Answer:
Part 1: 30.42
Part 2: 33.598 (33.6)
Step-by-step explanation:
Part 1:
First you're going to start by subtracting 142 from 360 to get 218
Then you're going to divide 218 by 360 to get a rounded .61
Then you're going to multiply that by pi (3.14)
.61 x 3.14 = 1.9
Then you're going to square 4
4 x 4 = 16
Then multiply 1.9 x 16
Your answer should be 30.42
<u>Part 2: </u>
<u>Since it gives you the measurment you need, you're going to skip the subtracting and just divide 107 by 360</u>
<u>This gives you .3 (rounded)</u>
<u>Multiply by pi</u>
<u>.3 x 3.14 = .94</u>
<u>multiply by square of 6 (36)</u>
<u>.94 x 36 = 33.84</u>
<u>if you shove it all into a calculator without rounding inbetween at all you get 33.59</u>
The equation of this sinusoidal function is either
f(x) = a sin(bx) + c
or
f(x) = a cos(bx) + c
Either way, the plot of f9x) has amplitude a, period 2π/b, and midline y = c.
If the period is π/2, then
2π/b = π/2 ⇒ b = 4
If the maximum value is 10 and the minimum value is -4, then
-4 ≤ a sin(4x) + c ≤ 10
-4 - c ≤ a sin(4x) ≤ 10 - c
-(4 + c)/a ≤ sin(4x) ≤ (10 - c)/a
Recall that sin(x) is bounded between -1 and 1. So we must have
-(4 + c)/a = -1 ⇒ a = c + 4
(10 - c)/a = 1 ⇒ a = -c + 10
Combining these equations and eliminating either variable gives
a + a = (c + 4) + (-c + 10) ⇒ 2a = 14 ⇒ a = 7
a - a = (c + 4) - (-c + 10) ⇒ 0 = 2c - 6 ⇒ c = 3
Finally, we have either
f(x) = a sin(bx) + c ⇒ f(0) = c = 3
or
f(x) = a cos(bx) + c ⇒ f(0) = a + c = 3
but the cosine case is impossible since a = 7.
So, the given function has equation
f(x) = 7 sin(4x) + 3
The formula for the surface area of a cylinder is:
Plug in what we know, use 3.14 to approximate for pi(radius is half the diameter, 30/2 = 15):
Simplify:
Subtract 1413 to both sides:
Divide 94.2 to both sides:
So the height is approximately 45 millimeters.
What percent of $68.73 is $12? We can find out what we have to multiply to $68.73 to get $12. We can substitute this with "x". So then, our equation becomes 68.73x = 12. From there, you just do basic algebra.
You should get <span>17.4596246% which can then be rounded down to 17% depending on which place you're rounding it by.</span>
