Loosely, "varies inversely" means that as one quantity increases, the other decreases. Specifically, if x and y vary inversely, then y = k/x where k is some constant (a particular number).
Another way to write that relationship is xy = k. To find the value of k for this problem, you need a numbers for x and y that go together.
Suppose x = number of children and y = number of candies (it doesn't matter what order these go in as long as you keep track!).
"When 12 children are present, 140 pieces of candy are consumed." So when x = 12, the value of y = 140.
xy = k
(12)(140) = k
1680 = k
Now, when x = 8 children,
8y = 1680
y = 210
Answer:
<m is equal to the measure of <Z
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<span>83 1/5 -108 2/5 - (-99 1/5) = 74</span>
Answer:
229.2
Step-by-step explanation:
Remark
There's a lot in this question. The x is not just any x. It is defined and limited by its relationship with the sine function.
The Sin is defined as Opposite over Hypotenuse in a right triangle. The 670 is the Hypotenuse. You know that by the definition of Sine.
So one thing you should always keep in mind: the x because of where it is in the definition, will always be smaller than the Hypotenuse. So you should get a value less than 670.
Formula
Just as you have it
Sin(20) = x / 670
Solution
Multiply both sides by 570
670 * sin(20) = x
sin(20) = 0.3420
x = 670 * 0.3420
x = 229.2
Answer:
Step-by-step explanation:
Let's use the definition of the Laplace transform and the identity given:
with
.
Now,
. Using integration by parts with u=e^(-st) and dv=cos(5t), we obtain that
.
Using integration by parts again with u=e^(-st) and dv=sin(5t), we obtain that
.
Solving for F(s) on the last equation,
, then the Laplace transform we were searching is