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Pandemonium
 one year ago
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 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?
A. 1.5 feet and 3.5 feet
B. 1.5 feet and 4 feet
C. 3.5 feet and 4 feet
D. 4 feet and 4 feet
Pandemonium
 one year ago
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 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? A. 1.5 feet and 3.5 feet B. 1.5 feet and 4 feet C. 3.5 feet and 4 feet D. 4 feet and 4 feet

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mathmate
 one year ago
Best ResponseYou've already chosen the best response.1Have you started thinking about It?

Pandemonium
 one year ago
Best ResponseYou've already chosen the best response.0ive tried solving it but i dont understand on how to start this

mathmate
 one year ago
Best ResponseYou've already chosen the best response.1To solve ANY math word problem, you go with the first step 1. read the question, understand everything that is supplied. Read it three times if necessary to understand the question perfectly. Then write a summary of the given information. Can you do that now?

Pandemonium
 one year ago
Best ResponseYou've already chosen the best response.0so look at the equation given and then read the question and what i need to find?

mathmate
 one year ago
Best ResponseYou've already chosen the best response.1After having fully understood the question, then 1. write a summary of the given information

Pandemonium
 one year ago
Best ResponseYou've already chosen the best response.0So i understand the question and its asking for me to find the height of a cross beam that crosses through points A and B

mathmate
 one year ago
Best ResponseYou've already chosen the best response.1I would put the summary like this: Given: Equation of arch : y=0.5x^2+3x Equation of beam: 0.5x + 2.42y = 7.65, or \(y=\frac{0.5x+7.65}{2.42} Need to find intersection points of arch and beam

mathmate
 one year ago
Best ResponseYou've already chosen the best response.1* \( \Large y=\frac{0.5x+7.65}{2.42}\)

mathmate
 one year ago
Best ResponseYou've already chosen the best response.1This way, you have a clear mind of what is mathematically needed, and don't have to worry about wordings. But do check that you have copied all the numbers correctly. From now on until the answer line, you are working with mathematics. The answer line is the \(last\) sentence of your solution that interprets the results of math calculations in the terms of the question.

Pandemonium
 one year ago
Best ResponseYou've already chosen the best response.0alright i have written down all the numbers correctly

Pandemonium
 one year ago
Best ResponseYou've already chosen the best response.0So from here on until we get to the answer line, will we only work with mathematics?

mathmate
 one year ago
Best ResponseYou've already chosen the best response.1Then we can proceed to the second step 2. Graph the curves/lines. Use a graphics calculator if your school allows it. If not, even better, use a sheet of paper and pencil. Can you draw that for me (use the "draw" button below). This step will help you find approximately the required answer, or check the final answer for gross mistakes.

Pandemonium
 one year ago
Best ResponseYou've already chosen the best response.0alright so what exactly am i suppose to draw?

mathmate
 one year ago
Best ResponseYou've already chosen the best response.1Draw the arch and the beam, approximately.

Pandemonium
 one year ago
Best ResponseYou've already chosen the best response.0so is it a triangle type or square?

Pandemonium
 one year ago
Best ResponseYou've already chosen the best response.0dw:1434978937794:dw

mathmate
 one year ago
Best ResponseYou've already chosen the best response.1An arch is a curve, and the beam is a line. Are you familiar with quadratic functions and linear functions?

Pandemonium
 one year ago
Best ResponseYou've already chosen the best response.0yea im familiar with it but i could never really understand it

Pandemonium
 one year ago
Best ResponseYou've already chosen the best response.0dw:1434979035876:dw

mathmate
 one year ago
Best ResponseYou've already chosen the best response.1That's the idea, but we have to put them in the context of the question.

Pandemonium
 one year ago
Best ResponseYou've already chosen the best response.0and would i do that?

mathmate
 one year ago
Best ResponseYou've already chosen the best response.1First, examine the equations. The arch is a quadratic function y=0.5x^2+3x the leading coefficient, or the coefficient of x^2, is 0.5. The negative sign means that the function is concave down, the way you drew it. The constant term (with no variable) is zero, means the function passes through the origin. If you complete the square, meaning writing it as y=0.5(x3)^2+4.5 It means that the maximum of the function is at x=3. So we end up with a graph like this: dw:1434979494256:dw

mathmate
 one year ago
Best ResponseYou've already chosen the best response.1Is that clear so far?

