The volume of the trough is V(w) = w³ + 20w² - 429w and the rate of change of the volume over a width of 38 inches to 53 inches is 4695 in³/in
<h3>What is an
equation?</h3>
An equation is an expression that shows the relationship between two or more variables and numbers.
Let w represent the width, hence:
length = w + 33, height = w - 13
Volume (V) = w(w + 33)(w - 13) = w³ + 20w² - 429w
V(w) = w³ + 20w² - 429w
Rate of change = dV/dw = 3w² + 40w - 429
When w = 38, dV/dw = 3(38)² + 40(38) - 429 = 5423
When w = 53, dV/dw = 3(53)² + 40(53) - 429 = 10118
Rate = 10118 - 5423 = 4695 in³/in
The volume of the trough is V(w) = w³ + 20w² - 429w and the rate of change of the volume over a width of 38 inches to 53 inches is 4695 in³/in
Find out more on equation at: brainly.com/question/2972832
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For the line y=4x+5 the parent function is y=x
Answer: 0
Explanation: 2(x+1) *distribute 2 to x and 1
2x+2=2x+2 *now subtract 2x+2 to the other side
Answer:
a)
b)
c)
d)
Step-by-step explanation:
Let X the random variable of interest and we know that the distribution is given by:
And for this problem we can use the cumulative distribution function in order to solve the items:
Part a
We want to find this probability:
Part b
Part c
And we can calculate the probability with this difference:
Part d
Since we have a continuous distribution the the probability for an unique value would be:
9514 1404 393
Answer:
43.2 grams
Step-by-step explanation:
The exponential equation for the decay can be written as ...
amount remaining = (initial amount)(1 -decay rate)^t
= 570(1 -0.18)^t
We want to find the amount remaining after 13 minutes. Evaluating this equation for t=13, we have ...
amount remaining = 570(0.82^13) ≈ 43.2 . . . grams