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# Line, parabola, hyperbola, or exponential?

Topic: How to write a linear function equation
July 19, 2019 / By Evelia
Question: ) In most businesses, increasing prices of products can negatively impact the number of customers. A bus company in a small town has an average number of riders of 800 per day. The bus company charges \$2.25 for a ride. They conducted a survey of their customers and found that they will lose approximately 40 customers per day for each \$.25 increase in fare. a) Let the number of riders be a function of the fare charged. Graph the function, identify the graph of the function (line, parabola, hyperbola, or exponential), find the slope of the graph, find the price at which there will be no more riders, and the maximum number of riders possible. Graph Type: What is the slope of the graph? b) The bus company has determined that even if they set the price very low, there is a maximum number of riders permitted each day. If the price is \$0 (free), how many riders are permitted each day? Answer: Show work in this space: c) If the bus company sets the price too high, no one will be willing to ride the bus. Beginning at what ticket price will no one be willing to ride the bus? Answer: Show work in this space: 3) It is approximately 480 miles from Los Angeles, California, to San Francisco, California. Allowing for various traffic conditions, a driver can average approximately 60 miles per hour. a) How far have you traveled after 3 hours? Answer: it takes a total of 8 hours to get there Show work in this space. b) How far have you traveled after 4 hours? Answer: d = 60(4) = Show work in this space. c) How far have you traveled after t hours (i.e., write a linear function that expresses the distance traveled, d, as a function of time, t). Answer: d) How far will you HAVE LEFT to travel to reach San Francisco after you have traveled 3 hours? Answer: Show work in this space. e) How far will you HAVE LEFT to travel to reach San Francisco after you have traveled 4 hours? Answer: Show work in this space. f) How far will you HAVE LEFT to travel to reach San Francisco after you have traveled t hours (i.e., write a linear function that expresses the distance to be traveled to reach San Francisco, s, as a function of time, t). Answer:

## Best Answers: Line, parabola, hyperbola, or exponential?

Coleen | 8 days ago
The equation is P = -160 x +1120, where P is the number of passengers and x is the bus fare. The slope of this straight line is -160. If the bus company charged 0 dallars the number of passengers would be 1,120. If the fare were 1120/160 = \$7.00 there would be zero passengers. a) rate X time = distance so 60*3 = 180 miles. 480/60 = 8 hours to get there assuming no stops. b) 4(60) = 240 miles c) d = 60t d) 480 -3(60) = 480 - 180 = 300 miles e) 480 -4(60) = 480 -240 = 240 miles f) 480 -60t
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We found more questions related to the topic: How to write a linear function equation

Originally Answered: Show that one can solve the equation x^3 +d =bx^2 by intersecting the hyperbola xy=d and the parabola y^2 +dx-?
y^2 +dx-db=0 --------------------------- 1 Substituting y = d/x ------------------------- 2, and simplifying we get d/x^2 +x -b = 0, multiplying by x^2, we get x^3 + d = bx^2 ------------------------------ 3 So if we can find a straight line with slope m which intersects both in same points or in points three of which are same we find the solution to the cubic equation. Consider a line y = mx +c ---------------- 4 Let the point of intersection with 1 be be (h, mh+c), we have (mh +c)^2 +dh - db = 0 or m^2 h^2 + 2mhc + c^2 + dh -db = 0 or m^2 h^2 + (2mc+d)h + c^2 -db = 0 This has two distinct roots if (2mc + d)^2 > 4m^2 * (c^2 -db) -------------- 5 Similarly, let (p, mp+c) be the point of intersection with 2, then p(mp+c) = d or mp^2 +cp -d = 0 This has two distinct roots if c^2 > -4md which is always true for md > 0 I wish to submit only this much as an answer for the time being
Originally Answered: Show that one can solve the equation x^3 +d =bx^2 by intersecting the hyperbola xy=d and the parabola y^2 +dx-?
Divine and Material intersect but in US. We as humans are the perfect examples of this phenomenon wherein the divine as a reflection and a spark within all of us (generally refered to as soul) intersects with our physical selves made of the elements. And our lifetimes are but that points in space where the divine and the material intersect. That cosmic instant is what we live and in which we learn and grow wise. Aint it great to be born in he human form? so lets be up and utilizing it to the best and spread love and peace and goodwill. Thanks

Belynda
for the 1st one, income is number of riders times price, so I = (800 - 40x)(2.25 + 0.25x), where x counts the number of \$0.25 price increases. That's a quadratic that opens downward (because of the - in front of the 40x). It crosses the x axis in 2 places. On the left, enough negative price increases drop the price to 0, and so there's no income. On the right, enough positive price increases drops the number of riders to 0. So questions about slope do not apply. Max income is halfway between the 2 x intercepts, easily solved for by letting I = 0. 0 = (800 - 40x)(2.25 + .25x) 800 = 40x x = 20 or 2.25 = -.25x x = -9. I'd do more for you but dinner, movie, wife are calling. Good luck.
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Adriane
math has a lot extra suitable application in life than maximum persons comprehend. as an occasion, architects might desire to be attentive to the slope to construct a staircase on the specific attitude or the assumption of perpendicular strains to construct a at present wall. did you be attentive to that in case you threw a ball into the air, its direction to the floor is a parabola? math is all around you. so in basic terms provide it a concept, and that i'm specific you will arise with some large examples.
👍 113 | 👎 -10

Originally Answered: Hyperbola word problem?
well the distance to the center of the tower is 150 feet from the bottom and 300 more feet till the top. if you want to find the radius from the center of the tower to one of the edges all you have to do is plug the y value into the equation, setting the midpoint of 150 to the origin. should be about 226 feet wide at the top of the tower ( x^2/90^2 = 300^2/130^2 +1 and solve for x). for the diameter just multiply the radius by 2. for the base of the tower plug in 150 for y again since the graph is symmetric it doesnt matter whether its positive or negative. when you plug this in for y you get about 137 feet for the radius. again multiply by two for your diameter.

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