Pandemonium
 one year ago
Best ResponseYou've already chosen the best response.0yea im learning this now :D

mathmate
 one year ago
Best ResponseYou've already chosen the best response.1Good! Now we'll work on the beam. \(\Large y=\frac{0.5x+7.65}{2.42}\)

Pandemonium
 one year ago
Best ResponseYou've already chosen the best response.0so we plug in something to that x and solve it?

mathmate
 one year ago
Best ResponseYou've already chosen the best response.1Kind of, but we will first write this in slope intercept form and get rid of the fractions!

mathmate
 one year ago
Best ResponseYou've already chosen the best response.1So that makes the equation \(approximately\) y=0.207x+3.161

Pandemonium
 one year ago
Best ResponseYou've already chosen the best response.0ok then whats next?

mathmate
 one year ago
Best ResponseYou've already chosen the best response.1Can you sketch the line on the graph?

mathmate
 one year ago
Best ResponseYou've already chosen the best response.1I'll give you something for the vertical scale: dw:1434979999842:dw

mathmate
 one year ago
Best ResponseYou've already chosen the best response.1Yes, these are the points we're looking for.

mathmate
 one year ago
Best ResponseYou've already chosen the best response.1Recall that in the equation y=0.207x+3.161 3.161 is the yintercept 0.207 is the slope.

Pandemonium
 one year ago
Best ResponseYou've already chosen the best response.0so i draw i line from the 3 up and somewhere in between the 4.5 and 0 across?

mathmate
 one year ago
Best ResponseYou've already chosen the best response.1What you can do is to find the point where x=6, and joint the point with the yintercept. Point at yintercept (0,3.161), and the point at x=6 has y=0.207*6+3.161=4.4 So you just need to join the points (0,3.161) and (6,4.4) to locate the beam.

Pandemonium
 one year ago
Best ResponseYou've already chosen the best response.0dw:1434980631856:dw

mathmate
 one year ago
Best ResponseYou've already chosen the best response.1Not quite. The slope is positive 0.2, so the line cannot be decreasing. Also, the point on the right is (6,4.4), you have drawn (6,0) :( dw:1434980741403:dw I have drawn the dots, now you do "connect the dots". :)

Pandemonium
 one year ago
Best ResponseYou've already chosen the best response.0dw:1434980772402:dw

Pandemonium
 one year ago
Best ResponseYou've already chosen the best response.0i saw where i made the mistake Sorry bout that

mathmate
 one year ago
Best ResponseYou've already chosen the best response.1That looks good! Can you now estimate the values of x at the intersection points?

Pandemonium
 one year ago
Best ResponseYou've already chosen the best response.0dw:1434980899618:dw Are those the intersection points?

mathmate
 one year ago
Best ResponseYou've already chosen the best response.1Exactly! dw:1434980969153:dw Can you now read off the values of x at the intersection points, approximately, of course.

Pandemonium
 one year ago
Best ResponseYou've already chosen the best response.0ok so my estimate would be 1.4, 3.3 and then 3.9,4.1

mathmate
 one year ago
Best ResponseYou've already chosen the best response.1Good, so your estimates for would be 1.4 and 3.9, right?

Pandemonium
 one year ago
Best ResponseYou've already chosen the best response.0and thats close to the answer 1.5 and 4 feet

mathmate
 one year ago
Best ResponseYou've already chosen the best response.1You can always continue to solve algebraically the solution (which turn out to be close to 1.5765 and 4.0102) but the graphical solution is good enough for you to choose the multiple choice answers, right?

Pandemonium
 one year ago
Best ResponseYou've already chosen the best response.0so the answer should be B if im correct

mathmate
 one year ago
Best ResponseYou've already chosen the best response.1The graphical solution method is very powerful. Once you master it, you can solve nonlinear problems like this in one, maybe 2 minutes!

Pandemonium
 one year ago
Best ResponseYou've already chosen the best response.0hahaha this one took a long time :D

mathmate
 one year ago
Best ResponseYou've already chosen the best response.1Can you please repeat the answer with the values instead of the letters?

Pandemonium
 one year ago
Best ResponseYou've already chosen the best response.0B. 1.5 feet and 4 feet

mathmate
 one year ago
Best ResponseYou've already chosen the best response.1Yes, that is correct, since this one is the closest to your estimate of 1.4 and 3.9, right?

mathmate
 one year ago
Best ResponseYou've already chosen the best response.1Hope you practise the graphics method more when you have a chance!

Pandemonium
 one year ago
Best ResponseYou've already chosen the best response.0i will thanks so much @mathmate

mathmate
 one year ago
Best ResponseYou've already chosen the best response.1You're welcome, Pande! :)

Pandemonium
 one year ago
Best ResponseYou've already chosen the best response.0you helped me alot to learn that and get me a better understanding of it :D

mathmate
 one year ago
Best ResponseYou've already chosen the best response.1Yes, understanding is the key to learning math! Well done!

Pandemonium
 one year ago
Best ResponseYou've already chosen the best response.0ok im closing this down bc i have one question to do and this one involves linearquadratic system

mathmate
 one year ago
Best ResponseYou've already chosen the best response.1You can try it a similar way!
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