Which of the following equals cos 80° ? A. sin 100° B. sin 20° C. sin 10° D. sin 80°

Mathematics

1 answer:

Rzqust [24]3 years ago

3 0

Answer:

Step-by-step explanation:

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75 points. Will give certified if work is shown and the answer is correct.

Svetach [21]

Volume of the first dwarf planet (r₁ = 832 mi):

$V_1=\dfrac{4}{3}\cdot\pi\cdot r_1^3=\dfrac{4}{3}\cdot\pi\cdot 832^3=\dfrac{2303721472}{3}\pi\approx7.679\cdot10^8\pi\,\text{mi}^3$

Volume of the second dwarf planet (r₂ = 829 mi):

$V_2=\dfrac{4}{3}\cdot\pi\cdot r_2^3=\dfrac{4}{3}\cdot\pi\cdot 829^3=\dfrac{2278891156}{3}\pi\approx7.5963\cdot10^8\pi\,\text{mi}^3$

So difference between the volumes is:

$V_1-V_2\approx7.679\cdot10^8\pi-7.5963\cdot10^8\pi=0.0827\cdot10^8\pi=\boxed{8270000\pi\,\text{mi}^3}$

or if we want exact value (we use (a³-b³) = (a-b)(a²+ab+b²) ):

$V_1-V_2=\dfrac{4}{3}\cdot\pi\cdot r_1^3-\dfrac{4}{3}\cdot\pi\cdot r_2^3=\dfrac{4}{3}\pi(r_1^3-r_2^3)=\dfrac{4}{3}\pi(832^3-829^3)=\\\\\\=\dfrac{4}{3}\pi(832-829)(832^2+832\cdot829+829^2)=\\\\\\=\dfrac{4}{3}\pi\cdot3(692224+689728+687241)=4\pi\cdot2069193=\boxed{8276772\pi\,\text{mi}^3}$

3 0

3 years ago

-6x + 3x = -21 linear equations

snow_tiger [21]

well combine like terms

-3x = -21

divide both sides by -3

x = 7

8 0

3 years ago

Read 2 more answers

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