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2 years ago

Express answer in exact form. Show all work for full credit.

Mathematics

1 answer:

liubo4ka [24]2 years ago

7 0

The chord length is sqrt(2) times the radius, so R = 6/sqrt(2) and R^2 = 18.
Area = (1/2)(18)(pi/2 - 1) = (9/2)(pi - 2)

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One of the roots of the equation 3x^2+7x−q=0 is −5. Find the other root and q.

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Answer: The answer is $\textup{The other root is }\dfrac{8}{3}~\textup{and}q=40.Step-by-step explanation: The given quadratic equation is[tex]3x^2+7x-q=0\\\\\Rightarrow x^2-\dfrac{7}{3}x-\dfrac{q}{3}=0.$

Also given that -5 is one of the roots, we are to find the other root and the value of 'q'.

Let the other root of the equation be 'p'. So, we have

$p-5=-\dfrac{7}{3}\\\\\\\Rightarrow p=5-\dfrac{7}{3}\\\\\\\Rightarrow p=\dfrac{8}{3},$

and

$p\times(-5)=-\dfrac{q}{3}\\\\\\\Rightarrow \dfrac{8}{3}\times 5=\dfrac{q}{3}\\\\\\\Rightarrow q=40.$

Thus, the other root is $\dfrac{8}{3}$ and the value of 'q' is 40.

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Read 2 more answers

Marisol is painting on a canvas that has an area of 180 square inches. The length of the painting is 11/4 times the width. What

Alona [7]

Notice the picture below, see the length "l"?

well $\bf Area=l\times w\qquad 
\begin{cases}
l=\frac{11}{4}w\\
Area=180
\end{cases}\\\\
-----------------------------\\\\
thus
\\\\
180=\cfrac{11}{4}w\times w$

solve for "w", to find the width,

what's the length? well, l = 11/4 w

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