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ozzi
3 years ago
8

One more time!

Mathematics
1 answer:
CaHeK987 [17]3 years ago
3 0
Since q(x) is inside p(x), find the x-value that results in q(x) = 1/4

\frac{1}{4} = 5 - x^2\ \Rightarrow\ x^2 = 5 - \frac{1}{4}\ \Rightarrow\ x^2 = \frac{19}{4}\ \Rightarrow \\
x = \frac{\sqrt{19} }{2}

so we conclude that
q(\frac{\sqrt{19} }{2} ) = 1/4

therefore

p(1/4) = p\left( q\left(\frac{ \sqrt{19} }{2} \right)  \right)

plug x=\sqrt{19}/2 into p( q(x) ) to get answer

p(1/4) = p\left( q\left( \frac{ \sqrt{19} }{2} \right) \right)\ \Rightarrow\ \dfrac{4 - \left(  \frac{\sqrt{19} }{2}\right)^2 }{ \left(  \frac{\sqrt{19} }{2}\right)^3 } \Rightarrow \\ \\ \dfrac{4 - \frac{19}{4} }{ \frac{19\sqrt{19} }{8}} \Rightarrow \dfrac{8\left(4 - \frac{19}{4}\right) }{ 8 \cdot \frac{19\sqrt{19} }{8}} \Rightarrow \dfrac{32 - 38}{19\sqrt{19}} \Rightarrow \dfrac{-6}{19\sqrt{19}} \cdot \frac{\sqrt{19}}{\sqrt{19}}\Rightarrow

\dfrac{-6\sqrt{19} }{19 \cdot 19} \\ \\ \Rightarrow  -\dfrac{6\sqrt{19} }{361}

p(1/4) = -\dfrac{6\sqrt{19} }{361}
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4 0
3 years ago
Write and solve an equation to find the unknown side length x (in inches). Perimeter =24.2 in. Sides of the shape are 8.3, 8.3,
Anastasy [175]

Answer:

Perimeter of shape,which is a convex polygon i.e quadrilateral = 24.2 in

Sides are 8.3 in, 8.3 in, 3.8 in ,and length of fourth side be x in.

As , Perimeter = Sum of all sides

                 → 24.2 = 8.3 + 8.3 + 3.8 + x

                 → 24.2 = 16.6 +3.8 + x

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Keeping like terms on one side, of equation

            → 24.2 - 20.4 = x

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            → x = 3.8

So, length of fourth side = 3.8 in

The given shape is definately either a Parallelogram or a kite.



7 0
3 years ago
Solve 7w = 56, where w is a real number.
steposvetlana [31]

Answer:

w = 8

Step-by-step explanation:

7w = 56

Divide both sides by 7

w = 56/7

w = 8

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