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ivanzaharov [21]
2 years ago
14

What is the volume of the prism? A rectangular prism with cubic units arranged in five rows of four. Each cubic unit is one cubi

c inch. a 10 cubic inches b 20 cubic inches c 40 cubic inches d 80 cubic inches
Mathematics
1 answer:
vodka [1.7K]2 years ago
3 0

Answer:

D. 80 cubic inches

Step-by-step explanation:

Arranged in five rows of four => we can say the length, depth and width as 5,4,4

So, the volume is equal to 5 x 4 x 4 = 80 cubic inches

Sorry that this answer might not make sense to you, I just can't think of any better explanation.

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Vlad1618 [11]

Answer:

Mean - 250, Median - 250, Mode - 250, range - 90

Step-by-step explanation:

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3 years ago
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Use De Moivre's theorem to write the complex number in trigonometric form: (cos(3pi/5) + i sin (3pi/5))^3
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By De Moivre's theorem,

\left(\cos\dfrac{3\pi}5+i\sin\dfrac{3\pi}5\right)^3=\boxed{\cos\dfrac{9\pi}5+i\sin\dfrac{9\pi}5}

We can stop here ...

# # #

... but we can also express these trig ratios in terms of square roots. Let x=\dfrac\pi5 and let c=\cos x. Then recall that

\cos5x=c^5-10c^3\sin^2x+5c\sin^4x

\cos5x=c^5-10c^3(1-c^2)+5c(1-2c^2+c^4)

\cos5x=16c^5-20c^3+5c

On the left, 5x=\pi so that

16c^5-20c^3+5c+1=(c+1)(4c^2-2c-1)^2=0

Since c=\cos\dfrac\pi5\neq1, we're left with

4c^2-2c-1=0\implies c=\dfrac{1+\sqrt5}4

because we know to expect \cos x>0. Then from the Pythagorean identity, and knowing to expect \sin x>0, we get

\sin x=\sqrt{1-c^2}=\sqrt{\dfrac58-\dfrac{\sqrt5}8}

Both \cos and \sin are 2\pi-periodic, so that

\cos\dfrac{9\pi}5=\cos\left(\dfrac{9\pi}5-2\pi\right)=\cos\left(-\dfrac\pi5\right)=\cos\dfrac\pi5

and

\sin\dfrac{9\pi}5=\sin\left(-\dfrac\pi5\right)=-\sin\dfrac\pi5

so that the answer we left in trigonometric form above is equal to

\cos\dfrac\pi5-i\sin\dfrac\pi5=\boxed{\dfrac{1+\sqrt5}4+i\sqrt{\dfrac58+\dfrac{\sqrt5}8}}

7 0
3 years ago
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