Tutors Answer Your Questions about Quadratic Equations (FREE)
Question 437300: 1. Suppose you are in the stands of a World Series baseball game. A foul ball is hit your way – you catch the ball, but in a moment of insanity (or too much beer), you throw the ball up in the air.
When a ball is thrown vertically upward from a height of 5 feet with an initial velocity of 96 ft/sec, its height can be modeled by a quadratic equation.
height=-16t^2+96t+5
a. Does the graph of this equation open up or down? How did you determine this? The ball graph of the equation opened down ward. I determined this because the coefficient of the highest power is negative.
b. Describe how the ball travels – what is the shape of its path? the path that the ball travels is upward into the air and bows slightly when returning downward.
c. Use the quadratic formula to determine how long it takes for the ball to land. Calculate to the decimal approximation for your answer.
Note. Your answer, t, will be in terms of seconds.
d. After how many seconds will the ball reach its maximum height?
e. What is the height that the ball will reach?
f. What is the point of the vertex of the quadratic equation? How does this number relate to your answers in parts d. and e?
g. How many solutions are there to the equation ? How do you know?
h. What do the solutions represent? Is there a solution that does not make sense? Why?
Click here to see answer by stanbon(75887)  |
Question 437547: Aki's bicycle designs has determined that when x hundred bikes are built, the average cost per bicycle is given by C(x)=0.2x^2-0.4x+5.998, where C(x) is in hundreds of dollars. How many bikes should the shop build to minimize the average cost per bike?
Click here to see answer by edjones(8007)  |
Question 438013: Carl wants to construct three rectangular dog-training arenas side-by-side using a total of 340 feet of fencing. What should the overall length and width be in order to maximize the area of the three combined arenas? (let x represent the width).
I used the formula A=3xy to find the area and I came up with:
A=3x(340-4x)/6
I also used the formula P=4x+6y to find the perimeter and I came up with:
Y=(340-4x)/6
I don't know where to go from here.
Click here to see answer by solver91311(24713)  |
Question 438360: I am working on a quadratic equation. A=3, B=6, C=-4. I have worked the problem out to the point that x=-6 + sqrt 84. I reduced the problem to -6+2(sq rt 21) over 6. The text key says that it can be further reduced to -3+sqrt21 over 3, but I just cannot see how they get from my answer to theirs. Can you explain?
Click here to see answer by nerdybill(7384)  |
Question 438428: How would you solve the problem:
The height of a ball is measured by the function h(t)=-16t^2+112t-64, where h(t) is measured in feet and t is time in seconds.
(a) Evaluate h(2) and explain what dependent and independent variables represent.
(b) What is the height of the ball at 3 seconds?
(c) When is the ball at a height of 128 ft.?
Click here to see answer by Alan3354(69443)  |
Question 438431: Solve the indicated variable. A=P(2+r)^2. r=? That should be the power of 2. I'm not sure how to start. I know I have to get the r by itself but the P is throwing me off. If the P wasn't there I would have squared both sides. Any help would be greatly appreciated.
Click here to see answer by Alan3354(69443) |
Question 438654: The question asks students to graph y=-x^2+4x+1 and to have all x intercepts and y intercepts labeled. I have figued out that the vertex is (2,5), the y intercept is (0,1) and I have worked out the problem to get points of (2,5) & (-1,-4) I am having an issue figurng out exactly what the points are when the lines cross the x axis. Thank you for your help.
Click here to see answer by stanbon(75887) |
Question 439340: I am no good at word problems, is there anyone who can help me with the problem below?
The cumulative number of car accidents from 2000 to 2010 can be modeled by the quadratic expression C= 25x^2 + 550x +7,300, where x=1 corresponds to 2000, x= 2 corresponds to 2001, and so on until x = 11 corresponds to 2010.
Find the number of car accidents in 2004 ?
Thank you so much.
Click here to see answer by jorel1380(3719)  |
Question 439340: I am no good at word problems, is there anyone who can help me with the problem below?
The cumulative number of car accidents from 2000 to 2010 can be modeled by the quadratic expression C= 25x^2 + 550x +7,300, where x=1 corresponds to 2000, x= 2 corresponds to 2001, and so on until x = 11 corresponds to 2010.
Find the number of car accidents in 2004 ?
Thank you so much.
Click here to see answer by stanbon(75887) |
Question 439434: 1. If a projectile is launched with an initial velocity of feet per second from an initial height of feet, then its height in feet is determined by the quadratic function where t is the time in seconds. When you graph the function you will have the parabolic shape where the maximum point is called the vertex. If a ball is tossed upward with velocity 64 feet per second from a height of 5 feet, the function to represent the height at any time t is given with the equation s(t)=-16t^2+64t+5
a) In how many seconds will the ball reach the maximum height? (5 pts)
b)What is the maximum height in feet that the ball reaches? (5 pts)
Click here to see answer by lwsshak3(11628) |
Question 439435: 2.The area of a rectangular tabletop is 6 square feet. If the width is 2 feet shorter than the length, then what are the dimensions? (You will need to use either completing the square or the quadratic formula. Round your answers with a calculator to 2 decimal places)
Click here to see answer by Gogonati(855)  |
Question 439522: Hello my name is ChristopherI am hoping you can help me on this HW problem...
Solve equation by putting in quadratic form (Use a U substitution)....?
Very confused could you please help me ? thankyou
4x^4-7x^2+3=0
Click here to see answer by stanbon(75887) |
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Older solutions: 1..45, 46..90, 91..135, 136..180, 181..225, 226..270, 271..315, 316..360, 361..405, 406..450, 451..495, 496..540, 541..585, 586..630, 631..675, 676..720, 721..765, 766..810, 811..855, 856..900, 901..945, 946..990, 991..1035, 1036..1080, 1081..1125, 1126..1170, 1171..1215, 1216..1260, 1261..1305, 1306..1350, 1351..1395, 1396..1440, 1441..1485, 1486..1530, 1531..1575, 1576..1620, 1621..1665, 1666..1710, 1711..1755, 1756..1800, 1801..1845, 1846..1890, 1891..1935, 1936..1980, 1981..2025, 2026..2070, 2071..2115, 2116..2160, 2161..2205, 2206..2250, 2251..2295, 2296..2340, 2341..2385, 2386..2430, 2431..2475, 2476..2520, 2521..2565, 2566..2610, 2611..2655, 2656..2700, 2701..2745, 2746..2790, 2791..2835, 2836..2880, 2881..2925, 2926..2970, 2971..3015, 3016..3060, 3061..3105, 3106..3150, 3151..3195, 3196..3240, 3241..3285, 3286..3330, 3331..3375, 3376..3420, 3421..3465, 3466..3510, 3511..3555, 3556..3600, 3601..3645, 3646..3690, 3691..3735, 3736..3780, 3781..3825, 3826..3870, 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