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dybincka [34]
3 years ago
7

Find the slope (-1,7)(5,7)

Mathematics
1 answer:
Komok [63]3 years ago
8 0

Answer:

The slope is zero

Step-by-step explanation:

(7-7)/(5+1)= 0/6= 0

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7/22 rounded to the nearest thousandth
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0.318

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What is the smallest number that has a remainder of 1, 2, and 3 when divided by 2, 3, and 4, respectively? Are there more number
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11 is the answer.

Step-by-step explanation:

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Find the volume of the cone.<br> Either enter an exact answer in terms of <br> π or use 3.14 for π
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Answer:

157.08

Step-by-step explanation:

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Prove by mathematical induction that
postnew [5]

For n=1, on the left we have \cos\theta, and on the right,

\dfrac{\sin2\theta}{2\sin\theta}=\dfrac{2\sin\theta\cos\theta}{2\sin\theta}=\cos\theta

(where we use the double angle identity: \sin2\theta=2\sin\theta\cos\theta)

Suppose the relation holds for n=k:

\displaystyle\sum_{n=1}^k\cos(2n-1)\theta=\dfrac{\sin2k\theta}{2\sin\theta}

Then for n=k+1, the left side is

\displaystyle\sum_{n=1}^{k+1}\cos(2n-1)\theta=\sum_{n=1}^k\cos(2n-1)\theta+\cos(2k+1)\theta=\dfrac{\sin2k\theta}{2\sin\theta}+\cos(2k+1)\theta

So we want to show that

\dfrac{\sin2k\theta}{2\sin\theta}+\cos(2k+1)\theta=\dfrac{\sin(2k+2)\theta}{2\sin\theta}

On the left side, we can combine the fractions:

\dfrac{\sin2k\theta+2\sin\theta\cos(2k+1)\theta}{2\sin\theta}

Recall that

\cos(x+y)=\cos x\cos y-\sin x\sin y

so that we can write

\dfrac{\sin2k\theta+2\sin\theta(\cos2k\theta\cos\theta-\sin2k\theta\sin\theta)}{2\sin\theta}

=\dfrac{\sin2k\theta+\sin2\theta\cos2k\theta-2\sin2k\theta\sin^2\theta}{2\sin\theta}

=\dfrac{\sin2k\theta(1-2\sin^2\theta)+\sin2\theta\cos2k\theta}{2\sin\theta}

=\dfrac{\sin2k\theta\cos2\theta+\sin2\theta\cos2k\theta}{2\sin\theta}

(another double angle identity: \cos2\theta=\cos^2\theta-\sin^2\theta=1-2\sin^2\theta)

Then recall that

\sin(x+y)=\sin x\cos y+\sin y\cos x

which lets us consolidate the numerator to get what we wanted:

=\dfrac{\sin(2k+2)\theta}{2\sin\theta}

and the identity is established.

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2 years ago
Write an equation representing the direct variation.
zalisa [80]

Answer:

y = -2.5x

Step-by-step explanation:

The constant of variation = y/ x = 5/-2 = -2.5

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-10 /4 = -2.5 and so on

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