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3 years ago

The lateral area of a cone is 4.8 pi in squared and the radius is 1.2 in. Find the slant height

Mathematics

1 answer:

katrin2010 [14]3 years ago

4 0

Lateral Area = pi*r*L

4.8pi = pi*1.2*L

L = 4.8 / 1.2 = 4 in.

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Is 0.09 squared a rational number?

Novay_Z [31]

Yes, 0.09 squared, or 0.0081, is a rational number.

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3 years ago

What heat transfer is Christmas lights radiation or convention or conduction

Firdavs [7]

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The heat from the sun or heat released from the filament of a light bulb is the example of radiation.

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2 years ago

Read 2 more answers

Find the interval of convergence of the power series. (Be sure to include a check for convergence at the endpoints of the interv

sleet_krkn [62]

Answer:

(0, 16]

Step-by-step explanation:

∑ₙ₌₁°° (-1)ⁿ⁺¹ (x−8)ⁿ / (n 8ⁿ)

According to the ratio test, if we define L such that:

L = lim(n→∞) |aₙ₊₁ / aₙ|

then the series will converge if L < 1.

aₙ = (-1)ⁿ⁺¹ (x−8)ⁿ / (n 8ⁿ)

aₙ₊₁ = (-1)ⁿ⁺² (x−8)ⁿ⁺¹ / ((n+1) 8ⁿ⁺¹)

Plugging into the ratio test:

L = lim(n→∞) | (-1)ⁿ⁺² (x−8)ⁿ⁺¹ / ((n+1) 8ⁿ⁺¹) × n 8ⁿ / ((-1)ⁿ⁺¹ (x−8)ⁿ) |

L = lim(n→∞) | -n (x−8) / (8 (n+1)) |

L = (|x−8| / 8) lim(n→∞) | n / (n+1) |

L = |x−8| / 8

For the series to converge:

L < 1

|x−8| / 8 < 1

|x−8| < 8

-8 < x−8 < 8

0 < x < 16

Now we check the endpoints. If x = 0:

∑ₙ₌₁°° (-1)ⁿ⁺¹ (0−8)ⁿ / (n 8ⁿ)

∑ₙ₌₁°° -(-1)ⁿ (-8)ⁿ / (n 8ⁿ)

∑ₙ₌₁°° -(8)ⁿ / (n 8ⁿ)

∑ₙ₌₁°° -1 / n

This is a harmonic series, and diverges.

If x = 16:

∑ₙ₌₁°° (-1)ⁿ⁺¹ (16−8)ⁿ / (n 8ⁿ)

∑ₙ₌₁°° (-1)ⁿ⁺¹ (8)ⁿ / (n 8ⁿ)

∑ₙ₌₁°° (-1)ⁿ⁺¹ / n

This is an alternating series, and converges.

Therefore, the interval of convergence is:

0 < x ≤ 16

Or, in interval notation, (0, 16].

4 0

3 years ago

Marti had of a pizza remaining after

o-na [289]

I think it is 1/2
hope this helped

8 0

3 years ago

6. Protein bars come in a 4-pack box or 12-pack

cricket20 [7]

Answer:

The 12 pack has a better value.

Step-by-step explanation:

1. create a ratio table.

you want to know how much the 4 pack would cost if it was a 12 pack.

you can see the ratio table in the picture above.

As you can see, when the 4 pack equals $7.68, making it a 12 pack will equal $23.04.

Then, compare 23.04 to 22.32.

In conclusion, the 12 pack has a better value.

5 0

3 years ago