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sweet-ann [11.9K]
3 years ago
12

I am multiple of 20 i have 3 digits my hundreds digit and tens digit add to make 9 half of me is less than 100 what am i

Mathematics
1 answer:
ASHA 777 [7]3 years ago
4 0

Answer:

180

Step-by-step explanation:

Given :

the number has three digits

it is multiple of 20

hundreds digit and tens digit add to make 9

half of it is less than 100.

I suppose 180 can correctly fit into all above criterions

It is 3 digit number. 1+8 =9, 180/2 =90 which is less than 100.

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The area enclosed by the graphs of y = 1/x, y = 1, and x = 3 is rotated about the line y = -1. Find the volume and show steps.
Natalija [7]

Answer:

A=\pi\displaystyle\biggr[\frac{16}{3}-2\ln(|3|)\biggr]\approx9.8524

Step-by-step explanation:

Use the Washer Method A=\pi\displaystyle \int\limits_{a}^{b}{\bigr[R(x)^2-r(x)^2\bigr] \, dx where R(x) is the outer radius and r(x) is the inner radius.

If we sketch out the graph, we see that y=1 intersects points (1,1) and (3,1), which will be our bounds of integration.

Here, our outer radius will be R(x)=(-1-1)=-2 and our inner radius will be r(x)=-1-\frac{1}{x}.

Thus, we can compute the integral and find the volume:

A=\pi\displaystyle\int\limits^{3}_{1} {(-2)^2-\biggr(-1-\frac{1}{x}\biggr)^2 } \, dx\\ \\A=\pi\displaystyle\int\limits^{3}_{1} {4-\biggr(1+\frac{2}{x}+\frac{1}{x^2}  \biggr) } \, dx\\\\A=\pi\displaystyle\int\limits^{3}_{1} {4-1-\frac{2}{x}-\frac{1}{x^2}} \, dx\\\\A=\pi\displaystyle\int\limits^{3}_{1} {3-\frac{2}{x}-\frac{1}{x^2}} \, dx\\\\A=\pi\displaystyle\biggr[3x-2\ln(|x|)+\frac{1}{x}\biggr]\Biggr|_{1}^{3}\\

A=\pi\displaystyle\biggr[\biggr(3(3)-2\ln(|3|)+\frac{1}{3}\biggr)-\biggr(3(1)-2\ln(|1|)+\frac{1}{1}\biggr)\biggr]\\\\A=\pi\displaystyle\biggr[\biggr(9-2\ln(|3|)+\frac{1}{3}\biggr)-\biggr(3+1\biggr)\biggr]\\\\A=\pi\displaystyle\biggr[\biggr(\frac{28}{3}-2\ln(|3|)\biggr)-\biggr(4\biggr)\biggr]\\A=\pi\displaystyle\biggr[\frac{16}{3}-2\ln(|3|)\biggr]\\A\approx9.8524

In conclusion, the volume of the solid of revolution will be about 9.8524 cubic units. See the attached graph for a helpful visual!

3 0
2 years ago
A researcher is interested in estimating the mean weight of a semi trailer truck to determine the potential load capacity. She t
Kaylis [27]

Answer: 95% confidence interval = 20,000 ± 2.12\times\frac{1500}{\sqrt{17} }

( 19228.736 , 20771.263 ) OR ( 19229 , 20771 )

Step-by-step explanation:

Given :

Sample size(n) = 17

Sample mean = 20000

Sample standard deviation = 1,500

5% confidence

∴ \frac{\alpha}{2} = 0.025

Degree of freedom (d_{f}) = n-1 = 16

∵ Critical value at ( 0.025 , 16 ) = 2.12

∴ 95% confidence interval = mean ± Z_{c}\times\frac{\sigma}{\sqrt{n} }

Critical value  at 95% confidence interval = 20,000 ± 2.12\times\frac{1500}{\sqrt{17} }

( 19228.736 , 20771.263 ) OR ( 19229 , 20771 )

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3 years ago
5. Bill is planning to paint the back of his house. If the paint costs $2 a square
USPshnik [31]

Answer:

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Step-by-step explanation:

8 0
3 years ago
X+y=-2 7x-4y=8 graph
Novay_Z [31]

Answer:

x+y=-2

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Step-by-step explanation:

3 0
3 years ago
Mario walked 7422 steps one day then he walks 5570 stops the next day. which calculation can be used to find the total number of
vovikov84 [41]

Answer:

A caucluation he can use is adding, just add 7422 and  5570 and you should get your answer.

Step-by-step explanation:

4 0
3 years ago
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