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White raven [17]
3 years ago
12

A rectangular prism has a length of 1/1/4 yards, a width of 2/1/2 yards, and a height of 4 yards. Enter the volume of the prism

as a mixed number in simplest form in the box. yd³
Mathematics
1 answer:
dmitriy555 [2]3 years ago
7 0
Prism volume = lbh

= 10*8*12

= 960cm^3

Note: I'm assuming the hole was cut right through it...

Hole volume = lbh

= 2*3*12

= 72cm^3

Final volume = 960 - 72 = 888cm^3
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Nikolay [14]

Replace x with π/2 - x to get the equivalent integral

\displaystyle \int_{-\frac\pi2}^{\frac\pi2} \cos(\cot(x) - \tan(x)) \, dx

but the integrand is even, so this is really just

\displaystyle 2 \int_0^{\frac\pi2} \cos(\cot(x) - \tan(x)) \, dx

Substitute x = 1/2 arccot(u/2), which transforms the integral to

\displaystyle 2 \int_{-\infty}^\infty \frac{\cos(u)}{u^2+4} \, du

There are lots of ways to compute this. What I did was to consider the complex contour integral

\displaystyle \int_\gamma \frac{e^{iz}}{z^2+4} \, dz

where γ is a semicircle in the complex plane with its diameter joining (-R, 0) and (R, 0) on the real axis. A bound for the integral over the arc of the circle is estimated to be

\displaystyle \left|\int_{z=Re^{i0}}^{z=Re^{i\pi}} f(z) \, dz\right| \le \frac{\pi R}{|R^2-4|}

which vanishes as R goes to ∞. Then by the residue theorem, we have in the limit

\displaystyle \int_{-\infty}^\infty \frac{\cos(x)}{x^2+4} \, dx = 2\pi i {} \mathrm{Res}\left(\frac{e^{iz}}{z^2+4},z=2i\right) = \frac\pi{2e^2}

and it follows that

\displaystyle \int_0^\pi \cos(\cot(x)-\tan(x)) \, dx = \boxed{\frac\pi{e^2}}

7 0
2 years ago
5/8 divided by 1 1/3 in lowest form
Shtirlitz [24]

<em>HOPE</em><em> </em><em>THIS</em><em> </em><em>WILL</em><em> </em><em>HELP</em><em> </em><em>U</em><em>.</em><em>.</em><em>.</em>

6 0
3 years ago
Read 2 more answers
Please answer my question!
Salsk061 [2.6K]

D is not a terminating decimal because it repeats *hint the dash mark above the 4*

6 0
3 years ago
1.13 Thank you! (Sorry it’s so blurry)
VikaD [51]
\sqrt[8]{48^4}  can be rewritten as 48^4 to the \frac{1}{8}  power:

(48^4)^ \frac{1}{8}

Now, applying exponent rules (multiply exponent inside parentheses by the one outside parentheses), we get:

(48^ \frac{1}{2})

This is equivalent to \sqrt{48}, so now, we just simplify:

\sqrt{48}=  \sqrt{16*3}= \sqrt{16}* \sqrt{3}=4 \sqrt{3}

So:

\sqrt[8]{48^4} =4 \sqrt{3} 


4 0
3 years ago
Carissa and Louann both have savings accounts. Carissa has $250 in her account and deposits $80 per month. Louann has $1230 in h
zlopas [31]
Carissa value after x months=current+amount deposited
louan value after x months=current-amount taken out

carissa depositied=amount per month times x months=80x
louan take out=amount per month tiems x months=60x

when wil amount be equal
se equal

cariss=lousa
250+80x=1230-60x
add 60x both sides
250+140x=1230
minus 250 both sides
140x=980
divide both sides by 140
x=7

find how much that is
250+80(7)=250+560=810


7 months both have $810
8 0
3 years ago
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