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Harlamova29_29 [7]
4 years ago
13

What is the difference between the permutations rule and the combinations​ rule? Choose the correct answer below. A. The permuta

tions rule takes order into​ account, whereas the combinations rule does not. B. The permutations rule takes replacement into​ account, whereas the combinations rule does not. C. The combinations rule takes replacement into​ account, whereas the permutations rule does not. D. The combinations rule takes order into​ account, whereas the permutations rule does not.
Mathematics
1 answer:
fgiga [73]4 years ago
7 0

Answer:

A. The permutations rule takes order into​ account, whereas the combinations rule does not.

Step-by-step explanation:

Permutation is an orderly form of combination. They both deal with numbers an element can be arranged in different ways.

The main difference is that permutation takes into account the order in which the arrangement takes place while combination doesn’t take that into account.

Combination formula: nCr = n! / r! * (n - r)!

Permutation formula: P(n,r)=n! (n−r)!

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the volume of a cone of radius r and height h is given by v=1/3pir^2h. If the radius and height is both increasing at a constant
Tamiku [17]

Answer:

The rate of change of the volume \frac{dV}{dt} when the height is 9 centimeters and the radius is 6 centimeters is 24\pi \:\frac{cm^3}{s}

Step-by-step explanation:

This is a related rate problem because you know a rate and want to find another rate that is related to it. If 2 variables both vary with respect to time and have a relation between them, we can express the rate of change of one in terms of the other.

From the information given we know:

  • \frac{dr}{dt}=\frac{1}{2}\:\frac{cm}{s}
  • \frac{dh}{dt}=\frac{1}{2}\:\frac{cm}{s}
  • The volume of a cone of radius r and height h is given by V=\frac{1}{3} \pi r^2 h

We want to find the rate of change of the volume \frac{dV}{dt} when the height is 9 centimeters and the radius is 6 centimeters.

Applying implicit differentiation to the formula of the volume of a cone we get

\frac{dV}{dt}=\frac{1}{3}\pi [r^2\frac{dh}{dt}+2rh\frac{dr}{dt} ]

Substituting the values we know into the above formula:

\frac{dV}{dt}=\frac{1}{3}\pi [(6)^2\frac{1}{2}+2(6)(9)\frac{1}{2} ]\\\\\frac{dV}{dt}=\frac{1}{3}\pi[18+54]\\\\\frac{dV}{dt}=\frac{72\pi}{3}=24\pi \:\frac{cm^3}{s}

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4 years ago
The volume of a cone can e calculated using the formula V=1/3*3.14*r^2*h. Which expression can e used to represent the height,h?
otez555 [7]
Just make the height the subject of the equation, by dividing the volume by everything else.

V / ((1/3) * <span>π</span> * r²) = h

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