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mel-nik [20]
3 years ago
15

Alex has a block of wood that is in the shape of a prism with the dimensions shown. He cuts a 10-cm square hole through the cent

er of the prism. What is the volume of the remaining solid?

Mathematics
1 answer:
Mekhanik [1.2K]3 years ago
4 0
I cannot see the question or answers .
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Please Help!!<br><br>Use Euler’s formula to write in exponential form.
LekaFEV [45]

Answer:

C, 4e^{i(7\pi/4)}

Step-by-step explanation:

To remind you, Euler's formula gives a link between trigonometric and exponential functions in a very profound way:

e^{ix}=\cos{x}+i\sin{x}

Given the complex number 2\sqrt{2}-2i\sqrt{2}, we want to try to get it in the same form as the right side of Euler's formula. As things are, though, we're unable to, and the reason for that has to do with the fact that both the sine and cosine functions are bound between the values 1 and -1, and 2√2 and -2√2 both lie outside that range.

One thing we could try would be to factor out a 2 to reduce both of those terms, giving us the expression 2(\sqrt{2}-i\sqrt{2})

Still no good. √2 and -√2 are still greater than 1 and less than -1 respectively, so we'll have to reduce them a little more. With some clever thinking, you could factor out another 2, giving us the expression 4\left(\frac{\sqrt{2}}{2} -i\frac{\sqrt{2}}{2}\right) , and <em>now </em>we have something to work with.

Looking back at Euler's formula e^{ix}=\cos{x}+i\sin{x}, we can map our expression inside the parentheses to the one on the right side of the formula, giving us \cos{x}=\frac{\sqrt2}{2} and \sin{x}=-\frac{\sqrt2}{2}, or equivalently:

\cos^{-1}{\frac{\sqrt2}{2} }=\sin^{-1}-\frac{\sqrt2}{2} =x

At this point, we can look at the unit circle (attached) to see the angle satisfying these two values for sine and cosine is 7π/4, so x=\frac{7\pi}{4}, and we can finally replace our expression in parentheses with its exponential equivalent:

4\left(\frac{\sqrt2}{2}-i\frac{\sqrt2}{2}\right)=4e^{i(7\pi/4)}

Which is c on the multiple choice section.

4 0
3 years ago
Help? im confused plss!<br> Find the area of the regular polygon with the given radius or apothem
Snezhnost [94]

Answer:

  50 cm²

Step-by-step explanation:

Given that the regular polygon is a square, there are multiple ways you can jump directly to the answer. Perhaps the simplest is to use the formula for the area of a rhombus:

  A = 1/2(d1)(d2)

where d1 and d2 are the lengths of the diagonals. Here, we see that half the diagonal is 5 cm, so the area is ...

  A = (1/2)(10 cm)(10 cm) = 50 cm² . . . . area of the polygon

__

<em>Alternate solution</em>

If you want to use the radius and the number of sides in a formula, you can consider the area of each triangle formed by radii and a side. That triangle has area ...

  A = 1/2r²sin(α)

where r is the radius and α is the central angle. For an n-sided polygon, the area is the sum of n of these triangles, and the central angle is 360°/n. Then the polygon area is ...

  A = n/2·r²·sin(360°/n)

For n = 4 and r = 5 cm, the area is ...

  A = (4/2)(5 cm)²(sin(360°/4)) = 2(5 cm)²(1) = 50 cm² . . . . area of square

_____

<em>Additional comment</em>

The formula is somewhat different if you start with the length of the apothem. One way to find the area is using the above formula and the relation between the radius and apothem:

  r = a·sec(180°/n)

Another formula uses the apothem directly:

  A = n·a²·tan(180°/n)

8 0
2 years ago
URGENT!!
Lapatulllka [165]

Answer:

f[g(4)] = 4

Step-by-step explanation:

Given table:

\begin{array}{| c | c | c | c | c | c |}\cline{1-6} x & -6 & -4 & 1 & 3 & 4\\\cline{1-6} f(x) & 4 & -1 & -6 & 1 & 3 \\\cline{1-6} g(x) & 1 & 4 & 3 & -4 & -6 \\\cline{1-6}\end{array}

f[g(4)] is a composite function.

When calculating <u>composite functions</u>, always work from inside the brackets out.

Begin with g(4):  g(4) is the value of function g(x) when x = 4.

From inspection of the given table, g(4) = -6

Therefore, f[g(4)] = f(-6)

f(-6) is the value of function f(x) when x = -6.

From inspection of the given table, f(-6) = 4

Therefore, f[g(4)] = 4

3 0
1 year ago
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If there are 2 girls per 3 boys What is<br> the ratio of girls to Boys
Phantasy [73]

Answer:

2:3

‎‎‎‎‎‎‎‎‎

‎ ‎

‎‎‎‎

‎‎‎‎‎‎‎‎‎

‎ ‎

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3 0
3 years ago
Helppppp will give the crown
Drupady [299]
-√121
10 1/11
10.13
10.2 repeating
3 0
2 years ago
Read 2 more answers
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