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4 years ago

What is the value of x in this question

Mathematics

1 answer:

lara31 [8.8K]4 years ago

7 0

The left triangle is a 30-60-90 triangle so line ST = 2 which means line RT is 4 (double the length of ST).

The right triangle is a 45-45-90 triangle which means RT and RQ are congruent.

So if RT = RQ and RT = 4, then x = 4

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3 years ago

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olasank [31]

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18in²

Step-by-step explanation:

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3 years ago

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Can somebody explain how trigonometric form polar equations are divided/multiplied?

koban [17]

Answer:

Attachment 1 : Option C

Attachment 2 : Option A

Step-by-step explanation:

( 1 ) Expressing the product of z1 and z2 would be as follows,

$14\left[\cos \left(\frac{\pi \:}{5}\right)+i\sin \left(\frac{\pi \:\:}{5}\right)\right]\cdot \:2\sqrt{2}\left[\cos \left(\frac{3\pi \:}{2}\right)+i\sin \left(\frac{3\pi \:\:}{2}\right)\right]$

Now to solve such problems, you will need to know what cos(π / 5) is, sin(π / 5) etc. If you don't know their exact value, I would recommend you use a calculator,

cos(π / 5) = $\frac{\sqrt{5}+1}{4}$ ,

sin(π / 5) = $\frac{\sqrt{2}\sqrt{5-\sqrt{5}}}{4}$

cos(3π / 2) = 0,

sin(3π / 2) = - 1

Let's substitute those values in our expression,

$14\left[\frac{\sqrt{5}+1}{4}+i\frac{\sqrt{2}\sqrt{5-\sqrt{5}}}{4}\right]\cdot \:2\sqrt{2}\left[0-i\right]$

And now simplify the expression,

$14\sqrt{5-\sqrt{5}}+i\left(-7\sqrt{10}-7\sqrt{2}\right)$

The exact value of $14\sqrt{5-\sqrt{5}}$ = $23.27510\dots$ and $(-7\sqrt{10}-7\sqrt{2}\right))$ = $-32.03543\dots$ Therefore we have the expression $23.27510 - 32.03543i$ , which is close to option c. As you can see they approximated the solution.

( 2 ) Here we will apply the following trivial identities,

cos(π / 3) = $\frac{1}{2}$ ,

sin(π / 3) = $\frac{\sqrt{3}}{2}$ ,

cos(- π / 6) = $\frac{\sqrt{3}}{2}$ ,

sin(- π / 6) = $-\frac{1}{2}$

Substitute into the following expression, representing the quotient of the given values of z1 and z2,

$15\left[cos\left(\frac{\pi \:}{3}\right)+isin\left(\frac{\pi \:\:}{3}\right)\right] \div \:3\sqrt{2}\left[cos\left(\frac{-\pi \:}{6}\right)+isin\left(\frac{-\pi \:\:}{6}\right)\right]$ ⇒

$15\left[\frac{1}{2}+\frac{\sqrt{3}}{2}\right]\div \:3\sqrt{2}\left[\frac{\sqrt{3}}{2}+-\frac{1}{2}\right]$

The simplified expression will be the following,

$i\frac{5\sqrt{2}}{2}$ or in other words $\frac{5\sqrt{2}}{2}i$ or $\frac{5i\sqrt{2}}{2}$

The solution will be option a, as you can see.

6 0

4 years ago

Please help out with this geometry homework I was assigned. And what formula do I use?

lozanna [386]

Answer:

$V_{cone} \approx 1,178.97 \: {in}^{3}$

Step-by-step explanation:

Diameter of cone = 16 in

Radius of cone r = 16/2 = 8 in

Height of cone h = 17.6 in

$V_{cone} = \frac{1}{3} \pi {r}^{2}h \\ \\ V_{cone} = \frac{1}{3} \times 3.14 \times {(8)}^{2} \times 17.6 \\ \\ V_{cone} = \frac{1}{3} \times 3,536.896 \\ \\ V_{cone} = 1,178.96533 \\ \\ V_{cone} \approx 1,178.97 \: {in}^{3} \\$