3 years ago

Simplify. 3^2 · 3^4 · 3^6 A) 3^0 B) 3^10 C) 3^12 D) 3^48

Mathematics

1 answer:

Setler [38]3 years ago

6 0

The answer is C.
The rule is:
When multiplying exponents with like bases, keep the base and add the powers.

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Given that x=3sinθ-2 and y=3cosθ+4.Show that (x+2)²+ (y-4)²=9

asambeis [7]

Answer:

First, plug-in x and y as 3sinθ-2 and 3cosθ+4 into the equation, respectively:

$((3\sin (\theta)-2)+2)^2 + ((3\cos (\theta)+4)-4)^2 = 9$

Then, +2 and -2 cancel out and +4 and -4 cancel out as well, leaving you with:

$(3\sin(\theta))^2+(3\cos(\theta))^2=9$

We can factor out 3^2 = 9 from both equations:

$9(\sin(\theta)^2+cos(\theta)^2) = 9$

We know from a trigonometric identity that $\sin(\theta)^2+cos(\theta)^2 = 1$ , meaning we can reduce the equation to:

$9(1) = 9$

$9=9$

And therefore, we have shown that (x+2)^2 + (y-4)^2 = 9, if x=3sinθ-2 and y=3cosθ+4.

Hope this helped you.

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3 years ago

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pshichka [43]

Answer:

Step-by-step explanation:

if he can walk 0.5 miles in 6 minutes at a constant rate then you can say that he can walk 1 mile in 12 minutes.

therefore he can walk 1/12 mile ever one minute

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3 years ago

The rectangular screen of a high-definition television set is 71 cm wide and 40 cm high. What is it’s area

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$A=lw=71\times 40=2840 \: {cm}^{2}$

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If Tom runs 3.5 miles in 29.4 minutes, how many hours would it take him to run 26 miles? Show your work.

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Answer:

Step-by-step explanation:

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Step-by-step explanation:

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