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kaheart [24]
1 year ago
11

A triangular prism is shown. A cylinder is cut out of the center of the prism. The triangular base has side lengths of 14 and 10

units. The heights of both the cylinder and prism are 8 units. The cylinder has a diameter of 5 units. Which expression represents the volume, in cubic units, of the shaded region of the composite figure?
Mathematics
2 answers:
Anuta_ua [19.1K]1 year ago
8 0

Answer:

Step-by-step explanation:

bogdanovich [222]1 year ago
8 0

Answer:

One-half(14)(10)(8) – π(2.52)(8)

Step-by-step explanation:

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Isabella saved 2 nickels today. If she doubles the number of nickels she saves each day, how many days, including today, will it
luda_lava [24]

Answer:

Step-by-step explanation:

Alright, lets gets started.

First day, she saves nickels = 2

As we know, she doubles the number of nickels she saves each day.

Means second day she saves nickels = 2*2 = 4

Third day she saves nickels = 2*4 = 8

Fourth day she saves nickels = 2*8=16

Hence we have 2 + 4 + 8 + 16...

It is like a geometric series, the sum of nickels she needs more than 500.

So, lets see how many days she will take to save 500 nickels first

Using the sum formula for geometric series

s=\frac{a(1-r^n)}{(1-r)}

where s is sum, r is multiplication factor, that is 2 in this case and a is first term of series that is 2 also

500=\frac{2(1-2^n)}{(1-2)}

Simplifying, dividing 2 in both sides

250=\frac{(1-2^n)}{(1-2)}

250=\frac{(1-2^n)}{-1}

Cross multiplying

-250=1-2^n

2^n-1=250

2^n=251

Taking log on both sides

nlog2=log251

n=\frac{log251}{log2}=7.971

It means it will take 8 days to save mmore than 500 nickels.   :  Answer

Hope it will help :)


8 0
2 years ago
A tennis coach divides her 9-player squad into three 3-player groups with each player in only one group. How many different sets
Lostsunrise [7]

Answer:

3

Step-by-step explanation:

The coach divides her 9-player squad into 3-player groups. This means that she has 9 players and she wants to share them into 3s.

The number sets of three groups she will have can be obtained by dividing the total number of her players by the 3. That is:

9 / 3 = 3 sets

Therefore, she will have 3 sets of 3-player groups.

7 0
2 years ago
The results of a survey show that the percent of adults in a certain town who want to change the name of the town is in the inte
Paha777 [63]
A) about 39.5%
b) +/ - 1.5%
c) I'd say no. It is very unlikely because less than the majority wanted it changed
7 0
1 year ago
Read 2 more answers
Expand the given power using the Binomial Theorem. (z – 11)4
nekit [7.7K]

Answer:

(z-11)^{4}=z^{4}-44z^{3}+726z^{2}-5324z+14641

Step-by-step explanation:

* Look to the attached file

Download docx
4 0
1 year ago
Read 2 more answers
Find the volume V of the solid obtained by rotating the region bounded by the given curves about the specified line. y = 1 + sec
masha68 [24]

Using the washer method, the volume is given by the integral

\displaystyle\pi\int_{-\pi/3}^{\pi/3}\bigg((3-1)^2-((1+\sec x)-1)^2\bigg)\,\mathrm dx=2\pi\int_0^{\pi/3}(4-\sec^2x)\,\mathrm dx

where 3 - 1 = 2 is the distance from <em>y</em> = 3 to the axis of revolution, and similarly (1 + sec(<em>x</em>)) - 1 = sec(<em>x</em>) is the distance from <em>y</em> = 1 + sec(<em>x</em>) to the axis. The integrand is symmetric about <em>x</em> = 0, so the integral "folds" in on itself, and the integral from -π/3 to π/3 is twice the integral from 0 to π/3.

So the volume is

\displaystyle2\pi\int_0^{\pi/3}(4-\sec^2x)\,\mathrm dx=2\pi(4x-\tan x)\bigg|_0^{\pi/3}=\boxed{\dfrac{8\pi^2}3-2\pi\sqrt3}

4 0
2 years ago
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