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3 years ago

Simplify the exponents using the rules of exponents (54b^3/b^15)^2/3

1 answer:

4 0

$(\frac{54b^{3}}{b^{15}})^{\frac{2}{3}} = (\frac{54}{b^{12}})^{\frac{2}{3}} = \frac{(54)^{\frac{2}{3}}}{(b^{12})^{\frac{2}{3}}} = \frac{\sqrt[3]{54^{2}}}{\sqrt[3]{b^{24}}} = \frac{\sqrt[3]{2916}}{b^{8}} = \frac{9\sqrt[3]{4}}{b^{8}}$

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If (cos)x= 1/2 what is sin(x) and tan(x)? Explain your steps in complete sentences.

Natasha_Volkova [10]

The correct answers are:
1) sin(x) = $\frac{ \sqrt{3} }{2}$
2) tan(x) = $\sqrt{3}$

Explanation:
Given:
$cos(x) = \frac{1}{2}$

Step 1:
Since, according to the Trigonometric identity:
$sin^2(x) + cos^2(x) = 1$ -- (1)

Step 2:
Plug in the value of cos(x) in equation (1):
$sin^2(x) + ( \frac{1}{2} )^2 = 1 \\ sin^2(x) + \frac{1}{4} = 1 \\ sin^2(x) = \frac{3}{4}$

Step 3:
Take square-root on both sides:
$\sqrt{sin^2(x)} = \sqrt{\frac{3}{4}}$

sin(x) = $\frac{ \sqrt{3} }{2}$

Now to find the tan(x), we would use the following formula:

tan(x) = $\frac{sin(x)}{cos(x)}$ --- (2)

Plug in the values of sin(x) and cos(x) in equation (2):
tan(x) = $\frac{ \frac{ \sqrt{3} }{2} }{ \frac{1}{2} }$

Hence tan(x) = $\sqrt{3}$

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2 years ago

Read 2 more answers

An algebraic equation is an equation that includes: A. No variables B. Only one variable C. One or more variables D.Just numbers

shutvik [7]

Answer:

Step-by-step explanation:

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3 years ago

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Answer:

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Step-by-step explanation:

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3 years ago

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2 years ago

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padilas [110]

Answer: Total Volume = 15π + 18 π= 33π cubic mm

Step-by-step explanation:

What is the volume of the composite figure? Leave the answer in terms of π.

_33π mm3

We have a cone here conjoined to a semi-sphere.

Cone volume: C = (1/3)*(πr^2) * h

semi-sphere volume : V = (1/2)* (4/3) * (π * r^3)

r = 3 mm and h = 5mm

so C = (1/3)*(π (3)^2) * 5 = 15π cubic mm

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3 years ago