets of berries are picked by workers in 1 hour.

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Question: (c) Use graph paper to draw a graph representing the situation. Label the axes appropriately.

Answer:

first we graph y-intercept that is at point (0,8)

slope = 6 means make another point which is 6 unit up then 1 unit right from (0,8) so the new point is at (1,14)

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3 years ago
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To answer the problem you take 13 and minus -2 to get 15 and divide 15 by 5/4 and you get 12. 
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