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faust18 [17]
4 years ago
9

A spherical balloon is inflated with a gas at the rate of 500 cm3/min. How fast is the radius of the balloon increasing at the i

nstant the radius is 30 cm? A. 5/(36pi)cm/min
B. 2/(18pi)cm/min
C. 4/(9pi)cm/min
D. 7/(24pi)cm/min
Mathematics
1 answer:
Burka [1]4 years ago
7 0

The volume of the sphere is expressed in the formula V = 4/3 pi r^3. The rate of change of volume is determined by differentiating the formula: dV/dt = 4pi r^2 dr/dt. When we substitute 500 cm3/min as dV/dt and 30 cm as r. Then dr/dt is equal to 0.0442 cm/min
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Multiply.
Crank
The main rules that we use here are :

i) \sqrt{a \cdot b}=  \sqrt{a} \cdot \sqrt{b} for nonnegative values a and b.

ii) \sqrt{a} \cdot  \sqrt{a} =a.


Thus, first 'decompose' the numbers in the radicals into prime factors:

4 \sqrt{3} \cdot 10 \cdot  \sqrt{2\cdot2\cdot3}\cdot  \sqrt{2\cdot 3}\cdot  \sqrt{2}..

By rule (i) we write:

4 \sqrt{3} \cdot 10 \cdot \sqrt{2}\cdot \sqrt{2}\cdot \sqrt{\cdot3}\cdot \sqrt{2} \cdot  \sqrt{3} \cdot \sqrt{2}.

We can collect these terms as follows:

40 \sqrt{3}\cdot (\sqrt{3}\cdot \sqrt{3}) \cdot (\sqrt{2}\cdot \sqrt{2}) \cdot( \sqrt{2} \cdot \sqrt{2}), and by rule (ii) we have:

40 \sqrt{3}\cdot 3 \cdot 2 \cdot2=40\cdot12\cdot \sqrt{3}=480 \sqrt{3}.


Answer: 480 \sqrt{3}.
8 0
4 years ago
A box contains 3 coins. One coin has 2 heads and the other two are fair. A coin is chosen at random from the box and flipped. If
Blababa [14]

Answer: Our required probability is \dfrac{1}{2}

Step-by-step explanation:

Since we have given that

Number of coins = 3

Number of coin has 2 heads = 1

Number of fair coins = 2

Probability of getting one of the coin among 3 = \dfrac{1}{3}

So, Probability of getting head from fair coin = \dfrac{1}{2}

Probability of getting head from baised coin = 1

Using "Bayes theorem" we will find the probability that it is the two headed coin is given by

\dfrac{\dfrac{1}{3}\times 1}{\dfrac{1}{3}\times \dfrac{1}{2}+\dfrac{1}{3}\times \dfrac{1}{2}+\dfrac{1}{3}\times 1}\\\\=\dfrac{\dfrac{1}{3}}{\dfrac{1}{6}+\dfrac{1}{6}+\dfrac{1}{3}}\\\\=\dfrac{\dfrac{1}{3}}{\dfrac{2}{3}}\\\\=\dfrac{1}{2}

Hence, our required probability is \dfrac{1}{2}

No, the answer is not \dfrac{1}{3}

5 0
3 years ago
What is the common ratio for this sequence? 40, 36, 32.4, 29.16 A) 1.1 B) 0.5 C) 2.2 D) 0.9​
Elena L [17]
Hope this might help u

8 0
3 years ago
Read 2 more answers
An instrument maker creates a triangle in the shape of an isosceles triangle by bending a metal rod. the rod is 13 inches long,
Gre4nikov [31]

The length of the longest slide is 5 inches. he other two sides will be 4  inches in length.

<h3>Length of the longest slide</h3>

Isosceles triangle

Given:

Total length=13 inches

Hence:

AC=BC<AB

Let AC=BC=x-1 inches

AB=x inches

Thus:

x-1+(x-1)+x=13

3x-2=13

3x=13+2

3x=15

divide both side by 3x

x=15/3

x=5 inches

Hence:

Other two side

x-1=5-1=4 inches

Therefore the length of the longest slide is 5 inches. he other two sides will be 4  inches in length.

Learn more about Length of the longest slide here:brainly.com/question/7807143

#SPJ1

8 0
2 years ago
43<br> Pwiehejejekkalwkfhd
ehidna [41]

Answer:

137°

Step-by-step explanation:

If we know that a set of angles form one of these special relationships, we can determine the measure of the other angle. To determine the supplement, subtract the given angle from 180. 180 - 43 = 137° The supplement of 43° is 137°.

8 0
3 years ago
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