5. Find the measures of the following supplementary angles.

Each side of a cube measures 5 cm in length. What is the cubes volume?

AysviL [449]

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Answer:

Your answer would be 125 cm³

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Step-by-step explanation:

In order to find the volume of a cube, we would need to use the right formula to find the volume for it.

Volume of a cube formula:

$V = a^{3}$

For our "a" value, we would need to plug in our side value, and for you case, the side value would be 5.

In a cube, all of the sides would be the same size, so you don't have to worry about using any different numbers.

Lets plug in 5 to our equation.

$V = 5^{3}$

Now we solve:

$5^{3} = 125\\$

This is also the same as:

$5 *5*5 = 125$

Your FINAL answer should be 125 cm³

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8 0

3 years ago

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In abc above,what is the length of ad

Nezavi [6.7K]

Answer:

B

Step-by-step explanation:

First calculate BD using sine ratio in Δ BCD and the exact value

sin60° = $\frac{\sqrt{3} }{2}$ , thus

sin60° = $\frac{opposite}{hypotenuse}$ = $\frac{BD}{BC}$ = $\frac{BD}{12}$ = $\frac{\sqrt{3} }{2}$ ( cross- multiply )

2BD = 12 $\sqrt{3}$ ( divide both sides by 2 )

BD = 6 $\sqrt{3}$

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Calculate AD using the tangent ratio in Δ ABD and the exact value

tan30° = $\frac{1}{\sqrt{3} }$ , thus

tan30° = $\frac{opposite}{adjacent}$ = $\frac{AD}{BD}$ = $\frac{AD}{6\sqrt{3} }$ = $\frac{1}{\sqrt{3} }$ ( cross- multiply )

$\sqrt{3}$ AD = 6 $\sqrt{3}$ ( divide both sides by $\sqrt{3}$ )

AD = 6 → B

4 0

3 years ago

9. A circle has an arc of length 56pi that is intercepted by a central angle of 120 degrees. What is the radius of the circle?

SSSSS [86.1K]

Answer:

Part 4) $r=84\ units$

Part 9) $sin(\theta)=-\frac{\sqrt{5}}{3}$

Part 10) $sin(\theta)=-\frac{9\sqrt{202}}{202}$

Step-by-step explanation:

Part 4) A circle has an arc of length 56pi that is intercepted by a central angle of 120 degrees. What is the radius of the circle?

we know that

The circumference of a circle subtends a central angle of 360 degrees

The circumference is equal to

$C=2\pi r$

using proportion

$\frac{2\pi r}{360^o}=\frac{56\pi}{120^o}$

simplify

$\frac{r}{180^o}=\frac{56}{120^o}$

solve for r

$r=\frac{56}{120^o}(180^o)$

$r=84\ units$

Part 9) Given cos(∅)=-2/3 and ∅ lies in Quadrant III. Find the exact value of sin(∅) in simplified form

Remember the trigonometric identity

$cos^2(\theta)+sin^2(\theta)=1$

we have

$cos(\theta)=-\frac{2}{3}$

substitute the given value

$(-\frac{2}{3})^2+sin^2(\theta)=1$

$\frac{4}{9}+sin^2(\theta)=1$

$sin^2(\theta)=1-\frac{4}{9}$

$sin^2(\theta)=\frac{5}{9}$

square root both sides

$sin(\theta)=\pm\frac{\sqrt{5}}{3}$

we know that

If ∅ lies in Quadrant III

then

The value of sin(∅) is negative

$sin(\theta)=-\frac{\sqrt{5}}{3}$

Part 10) The terminal side of ∅ passes through the point (11,-9). What is the exact value of sin(∅) in simplified form?

see the attached figure to better understand the problem

In the right triangle ABC of the figure

$sin(\theta)=\frac{BC}{AC}$

Find the length side AC applying the Pythagorean Theorem

$AC^2=AB^2+BC^2$

substitute the given values

$AC^2=11^2+9^2$

$AC^2=202$

$AC=\sqrt{202}\ units$

so

$sin(\theta)=\frac{9}{\sqrt{202}}$

simplify

$sin(\theta)=\frac{9\sqrt{202}}{202}$

Remember that

The point (11,-9) lies in Quadrant IV

then

The value of sin(∅) is negative

therefore

$sin(\theta)=-\frac{9\sqrt{202}}{202}$

5 0

3 years ago

If cot 0=12/5 find tan 0

jek_recluse [69]

cot 0=12/5 find tan 0

cot = adjacent/opp

tan = opp/adjacent

cot = 12/5

tan = 5/12

8 0

3 years ago

PLZ PLZ HURRY I WILL GIVE BRIANLEST

Colt1911 [192]

The answer is D Explanation: since the the slope is negative the x should be negative and D is the only one that has a negative X.

8 0

3 years ago

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