B - check your answers and present the solution
The functions supplied appear to be the same? Regardless:
We have the equation y = 5x.
Therefore the gradient of this graph will be 5, so for every 1 increase in the y axis, there will be 5 in the x.
It will appear as a straight line passing through the origin and the point (1, 5).
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:
x = 0.1515...
100 x = 15.1515...
100 x - x = 15.1515... - 0.1515...
99 x = 15
x = 15 / 99 = 3 ∙ 5 / 3 ∙ 33 = 5 / 33
0.1515... = 5 / 33
Step-by-step explanation:
Answer:
(C)
Step-by-step explanation:
Given the distance, d(t) of a particle moving in a straight line at any time t is:
To find an expression for the instantaneous velocity v(t) of the particle at any given point in time, we take the derivative of d(t).
The correct option is C.
