The value of c such that the function f is a probability density function is 2
<h3>How to determine the value of c?</h3>
The density function is given as:
f(x) = cxe^(−x^2) if x ≥ 0
f(x) = 0 if x < 0.
We start by integrating the function f(x)
∫f(x) = 1
This gives
∫ cxe^(−x^2) = 1
Next, we integrate the function using a graphing calculator.
From the graphing calculator, we have:
c/2 * (0 + 1) = 1
Evaluate the sum
c/2 * 1 = 1
Evaluate the product
c/2 = 1
Multiply both sides of the equation by 2
c = 2
Hence, the value of c such that the function f is a probability density function is 2
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Answer:
The radius is growing at a rate of 
ft per minute.
Step-by-step explanation:
From the information given we know that
And we know as well that .
Since everything is changing with the time we can compute the implicit derivative and we would get that
We are told that we are looking for how fast is the radius growing at the instant when the radius has reached 1 ft, therefore 
And when we solve for
Answer:
0.252
Step-by-step explanation:
<u>0</u><u>.</u><u>2</u><u> </u> ×126
100
0.252
Answer:23%, 0.634, 3/4, 8/10
