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oksian1 [2.3K]
3 years ago
8

What is the radius of a circle if its area is 120 in2? (Round your answer to the nearest hundredth of an inch)

Mathematics
1 answer:
asambeis [7]3 years ago
8 0

Answer:

6.18

Step-by-step explanation:

120/3.14, square root then round

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For the annual rate of change of +70%, find the corresponding growth or Decay Factor.
omeli [17]
Hello there!
1. Okay. So 70% is positive, so it is a corresponding growth. 70% is 0.7 in decimal form. C and D are both eliminated, because that's too large. When something grows by 70%, that is less than double. 0.7 is not right either, because that's more of a decay than a growth. The only answer that makes sense id 1.70, because you are going up, and adding 1 to decimal form brings you to the decimal that when multiplied will bring you to the total. The answer is B: 1.70.

2. So, -75% is negative, so it is a decay factor. A is eliminated, because it makes no sense and B is out, because that represents growth, not decay. You lose 75% of the amount overtime compounded, but you still have 25% that remains. To find that amount, you would subtract that amount from 1 to get the decay. 1 - 0.75 is 0.25. The decay factor is 0.25. The answer is D: 0.25.
4 0
3 years ago
Mohamed and Li Jing were asked to find an explicit formula for the sequence -5, -25, -125, -625,....
Nuetrik [128]

Answer:

Li Jing's formula i.e.  \boxed{g_n=-5\cdot \:5^{n-1}}  is right.

Step-by-step explanation:

Considering the sequence

-5,\:-25,\:-125,\:-625,...

A geometric sequence has a constant ratio r and is defined by

g_n=g_0\cdot r^{n-1}

\mathrm{Compute\:the\:ratios\:of\:all\:the\:adjacent\:terms}:\quad \:r=\frac{g_{n+1}}{g_n}

\frac{-25}{-5}=5,\:\quad \frac{-125}{-25}=5,\:\quad \frac{-625}{-125}=5

\mathrm{The\:ratio\:of\:all\:the\:adjacent\:terms\:is\:the\:same\:and\:equal\:to}

r=5

So, the sequence is geometric.

as

\mathrm{The\:first\:element\:of\:the\:sequence\:is}

g_1=-5

r=5

so

g_n=g_1\cdot r^{n-1}

\mathrm{Therefore,\:the\:}n\mathrm{th\:term\:is\:computed\:by}\:

g_n=-5\cdot \:5^{n-1}

Therefore, Li Jing's formula i.e.  \boxed{g_n=-5\cdot \:5^{n-1}}  is right.

8 0
3 years ago
The radius of the base of a cylinder is decreasing at a rate of 121212 kilometers per second. The height of the cylinder is fixe
WARRIOR [948]

Answer:

7536 km^3/sec

Step-by-step explanation:

Given that:

Rate of decreasing of radius = 12 km/sec

Height of cylinder is fixed at = 2.5 km

Radius of cylinder = 40 km

To find:

The rate of change of Volume of the cylinder?

Solution:

First of all, let us have a look at the formula for volume of a cylinder.

Volume = \pi r^2h

Where r is the radius and

h is the height of cylinder.

As per question statement:

r = 40 km (variable)

h = 2.5 (constant)

\dfrac{dV}{dt} = \dfrac{d}{dt}\pi r^2h

As \pi, h are constant:

\dfrac{dV}{dt} = \pi h\dfrac{d}{dt} r^2\\\Rightarrow \dfrac{dV}{dt} = \pi h\times 2 r\dfrac{dr}{dt} \\$Putting the values:$\\\Rigghtarrow\dfrac{dV}{dt} = 3.14 \times 2.5\times 2 \times 40\times 12 \\\Rigghtarrow\dfrac{dV}{dt} = 7536\ km^3/sec

4 0
2 years ago
Sally purchased a Pokemon game for $10.50, and a racing game for $6.50 with a $20 bill. How much change did Sally get?
pantera1 [17]

Answer:

$3

Step-by-step explanation:

1. Add the total of the price. 10.50+6.50=17 The total of the items cost $17.

2. Subtract the cost from the amount you are paying. 20-17=3 Sally gets $3 of change.

7 0
3 years ago
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2 years ago
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