Problem 3
If we peel off the sticker off the side of a 3D cylinder, then we can form a rectangle (imagine we're able to peel it off completely without any folds or tears).
The length of the rectangular sticker is the distance around the curved circular base. So it's C = pi*d = pi*1.5 = 1.5pi inches across. The height of the rectangle is the same as the height of the cylinder. So the height is 5 inches.
The area of the rectangle is: length*width = (1.5pi)*(5) = 7.5pi
That's the exact area in terms of pi
If you use the approximation pi = 3.14, then we'll get 7.5*3.14 = 23.55 square inches as the final answer
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Problem 4
The square base has area of 38*38 = 1444 square cm
The side panels are 4 identical triangles. Each triangle has area base*height/2 = 38*55/2 = 1045 square cm. Meaning that all four triangles combine to a lateral surface area of 4*1045 = 4180 sq cm.
The total surface area is: 1444+4180 = 5624 square cm.
When you wrote 55*38*2+38*38 on your paper, you had the right idea because that evaluates to 5624
Answer:
The average rate of change = -10
The crop yield decreased by 10 pounds per acre from year 10 to year 20.
Step-by-step explanation:
A farmer is tracking the number of soybeans his land is yielding each year. He finds that the function models the crops in pounds per acre over x years.
The average rate of change can be calculated using formula
In your case,
then
and the average rate of change is
This means the crop yield decreased by 10 pounds per acre (negative rate of change) from year 10 to year 20.
8.0 is greater than 0.8 because 8.0 is a unit but 0.8 is lesser than uint
We are given expression : .
We need to simplify it.
<em>First we need to apply quotient rule of exponents.</em>
According to quotient rule of exponents, we need to subtract powers.
Therefore, .
<em>Now, we need to apply exponents of exponent rule in next step.</em>
According to exponents of exponent rule, we need to distribute whole exponent inside exponent.
Therefore, .
<h3>Therefore, final answer is
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