<img src="https://tex.z-dn.net/?f=p%5E%7B2%7D%20%2B6p%3Dq%5E%7B2%7D%2B6q.%5C%5Cp%5Cneq%20q.%5C%5CSolve%20for%20p%2Bq." id="TexFo

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2 years ago

rmula1" title="p^{2} +6p=q^{2}+6q.\\p\neq q.\\Solve for p+q." alt="p^{2} +6p=q^{2}+6q.\\p\neq q.\\Solve for p+q." align="absmiddle" class="latex-formula">

Mathematics

1 answer:

Rainbow [258]2 years ago

5 0

Answer:

$p + q = -6$

Step-by-step explanation:

$p^{2} + 6 p = q^{2} + 6q \\p^{2} - q^{2} = 6q - 6p$

$( p + q) ( p-q) = 6 ( q - p )$

$p + q = \frac{6 ( q - p)}{(p-q)} \\p + q = \frac{-6( p - q)}{(p - q)} \\p + q = -6$

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A ball is tossed between three friends. The first toss is 8.6 feet, the second is 5.8 feet, and the third toss is 7.5 feet, whic

Rainbow [258]

angles formed by these tosses are $79.45, 59.02$ and $41.53$ degrees to the nearest hundredth.

<u>Step-by-step explanation:</u>

Here , We have a triangle with sides of length 8.6 feet, 5.8 feet and 7.5 feet.

The Law of Cosines (also called the Cosine Rule) says:

$c^2 = a^2 + b^2 - 2ab (cosx)$

Using the Cosine Rule to find the measure of the angle opposite the side of length 8.6 feet:

⇒ $c^2 = a^2 + b^2 - 2ab (cosx)$

⇒ $c^2 -a^2 - b^2 = -2ab (cosx)$

⇒ $(cosx) =\frac{ c^2 -a^2 - b^2}{ -2ab}$

⇒ $(cosx) =\frac{(8.6^2 - 5.8^2 - 7.5^2)}{ ( -2(5.8)7.5)}$

⇒ $(cosx) =0.18310$

⇒ $cos^{-1}(cosx) = cos^{-1}(0.18310)$

⇒ $x = 79.45$

The Law of Sines (or Sine Rule) is very useful for solving triangles:

$\frac{a}{sin A} = \frac{ b}{sin B} = \frac{c}{sin C}$

We can now find another angle using the sine rule:

⇒ $\frac{ 8.6 }{ sin 79.45} = \frac{7.5}{ sin Y}$

⇒ $sin Y = \frac{(7.5 (sin 79.45))}{ 8.6}$

⇒ $Y = 59.02 degrees$

So, the third angle = $180 - 79.45 - 59.02 = 41.53 degrees.$

Therefore, angles formed by these tosses are $79.45, 59.02$ and $41.53$ degrees to the nearest hundredth.

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