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2 years ago

9

You are buying party favors that cost $2.47 each. You can spend no more than $30 on the party favors. What domain and range are

reasonable for this situation?

1 answer:

Damm [24]2 years ago

8 0

The answer is 15 hope this helps

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2 years ago

Someone pls help me with 7 and 8, thank you so much!!

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3 years ago

Find formula of s in terms of a, b, cos(x)

Alecsey [184]

Answer:

$\displaystyle s = \frac{2ab\cos x}{a+b}$

Step-by-step explanation:

We want to find a formula for <em>s</em> in terms of <em>a, b, </em>and cos(x).

Let the point where <em>s</em> intersects AB be D.

Notice that <em>s</em> bisects ∠C. Then by the Angle Bisector Theorem:

$\displaystyle \frac{a}{BD} = \frac{b}{AD}$

We can find BD using the Law of Cosines:

$\displaystyle BD^2 = a^2 + s^2 - 2as \cos x$

Likewise:

$\displaystyle AD^2 = b^2+ s^2 - 2bs \cos x$

From the first equation, cross-multiply:

$bBD = a AD$

And square both sides:

$b^2 BD^2 =a^2 AD^2$

Substitute:

$\displaystyle b^2 \left(a^2 + s^2 - 2as \cos x\right) = a^2 \left(b^2 + s^2 - 2bs \cos x\right)$

Distribute:

$a^2b^2 + b^2s^2 - 2ab^2 s\cos x = a^2b^2 + a^2s^2 - 2a^2 bs\cos x$

Simplify:

$b^2 s^2 - 2ab^2 s \cos x = a^2 s^2 - 2a^2 b s \cos x$

Divide both sides by <em>s </em>(<em>s</em> ≠ 0):

$b^2 s -2ab^2 \cos x = a^2 s - 2a^2 b \cos x$

Isolate <em>s: </em>

$b^2 s - a^2s = -2a^2 b \cos x + 2ab^2 \cos x$

Factor:

$\displaystyle s (b^2 - a^2) = 2ab^2 \cos x - 2a^2 b \cos x$

Therefore:

$\displaystyle s = \frac{2ab^2 \cos x - 2a^2 b \cos x}{b^2- a^2}$

Factor:

$\displaystyle s = \frac{2ab\cos x(b - a)}{(b-a)(b+a)}$

Simplify. Therefore:

$\displaystyle s = \frac{2ab\cos x}{a+b}$

5 0

2 years ago