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Nesterboy [21]
3 years ago
6

On a movie set, an archway is modeled by the equation y = -0.5x2 + 3x, where y is the height in feet and x is the horizontal dis

tance 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?
Mathematics
1 answer:
tino4ka555 [31]3 years ago
5 0
This question really just needs you to solve the system of equations.  These solutions will be the two points when the curve (archway) and the line (laser) intersect.

Let us express the laser line in terms of y.

-.5x+2.42y=7.65

2.42y=.5x+7.65

y=(.5x+7.65)/2.42

The curve is just y=-.5x^2+3x so when it intersects the curve, y=y and x=x so  we can say:

(.5x+7.65)/2.42=-.5x^2+3x

.5x+7.65=-1.21x^2+7.26x

1.21x^2-6.76x+7.65=0  using the quadratic for simplicity and solving for x:

x=(6.76±√8.6716)/2.42

x≈1.577, 4.010  (to nearest thousandth)

So the heights can found using the simple linear equation y=(.5x+7.65)/2.42 with those values of x...

y≈3.49, 3.99


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X2-3xy-5xy-7y2+4x2+8y2
Zepler [3.9K]

For this case we must simplify the following expression:

x ^ 2-3xy-5xy-7y ^ 2 + 4x ^ 2 + 8y ^ 2

We must add similar terms taking into account that:

  • Equal signs are added and the same sign is placed.
  • Different signs are subtracted and the major sign is placed.

(x ^ 2 + 4x ^ 2) + (- 3xy-5xy) + (- 7y ^ 2 + 8y ^ 2) =\\5x ^ 2-8xy + y ^ 2

Thus, the simplified expression is:

5x ^ 2-8xy + y ^ 2

Answer:

5x ^ 2-8xy + y ^ 2

4 0
3 years ago
Se deposita 4000 soles a una tasa de interés del 0,8% quincenas .¿Que interes producirá en cinco quincenas?
katen-ka-za [31]

Answer:

Interes= 162,58

Step-by-step explanation:

Dada la siguiente información:

Se deposita 4000 soles a una tasa de interés del 0,8% quincenas

<u>Primero, debemos calcular el valor final de la inversión:</u>

VF= [VP*( 1 + i)^n]

VF= 4.000*(1,008^5)

VF= 4.162,58

<u>Para calcular el interés ganado en 5 quincenas, debemos usar la siguiente formula:</u>

Interes= 4.162,58  - 4.000

Interes= 162,58

5 0
3 years ago
Give the domain and range.
Ymorist [56]

Answer:Graphs of inverse functions have a domain and range just like any other graph of a function. The domain of an inverse function is the range of the original, and the range of an inverse function is the domain of an original.

Step-by-step explanation:

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3 years ago
The question, “How many ways can 4 students be chosen from a class of 30 students?”, is a(n) _____.
Ahat [919]
The answer to your question is A 
7 0
3 years ago
Read 2 more answers
What is the domain of the function graphed below?
WITCHER [35]

From the graph, the domain of the function will be {x| x = −2,1}. Then the correct option is D.

<h3>What is an asymptote?</h3>

An asymptote is a line that constantly reaches a given curve but does not touch at an infinite distance.

From the graph, the domain of the function will be

The function is not defined for x = 2 and x = -1.

Then the domain will be

{x| x = −2,1}

Then the correct option is D.

More about the asymptote link is given below.

brainly.com/question/17767511

#SPJ1

5 0
1 year ago
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