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vlabodo [156]
2 years ago
12

A cheese processing plant keeps the heavy cream for their product in a silo with a dome top. The silo has an overall diameter of

25. The height of the cylinder part is 31 feet tall. What is the volume of the silo as a whole? Round your answer to the nearest hundredth, if necessary. Use 3.14 for pi.​
Mathematics
1 answer:
Leya [2.2K]2 years ago
8 0
V = 3.14(r^2)h
V = 3.14(12.5^2)(31)
V = 15209.38
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What is the solution to <img src="https://tex.z-dn.net/?f=-12%5Cgeq%20x-4" id="TexFormula1" title="-12\geq x-4" alt="-12\geq x-4
Murljashka [212]
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4 0
2 years ago
All in standard Notation please :/ 2.09 x 10^5
Assoli18 [71]

9514 1404 393

Answer:

  • 209,000
  • 94,387
  • 0.0013

Step-by-step explanation:

Write the power of ten in standard form and do the multiplication.

  2.09 × 10^5 = 2.09 × 100,000 = 209,000

  9.4387 × 10^4 = 9.4387 × 10,000 = 94,387

  1.3 × 10^-3 = 1.3 × 0.001 = 0.0013

5 0
3 years ago
For <img src="https://tex.z-dn.net/?f=e%5E%7B-x%5E2%2F2%7D" id="TexFormula1" title="e^{-x^2/2}" alt="e^{-x^2/2}" align="absmiddl
nevsk [136]
I'm assuming you're talking about the indefinite integral

\displaystyle\int e^{-x^2/2}\,\mathrm dx

and that your question is whether the substitution u=\dfrac x{\sqrt2} would work. Well, let's check it out:

u=\dfrac x{\sqrt2}\implies\mathrm du=\dfrac{\mathrm dx}{\sqrt2}
\implies\displaystyle\int e^{-x^2/2}\,\mathrm dx=\sqrt2\int e^{-(\sqrt2\,u)^2/2}\,\mathrm du
=\displaystyle\sqrt2\int e^{-u^2}\,\mathrm du

which essentially brings us to back to where we started. (The substitution only served to remove the scale factor in the exponent.)

What if we tried u=\sqrt t next? Then \mathrm du=\dfrac{\mathrm dt}{2\sqrt t}, giving

=\displaystyle\frac1{\sqrt2}\int \frac{e^{-(\sqrt t)^2}}{\sqrt t}\,\mathrm dt=\frac1{\sqrt2}\int\frac{e^{-t}}{\sqrt t}\,\mathrm dt

Next you may be tempted to try to integrate this by parts, but that will get you nowhere.

So how to deal with this integral? The answer lies in what's called the "error function" defined as

\mathrm{erf}(x)=\displaystyle\frac2{\sqrt\pi}\int_0^xe^{-t^2}\,\mathrm dt

By the fundamental theorem of calculus, taking the derivative of both sides yields

\dfrac{\mathrm d}{\mathrm dx}\mathrm{erf}(x)=\dfrac2{\sqrt\pi}e^{-x^2}

and so the antiderivative would be

\displaystyle\int e^{-x^2/2}\,\mathrm dx=\sqrt{\frac\pi2}\mathrm{erf}\left(\frac x{\sqrt2}\right)

The takeaway here is that a new function (i.e. not some combination of simpler functions like regular exponential, logarithmic, periodic, or polynomial functions) is needed to capture the antiderivative.
3 0
3 years ago
Which shape is both a parallelogoram and a rhombus
Morgarella [4.7K]

Answer:

A square can be defined as a rhombus which is also a rectangle and a parellelogram with four congruent sides and four right angles

I hope this helps

3 0
3 years ago
Find the seventh term of the following sequence 2,6,18, and 54
enot [183]
This is a geometric sequence since there is a common ratio between each term. In this case, multiplying the previous term in the sequence by <span>33</span> gives the next term. In other words, <span><span><span>an</span>=<span>a1</span>⋅<span>r<span>n−1</span></span></span><span><span>an</span>=<span>a1</span>⋅<span>r<span>n-1</span></span></span></span><span>.</span>
8 0
3 years ago
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