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lorasvet [3.4K]

2 years ago

5

I am thinking of a positive number. If I square it, double the result, take half of that result, and then add 12, I get 21. What

is my number?

1 answer:

Margarita [4]2 years ago

8 0

Answer:

3

Step-by-step explanation:

work backwards.

x^2*2/2+12=21

x^2+12=21

x^2=9

x=3

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To obtain an average (arithmetic mean) of exactly 2/3, what fraction must be added to 1/6, 1/2, and 1/3?

ollegr [7]

Answer:

D. 5/3

Step-by-step explanation:

$\frac{1/6+1/2+1/3+x}{4} =2/3$

$1/6+1/2+1/3+x=8/3$

$x=8/3-1/6-1/2-1/3$

$x=8/3-1/6-3/6-2/6$

$x=8/3-6/6$

$x=16/6-6/6=10/6$

simplified

$x=5/3$

Hope this helps

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2 years ago

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Algebraic expression the sum of 27 and twice the opposite of why

gogolik [260]

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2 years ago

A ball is thrown from an initial height of 4 feet with an initial upward velocity of 17ft/s. The ball's height h (in feet) after

iVinArrow [24]

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3 years ago

Show tan(???? − ????) = tan(????)−tan(????) / 1+tan(????) tan(????)<br> .

anyanavicka [17]

Answer:

See the proof below

Step-by-step explanation:

For this case we need to proof the following identity:

$tan(x-y) = \frac{tan(x) -tan(y)}{1+ tan(x) tan(y)}$

We need to begin with the definition of tangent:

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

So we can replace into our formula and we got:

$tan(x-y) = \frac{sin(x-y)}{cos(x-y)}$ (1)

We have the following identities useful for this case:

$sin(a-b) = sin(a) cos(b) - sin(b) cos(a)$

$cos(a-b) = cos(a) cos(b) + sin (a) sin(b)$

If we apply the identities into our equation (1) we got:

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

Now we can divide the numerator and denominato from expression (2) by $\frac{1}{cos(x) cos(y)}$ and we got this:

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

And simplifying we got:

$tan(x-y) = \frac{tan(x) -tan(y)}{1+ tan(x) tan(y)}$

And this identity is satisfied for all:

$(x-y) \neq \frac{\pi}{2} +n\pi$

8 0

2 years ago