Answer:
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Step-by-step explanation:
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a. Parameterize
by

with
.
b/c. The line integral of
over
is




d. Notice that we can write the line integral as

By Green's theorem, the line integral is equivalent to

where
is the triangle bounded by
, and this integral is simply twice the area of
.
is a right triangle with legs 2 and 5, so its area is 5 and the integral's value is 10.
The length of the other two sides is 10 and 35 respectively.
<h3>What is a ratio?</h3>
A ratio is a quantitative relation showing the comparison between two or more numbers. It can also be written in the fractional form where the first part is the numerator and the second part is called the denominator.
From the given information:
- The sides of the triangle = 2:7:8
- The total sides of the triangle = 2+7+8 = 17
We are being told that the longest side is the triangle is equal to 40.
i.e.



x = 85
Now for the other two sides 2 and 7, their length is as follows.


Therefore, we can conclude that the length of the other two sides is 10 and 35 respectively.
Learn more about ratios here:
brainly.com/question/2328454
Answer:
Correct answer: Hmax = 22.11 m
Step-by-step explanation:
The subject of this problem is a vertical shot upwards, to which the following formula applies:
V₀² - V² = 2 · g · H where is:
V₀ - initial velocity
V - final velocity
g = 10 m/s²
H - final height
Given:
V₀ = 69 ft/s = 21.03 m/s
V = 0 m/s
Hmax = ?
V₀² = 2 · g · Hmax ⇒ Hmax = V₀² / 2 · g
Hmax = 21.03² / 2 · 10 = 442.26 / 20 = 22.11 m
Hmax = 22.11 m
God is with you!!!