2x(27x+5) Evaluate this please

(4) A spherical balloon is being inflated so that its diameter is increasing at a constant rate of 6 cm/min. How quickly is the

fredd [130]

In terms of its radius $r$ , the volume of the balloon is

$V(r)=\dfrac{4\pi}3r^3$

The diameter $d$ is twice the radius, so that in terms of its diameters, the balloon's volume is given by

$V(d)=\dfrac{4\pi}3\left(\dfrac d2\right)^3=\dfrac\pi6d^3$

Differentiate both sides with respect to time $t$ :

$\dfrac{\mathrm dV}{\mathrm dt}=\dfrac\pi2d^2\dfrac{\mathrm dd}{\mathrm dt}$

The diameter increases at a rate of $\frac{\mathrm dd}{\mathrm dt}=6\frac{\rm cm}{\rm min}$ . When the diameter is $d=50\,\mathrm{cm}$ , we have

$\dfrac{\mathrm dV}{\mathrm dt}=\dfrac\pi2(50\,\mathrm{cm})^2\left(6\frac{\rm cm}{\rm min}\right)=7500\pi\dfrac{\mathrm{cm}^3}{\rm min}$

or about 23,562 cc/min (where cc = cubic centimeters)

5 0

3 years ago

Hey! i’ll give brainliest please help

balu736 [363]

Answer:A!

Step-by-step explanation:

8 0

2 years ago

Read 2 more answers

QuizBIGPOINT

lianna [129]

The number of permutations of the problem is

This = 24
Outfit = 360

<h2>Combination</h2>

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Combinations are the number of ways to choose members from a certain number, namely from members of a set, combinations can also be interpreted as many ways to make subsets, namely with a certain number of members, namely from members of a set, if a set has n members then the selection of r members, and the combination of n is where r is less than n.

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<h3>The Formula : </h3>

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<h2>Permutation</h2>

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Permutations are a way to determine the number of arrangements that occur by paying attention to the order. So in permutations, position/order is very important, namely AB is considered different from BA (AB ≠ BA). Permutation formula

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<h3>The Formula :</h3>

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$\frac {n!}{k!}$ (With Double Elements)

n! (Without Double Elements)

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<h2>Factorial</h2>

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The factorial of a natural number is the successive multiplication of a natural number that begins with the number one and arrives at the natural number, the factorial is used in calculating combinations, probabilities, and permutations.

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<h3>For example</h3>

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》2! = 1 × 2
》3! = 1 x 2 x 3
》4! = 1 x 2 x 3 x 4
》5! = 1 x 2 x 3 x 4 x 5
》6! = 1 × 2 × 3 × 4 × 5 × 6
》7! = 1 × 2 × 3 × 4 × 5 × 6 × 7
》8! = 1 × 2 × 3 × 4 × 5 × 6 × 7 × 8
》9! = 1 × 2 × 3 × 4 × 5 × 6 × 7 × 8 × 9
》10! = 1 × 2 × 3 × 4 × 5 × 6 × 7 × 8 × 9 × 10

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The following is an example of a factorial that does not involve mixed arithmetic operations, so if you want to add it up we just need to calculate it like a normal number, a factorial number that only multiplies the difference between a factorial number that is added up by addition, subtraction, multiplication, division, for example see below.

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6! x2! - 3! : 4!

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The example above is a mixed arithmetic operation that contains multiplication, subtraction, and division. Remember that in mixed arithmetic operations, multiplication/division must be completed before addition/subtraction.

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<h3>The Formula : </h3>

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n! (Combined Multiplication)

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<h2>Place Filling Rules</h2>

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The Place Fill Rule is a method or method that can be used to determine the number of ways an object occupies its place. The filling slots rule is a method of calculating how many possible ways there are in an experiment or event. If a first event can be done in m different ways and the second event can be done in a different way and so on until the last event in k.

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<h3>The formula</h3>

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n1 × n2 × n3 × ... × nr

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<h2><u>Question</u></h2>

Find the number of permutations of letters of the word

- this

- outfit

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<h2><u>Answer</u></h2>

"Number One"