sand is falling at the rate 27 cubic feet per minute onto a conical pile whose radius is always equal to its height. how fast is the height of the pile growing when the height is exactly (a) 3 feet (b) 6 feet (c) 9 feet.
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Answer:
Step-by-step explanation:
The formula for the volume of a cone is V = (1/3)(area of base)(height). If the radius is always equal to the height of the cone, then V = (1/3)(πh²)(h), where we have eliminated r. Shortened, this comes out to V = (1/3)(π)(h³).
We want to know how fast h is increasing when h = 3 ft.
Taking the derivative dV/dt, we get dV/dt = (1/3)π(3h²)(dh/dt), or, in simpler terms, dV/dt = πh²(dh/dt). Set this derivative = to 27 ft³/min and set h = 3 ft.
Then 27 ft³/min = π(3 ft)²(dh/dt) and solve for dh/dt: (3/π) ft/min = dh/dt when h = 3 ft.
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URGENT PLEASE HELP WILL MARK U AS BRAINLIEST!!!!!
Which mistake did Columbus make in the expedition that led him to the Americas? A. He miscalculated the size of the earth and thought he had reached Asia. B. He thought the language of the people he met was Chinese and didn't realize he was in the Americas. C. He did not bring enough supplies, so he had to stop in the Americas instead of going all the way to Asia. D. He did not realize how bad storms could be and got so far off course that he reached the Americas instead of Asia.
B. 4/3
C. 3
D. 12
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Using a proportional relationship, the constant of variation is given as follows:
C. 3
What is a proportional relationship?
A proportional relationship is a function in which the output variable is given by the input variable multiplied by a constant of proportionality, that is:
y = kx
In which k is the constant of proportionality.
If the measures are inverse proportional, the relation is:
y = k/x
A quantity h varies directly with w and inversely with p, hence the quantity h is given by:
h = kw/p
h = 2, w = 4, and p = 6, hence we can solve for the constant k.
2 = 4k/6
4k = 12
k = 3.
Hence option C is correct.
More can be learned about proportional relationships at brainly.com/question/10424180
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Answer:c
Step-by-step explanation:
Took test on edg
Mcdonalds calories 280
Jack in the box calories 250
Wendy's calories 270
Find the mean number of calories for the hamburgers.
and the median number of calories for the hamburgers
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250 cal., 270 cal., 280 cal., 280 cal., 320 cal.,
Mean =
(5 because there is a total of 5 fast food restaurants' hanburgers)
=
Mean = 280 calories
Median = The number exactly in between,
In midst of these numbers, 280 is in the mid-way
Median = 280 calories
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Answer:
Hope you find it helpful and usef
log5 + log2 =
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The sum of logs = the log of the product .
log(5) + log(2) = log(5·2) = log(10)
If these are all logs to the base 10, then log(10) = 1
log(5) + log(2) = 1
Let's try it out !
According to my calculator ...
log(5) = 0.69897...
log(2) = 0.30103...
Log(5) + log(2) = 0.99999... yay ! not bad
The solution of the equation log5 + log2 using the properties of Logarithm is log(10) or 1.
Logarithms are used to solve exponential equations by converting them into simpler forms.
A number that represents the power to which a fixed number (the base) must be increased in order to get a specific number is called as logarithm.
The property of logarithms states that:
log(a) + log(b) = log(ab).
Applying this property, we get:
log5 + log2
=
= log(10)
Logarithm base 10 (log) gives the power to which 10 must be raised to obtain the given value. So, log(10) represents the exponent required to obtain 10, which is 1.
Thus, the solution of log5 + log2 is equal to log(10) or 1.
Learn more about Logarithm here:
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Answers
♥ X in this case is representing a unknown variable, meaning we are not sure of the number x, and to finish the solution to your problem we have to find x.
♥ So to find x the first step is to simplify both sides of the equation.
♥ Starting with distribution:
♥ Now we want to flip the equation.
♥ Our next and almost final step, is to add the number -3 to both sides of our problem. This is going to help us tremendously.
♥ Now our last step before we get our answer is to divide both sides of the problem. In this case we are going to do this:
♥ And then because of that we get our final answer of: -4.
♥ x=-4 ♥