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3 years ago

Find the volume of this right rectangular prism. 3 in 9 in . 3 in [ ? ]in3

Mathematics

2 answers:

mel-nik [20]3 years ago

3 0

Answer:

penge po pic nyan

Step-by-step explanation:

ty po

hope l help

Shkiper50 [21]3 years ago

3 0

Answer 8.1

Step-by-step explanation:

3 x 9 x 0.3 = 8.1

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Given cos alpha = 8/17, alpha in quadrant IV, and sin beta = -24/25, beta in quadrant III, find sin(alpha-beta)

polet [3.4K]

Given $\cos\alpha=\frac{8}{17}$ , $\alpha$ is in Quadrant IV, $\sin\beta=-\frac{24}{25}$ , and $\beta$ is in Quadrant III, find $\sin(\alpha-\beta)$

We can use the angle subtraction formula of sine to answer this question.

$\sin(\alpha-\beta)=\sin\alpha\cos\beta-\cos\alpha\sin\beta$

We already know that $\cos\alpha=\frac{8}{17}$ .

We can use the Pythagorean identity $\sin^2\theta+\cos^2\theta=1$ to find $\sin\alpha$ .

$\sin^2\alpha+(\frac{8}{17})^2=1 \\ \sin^2\alpha+\frac{64}{289}=1 \\ \sin^2\alpha=\frac{225}{289} \\ \\\sin\alpha=\pm\frac{15}{17}$

Since $\alpha$ is in Quadrant IV, and sine is represented as y value on the unit circle, we must assume the negative value $\sin\alpha=-\frac{15}{17}$ .

As similar process is then done with $\sin\beta=-\frac{24}{25}$ .

$(-\frac{24}{25})^2+\cos^2\beta=1 \\ \frac{576}{625}+\cos^2\beta=1 \\ \cos^2\beta=\frac{49}{625} \\ \\\cos\beta=\pm\frac{7}{25}$

And since $\beta$ is in Quadrant III, and cosine in represented as x value on the unit cercle, we must assume the negative value $\cos\beta=-\frac{7}{25}$ .

Now we can fill in our angle subtraction formula!

$\sin(\alpha-\beta)=\sin\alpha\cos\beta-\cos\alpha\sin\beta \\\\ \sin(\alpha-\beta)=(-\frac{15}{17}\times-\frac{7}{25})-(\frac{8}{17}\times-\frac{24}{25}) \\\\\sin(\alpha-\beta)=\frac{105}{425}-(-\frac{192}{425}) \\\\ \boxed{\sin(\alpha-\beta)=\frac{297}{425}}$

7 0

3 years ago

Write 100 times 100 as multiplying 10 to a power by 10 to a power.

Oliga [24]

Answer:

10^2*10^2

Step-by-step explanation:

1) Write 100*100 in as powers of 10: 10^2 * 10^2

8 0

3 years ago

Celia simplified the expression Negative 4 x (1 minus 3) minus (2 x + 2). She checked her work by letting x = 5 in both expressi

guapka [62]

Answer:

6x-2

Step-by-step explanation:

-4x(1-3)-(2x+2)

= 4x+12x-2x-2

6x-2

(simplify)

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2 years ago

Any number raised to the power of zero is zero true or false

beks73 [17]

Answer: Any number times zero is zero, it can never equal something else.

Step-by-step explanation: My teacher taught me this before so i know :)

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3 years ago

Read 2 more answers

Translate this sentence into an equation: 162 is the product of 9 and Gall's age. Use the variable g to represent Gall's age.

oksano4ka [1.4K]

The equation is
9 × g = 162
9g = 162

Solving foe Gall's age,
9g = 162
g = 162 ÷ 9
g = 18

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3 years ago