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NemiM [27]
3 years ago
14

The function describes the volume of a right circular cylinder of height 3 ft and radius r feet. find the instantaneous rate of

change of the voume with respect to the radius when r = 5
Mathematics
1 answer:
xxMikexx [17]3 years ago
8 0
The volume of a right circular cone is calculated through the equation,

                  V = πr²h

where V is volume, r is radius of the base, and h is height. Given that height is 3 ft, this can be simplied into,
 
                V = 3πr²

The rate of change with respect to r is,
                dV/dr = 6πr

Substituting the DALE,

                dV/dr = (6)π(2 m)² = 24π

Answer: 24π. 
You might be interested in
A regular octagon has side lengths of 9 units. Each side of the octagon is
nirvana33 [79]

Answer:

The perimeter of the original octagon is:

  • <u>72 units. </u>

The perimeter of the new octagon is:

  • <u>288 units.</u>

Step-by-step explanation:

When it is mentioned that an octagon is regular, it means that all its sides are equal, therefore, each side of the original octagon has a length of 9 units, considering the formula of the octagon's perimeter:

  • Perimeter of an octagon = 8 * length.

By replacing you get:

  • Perimeter of the original octagon = 8 * 9 = 72 units.

For the new octagon, it is mentioned that each side increases by 27 units, therefore:

  • New length = 27 + 9 = 36 units.

Applying the formula of perimeter of an octagon with the new values we obtain:

  • <u>Perimeter of the new octagon = 8 * 36 = 288 units.</u>
3 0
3 years ago
1)Simplify: 4d - 3e - 9d + 8e
Evgesh-ka [11]
Combine like terms:

-5d+5e or 5e-5d

If you want, you can factor out the common 5:

5(e-d) is your answer
5 0
2 years ago
What's 3,897.003 in expanded form.
Art [367]
3,897.003 in expanded form is:

3,000 + 800 + 90 + 7 + 0.003
3 0
3 years ago
3. Consider the functions f(x) = x2 + 10x – 5, g(x) = 8x + 1, and h(x) = 3x – 4. List the functions from least to greatest value
weeeeeb [17]
<u>x = 3</u>
f(x) = x²+ 10x - 5
f(3) = (3)² + 10(3) - 5
f(3) = 9 + 30 - 5
f(3) = 39 - 5
f(3) = 34

g(x) = 8x + 1
g(3) = 8(3) + 1
g(3) = 25

h(x) = 3x - 4
h(3) = 3(3) - 4
h(3) = 9 - 4
h(3) = 5

<u>x = 6
</u>f(x) = x² + 10x - 5
f(6) = (6)² + 10(6) - 5
f(6) = 36 + 60 - 5
f(6) = 96 - 5
f(6) = 91

g(x) = 8x + 1
g(6) = 8(6) + 1
g(6) = 48 + 1
g(6) = 49

h(x) = 3x - 4
h(6) = 3(6) - 4
h(6) = 18 - 4
h(6) = 14

I would explain to someone that you don't need to do any calculations to know the order of the functions when x is equal to 15 by knowing that f(x) is equal to 370, g(x) is equal to 121, and h(x) is equal to 41 to know that it is easy finding the function of x without calculating the answer.
4 0
3 years ago
We have 10 gallons of gas in the car. We use 1 5/8 gallons each hour. How many hours of gas do we have?
Sindrei [870]
You have a little over 6 hours of gas.
8 0
2 years ago
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