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3 years ago

What is the value of x in the trangle? Enter your answer in the box. Round your final answer to the nearest hundredth.

Mathematics

1 answer:

-Dominant- [34]3 years ago

4 0

Use trigonometry.

cos(18°) = x/25

Multiply both sides by 25.

cos(18°)25 = x

23.7764129074 = x

We round off to the nearest hundredth. This means to round off to two decimal places.

Doing so, we get 23,78 cm = x.

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Find the surface area of a hemisphere that has a volume of 486π <img src="https://tex.z-dn.net/?f=cm%5E%7B3%7D" id="TexFormula1"

Xelga [282]

$\textit{volume of a hemisphere}\\ V=\cfrac{4\pi r^3}{3}\cdot \cfrac{1}{2}~~ \begin{cases} r=radius\\[-0.5em] \hrulefill\\ V=486\pi \end{cases}\implies 486\pi =\cfrac{4\pi r^3}{6} \implies 6(486\pi )=4\pi r^3 \\\\\\ \cfrac{6(486\pi )}{4\pi }=r^3\implies 729=r^3\implies \sqrt[3]{729}=r\implies \boxed{9=r} \\\\[-0.35em] ~\dotfill$

$\textit{surface area of a hemisphere}\\\\ SA=4\pi r^2\cdot \cfrac{1}{2}\implies \stackrel{\textit{we know that r = 9}}{SA=2\pi (9)^2}\implies SA=162\pi \implies SA\approx 508.94$

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2 years ago

Read 2 more answers

What are the solutions to the following system of equations? y = x2 + 3x − 7 3x − y = −2 (2 points) (3, 11) and (−3, −7) (11, 3)

Minchanka [31]

ANSWER

(3, 11) and (−3, −7)

EXPLANATION

The given system of equations are:

$y = {x}^{2} + 3x - 7$

and

$3x - y = - 2$

or

$y = 3x + 2$

We equate the two equations to obtain,

${x}^{2} + 3x - 7 = 3x + 2$

We rewrite in standard quadratic form to obtain,

${x}^{2} + 3x - 3x - 7 - 2 = 0$

This simplifies to

${x}^{2}- 9= 0$

We solve for x to obtain,

${x}^{2} = 9$

$x = \pm \sqrt{9}$

$x = \pm 3$

$x = 3 \: or \: x = - 3$

When
$x = 3$

$y = 3(3) + 2 = 11$

When x=-3,

$y = 3( - 3) + 2 = - 7$

Therefore the solution for the system is (3, 11) and (−3, −7).

7 0

2 years ago

Read 2 more answers

What is the value of x in the trangle? Enter your answer in the box. Round your final answer to the nearest hundredth.​

What is the value of x in the trangle? Enter your answer in the box. Round your final answer to the nearest hundredth.