Question 3 of 10 Complete the square to solve the equation below. x2-10X-2 = 17

Mathematics

1 answer:

stellarik [79]3 years ago

4 0

Answer:

Step-by-step explanation:

$x^2-10x-2=17$

Add 2 to both sides:

$x^2-10x-2+2=17+2$

$x^2-10x=19$

Add half of the coefficient of the x, squared to both sides:

$x^2-10x+\left(-5\right)^2=19+\left(-5\right)^2$

Simplify:

$x^2-10x+\left(-5\right)^2=44$

Complete the square:

$\left(x-5\right)^2=44$

$x-5=\sqrt[]{44}$ or $x-5=-\sqrt[]{44}$

$x=\sqrt{44} +5$ or $x=-\sqrt{44} +5$

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Point) a norman window has the shape of a rectangle with a semi circle on top; diameter of the semicircle exactly matches the wi

svetlana [45]

Let d represent the diameter of the semicircle (and the width of the window). Then the length of the semicircular arch is π/2*d. The remaining perimeter available for the height of the rectangular shape is then
.. 1000 -(d +π/2*d)
and that amount will be divided between the two sides of the window.

Then the height of the rectangular section is
.. h = (1/2)*(1000 -d(1 +π/2))
.. = 500 -d(1/2 +π/4)
The total area of the window is ...
.. A = dh +(1/2)(π/4)d^2
.. = d(500 -d(1/2 +π/4)) +π/8d^2
.. = 500d +d^2*(π/8 -π/4 -1/2)
.. = d(500 -d(1/2 +π/8))

This downward-opening quadratic function has its vertex (maximum) at
.. d = 500/(1 +π/4) = 2000/(4 +π)

The corresponding rectangle height is
.. h = 500 -500/(1 +π/4)*(1/2 +π/4)
.. = 500(1 - (2 +π)/(4 +π)) = 500(4 +π -2 -π)/(4 +π) = 1000/(4 +π)

That is, the height of the rectangular section is 1/2 the diameter of the circular section, so the overall window has the same overall height and width.

The height and width of the window with maximum area are ...
2000/(4+π) in ≈ 280.0 in

_____
The graph shows both the area function and the (d, h) dimensions of the rectangle.