Mathematics, 28.12.2019 22:31 iamabouttofail

Im giving 15 points
on a movie set, an archway is modeled by the equation y = -0.5x^2 + 3x, where y is the height in feet and x is the horizontal distance in feet. a laser is directed at the archway at an angle modeled by the equation -0.5x + 2.42y = 7.65 such that the beam crosses the archway at points a and b. at what height from the ground are the points a and b?

Answers: 2

Show answers

Answers

Check the picture below.

so, the distance from the ground to points A and B are those two green lines, namely the y-coordinate of their intersection, or solution.

$\bf \begin{cases}
\boxed{y}=-0.5x^2+3x\\
-0.5x+2.42y=7.65\\
----------------\\
-0.5x+2.42\left( \boxed{-0.5x^2+3x} \right)=7.65
\end{cases}
\\\\\\
-0.5x-1.21x^2+7.26x=7.65\implies -1.21x^2+6.76x=7.65
\\\\\\
0=1.21x^2-6.76x+7.65
\\\\\\
~~~~~~~~~~~~\textit{quadratic formula}
\\\\
0=\stackrel{\stackrel{a}{\downarrow }}{1.21}x^2\stackrel{\stackrel{b}{\downarrow }}{-6.76}x\stackrel{\stackrel{c}{\downarrow }}{+7.65}
\qquad \qquad 
x= \cfrac{ - b \pm \sqrt { b^2 -4 a c}}{2 a}$

anyhow, if we run the quadratic formula on those coefficients, we'll end up with x ≈ 4.01023060106514842416, and x ≈ 1.57654625843898380724.

now, what's the y-coordinate for each? well, we can just plug that on say the first equation.

$\bf y=-0.5(4.0102306010651484)^2+3(4.0102306010651484)
\\\\\\
y\approx 3.9897170663357744678\\\\
-------------------------------\\\\
y=-0.5(1.5765462584389838)^2+3(1.5765462584389838)
\\\\\\
y\approx 3.486889722817971861$

Im giving 15 points on a movie set, an archway is modeled by the equation y = -0.5x^2 + 3x, where y

Im giving 15 points on a movie set, an archway is modeled by the equation y = -0.5x^2 + 3x, where y

Answer from: makaylahendrix8808

The points of intersection are the points where the (x, y) values satisfy both equations. Since we're interested in the y-values, we can use the second equation to substitute for x in the first equation.

From the second equation,
x - 4.84y = -15.30 . . . . . multiply the second equation by -2
x = 4.84y -15.30 . . . . . . add 4.84y to get an expression for x

Now, we can substitute this expression for x into the first equation.
y = -0.5(4.84y -15.30)² +3(4.84y -15.30)
y = -0.5(23.4256y² -148.104y +234.09) + 14.52y -45.90
Subtracting the right side from the whole equation we get
11.7128y² -87.572y +162.945 = 0

This equation may be best solved using the quadratic formula. For
ax²+bx+c = 0
it tells you the solutions are
x = (-b ±√(b²-4ad))/(2a)

For our equation, with a=11.7128, b=-87.572, c=162.945, the solutions are
y = (87.572 ±√((-87.572)²-4(11.7128)(162.945)))/(2·11.7128)
y = (87.572 ±√34.6864)/23.4256
y ≈ 3.487 ft, 3.990 ft

Points A and B are 3.487 ft and 3.990 ft above the ground.

_____
The numbers might be easier to work with if you solve the second equation for y, then equate the two y expressions. This gives you a quadratic in x. Once you find the solutions for x, you then need to put them back into the equation for y to find the y-values of points A and B. The method used here gives you the answer directly, even if the numbers are a little longer.

Of course, a graphing calculator can help you avoid all the algebra. It will give you the points of intersection without much trouble.
Im giving 15 points on a movie set, an archway is modeled by the equation y = -0.5x^2 + 3x, where y

Answer from: Quest

2,600 divided by 80 = 32.5

step-by-step explanation:

Answer from: Quest

560

step-by-step explanation:

giggidy

Another question on Mathematics

Mathematics, 21.06.2019 21:30

Apool measures 100 meters by 100 meters a toddler inside the pool and trows a ball 60 centimeters from one edge of the pool.how far is the ball from the opposite edge of the pool

Answers: 1

Answer

Mathematics, 21.06.2019 23:00

Of the 304 people who attended a school play, 5/8 were students. how many of the people who attended were students.

Answers: 1

Answer

Mathematics, 22.06.2019 01:40

Astandard deck of cards contains 52 cards. one card is selected from the deck. (a) compute the probability of randomly selecting a diamond or heart. (type an integer or a decimal rounded to three decimal places as needed.) (b) compute the probability of randomly selecting a diamond or heart or club. (type an integer or a decimal rounded to three decimal places as needed.) (c) compute the probability of randomly selecting queen or club. (type an integer or a decimal rounded to three decimal places as needed.)

Answers: 2

Answer

Mathematics, 22.06.2019 03:30

The area of a square floor on a scale drawing is 64 square centimeters, and the scale drawing is 1 centimeter: 3 ft. what is the area of the actual floor? what is the ratio of the area in the drawing to the actual area? the area of the actual floor is square feet. the ratio of the area in the drawing to the actual area is 1 square centimeter: square feet.

Answers: 3

Answer

You know the right answer?

Im giving 15 points
on a movie set, an archway is modeled by the equation y = -0.5x^2 + 3x, wh...

Questions