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3 years ago

A scale model of a building has a height of 18 inches and a length of 14 inches.

Mathematics

2 answers:

miss Akunina [59]3 years ago

7 0

The answer is 280.
[18/14 and 360/x use cross products.

pogonyaev3 years ago

4 0

The scale is times 20, because 360 divided by 18 equals 20, 20 times 14 = 280 when put to scale.

Your answer would be 280!

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Let f be defined by the function f(x) = 1/(x^2+9)

riadik2000 [5.3K]

(a)

$\displaystyle\int_3^\infty \frac{\mathrm dx}{x^2+9}=\lim_{b\to\infty}\int_{x=3}^{x=b}\frac{\mathrm dx}{x^2+9}$

Substitute x = 3 tan(t ) and dx = 3 sec²(t ) dt :

$\displaystyle\lim_{b\to\infty}\int_{t=\arctan(1)}^{t=\arctan\left(\frac b3\right)}\frac{3\sec^2(t)}{(3\tan(t))^2+9}\,\mathrm dt=\frac13\lim_{b\to\infty}\int_{t=\arctan(1)}^{t=\arctan\left(\frac b3\right)}\mathrm dt$

$=\displaystyle \frac13 \lim_{b\to\infty}\left(\arctan\left(\frac b3\right)-\arctan(1)\right)=\boxed{\dfrac\pi{12}}$

(b) The series

$\displaystyle \sum_{n=3}^\infty \frac1{n^2+9}$

converges by comparison to the convergent p-series,

$\displaystyle\sum_{n=3}^\infty\frac1{n^2}$

$\displaystyle \sum_{n=1}^\infty \frac{(-1)^n (n^2+9)}{e^n}$

converges absolutely, since

$\displaystyle \sum_{n=1}^\infty \left|\frac{(-1)^n (n^2+9)}{e^n}\right|=\sum_{n=1}^\infty \frac{n^2+9}{e^n} < \sum_{n=1}^\infty \frac{n^2}{e^n} < \sum_{n=1}^\infty \frac1{e^n}=\frac1{e-1}$

That is, ∑ (-1)ⁿ (n ² + 9)/eⁿ converges absolutely because ∑ |(-1)ⁿ (n ² + 9)/eⁿ| = ∑ (n ² + 9)/eⁿ in turn converges by comparison to a geometric series.

5 0

2 years ago

What is the image point of (-7,7) after a translation right 1 unit and down 3 units?

ZanzabumX [31]

Answer:

(-6, 4)

Step-by-step explanation

translation rule: (x+1,y-3)

(-7+1, 7-3)

(-6, 4)

6 0

2 years ago

A doorway is 7 1/2 feet tall. How many inches tall is the doorway?

neonofarm [45]

Answer:

6.07/212

Step-by-step explanation:

5 0

2 years ago

Read 2 more answers

What is the volume of a hemisphere with a radius of 26.7 m, rounded to the nearest tenth of a cubic meter?

attashe74 [19]

Answer:

$39,865.1m^3$

Step-by-step explanation:

a hemisphere is half a sphere.

And if the formula for the volume of a sphere is:

$V=\frac{4\pi r^3}{3}$

we must calculate the volume of the sphere and in the end divide by two to find the volume of the hemisphere.

Since the radius is:

$r=26.7m$

substituting this into the formula for volume:

$V=\frac{4\pi (26.7m)^3}{3} \\\\V=\frac{4(3.1416)(19,034.163m^3)}{3} \\\\V=79,730.12m^3$

this is the volume of the total sphere, thus the volume of a hemisphere is:

$\frac{V}{2}=\frac{79,730.12m^3}{2}\\ =39,865.06m^3$

rounding to the nearest tenth:

$39,865.1m^3$

8 0

3 years ago

Read 2 more answers

A laptop has a listed price of $843.88 before tax if the sales tax rate is 7.25% find the total cost of the laptop with sales ta

Step2247 [10]

Answer:

$905.06 dollars

Step-by-step explanation:

Given the following question:

7.25% of 843.88

In order to find the answer, we use the formula to calculate percentages, then we add that answer to the initial cost of the laptop.

$\frac{p\times c}{100}$
$\frac{7.25\times843.88}{100}=7.25\times843.88=6118.13\div100=61.1813$
$61.1813$
$1 < 5$
$61.18$

Now add:
 $843.88+61.18=905.06$
$=905.06$

Which means the laptop after a 7.25% sales tax costs "$905.06 dollars."

Hope this helps.

7 0

2 years ago