The parametric equations for x and y describe a circle of radius 10 m, so the length of the base of the fence is the length of the circumference of a circle of radius 10 m. The formula for that circumference (C) is ...
... C = 2πr
... C = 2π·(10 m) = 20π m
The height as a function of angle (t) is found by substituting for x and y.
... h(t) = h(x(t), y(t)) = 4 + 0.01·((10cos(t))²-)10sin(t))²) = 4+cos(2t)
The average value of this over the range 0 ≤ t ≤ 2π is 4, since the cosine function has two full cycles in that range, and its average value over a cycle is zero.
Thus, the area of one side of the fence is that of a rectangle 20π m long and 4 m wide. That will be
... (20π m)·(4 m) = 80π m²
The amount of paint required to cover both sides of the fence is
... 2×(80π m²)×(1 L)/(10 m²) = 16π L ≈ 50.3 L
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You can work out the integral for area as a function of t. When you do, you will find it gives this same result.
Answer:
12.5
Step-by-step explanation:
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The answer is a. (-2, 4). The horizontal line is the x-axis, and the vertical line is the y-axis, so the coordinate points would be (x, y) and (-2, 4) fit those coordinates. Hope this helps! :)
Answer:
it D
Step-by-step explanation:
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- Find square root of 144 by factorisation method.
We can find the square root of 144 using the factorisation method. In this method, you need to factorise 144 first. Then, you'll get your answer in the form of prime factors. In this case, it's ⇨ 2 × 2 × 2 × 2 × 3 × 3.
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To find the square root using factorisation, we need to group the same number in pairs. That is, 2 × 2 × 2 × 2 × 3 × 3 by grouping same numbers in pairs will become ⇨ (2, 2), (2, 2), (3, 3).
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Now, you should take only 1 of the number from these groups. So, (2, 2), (2, 2), (3, 3) will change to ⇨ 2 × 2 × 3.
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Finally, just multiply this set of numbers to find the square root of 144. 2 × 2 × 3 = 4 × 3 = 
⇨ square root of 144.
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- The square root of 144 is <em><u>1</u></em><em><u>2</u></em><em><u>.</u></em>
