hamada11617
25.07.2019 •
Mathematics
Base of a circular fence with radius 10 m is given by x = 10 cos(t), y = 10 sin(t). the height of the fence at position (x, y) is given by the function h(x, y) = 3 + 0.03(x2 − y2), so the height varies from 0 m to 6 m. suppose that 1 l of paint covers 100 m2. determine how much paint you will need if you paint both sides of the fence. (round your answer to two decimal places.)
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Ответ:
Therefore, you need to find how the height varies with the only parameter you know: the angle t. Then, you can integrate to find the area of the fence.
First, you need to write h(x,y) only as a function of x (or y, you can choose). Since the base is circular, you have:
x² + y² = 100
y² = 100 - x²
You can now substitute:
h(x) = 3 + 0.03(x² - y²)
= 3 + 0.03[x² - (100 - x²)]
= 3 + 0.03(2x² - 100)
= 3 + 0.06(x² - 50)
Now, you have to write h as a function of t; you know:
x = 10·cos(t)
Therefore:
h(t) = 3 + 0.06[(10·cos(t)² - 50]
= 3 + 0.06[100·cos²(t) - 50]
= 3 + 6·cos²(t) - 3
= 6·cos²(t)
This function is correct because we know that the height varies between 0 and 6m.
In order to find the area, you need to integrate:
=
=
6·(1/2)[sin(2π)cos(2π) + 2π] - 6·(1/2)[sin(0)cos(0) + 0] =
6·(1/2)(2π) =
6π
This is one side of the fence, therefore the total area to be painted is 12π m². You need 1l for 100m², therefore:
(1 / 100) · 12π = 0.38 l
Hence, you will need 0.38 liters of paint to cover both sides of the fence.
Ответ:
Number of Small Cones Sold=22
Number of Large Cones Sold=34
Step-by-step explanation:
Suppose,
Number of Small Cones Sold: s
Number of Large Cones Sold: l
For the condition that, larges cones sold were 12 more than small ones, equation would be
and for the total revenue condition of $163
By solving equation (i) and (ii) simultaneously, we get
s=22
and
l=34
Hence, small cones sold would be 22 and large cones sold would be 34.