Tutors Answer Your Questions about Quadratic Equations (FREE)
Question 32000: Story Problem
The period T (time in seconds for one complete cycle) of a simple pendulum is related to the length L (in feet) of the pendulum by the formula 8T^2 = n^2L. If a child is on a swing with a 10-foot chain, then how long does it take to complete one cycle of the swing?
Textbook Elementary and Intermediate Algebra. Mark Dugopolski
ISBN: 13978-0-07-326862-0
Click here to see answer by stanbon(75887)  |
Question 32168: In dire need of help, I'm drowning and trying to stay afloat.
When using the quadratic formula to solve a quadratic equation (ax2 + bx + c = 0), the discriminant is b2 - 4ac. This discriminant can be positive, zero, or negative.
Create three unique equations where the discriminant is positive, zero, or negative. For each case, explain what this value means to the graph of y = ax2 + bx + c.
Click here to see answer by venugopalramana(3286) |
Question 31912: 2) For the function y = x2 - 4x - 5, perform the following tasks:
a) Put the function in the form y = a(x - h)2 + k.
b) What is the line of symmetry?
c) Graph the function using the equation in part a. Explain why it is not necessary to plot points to graph when using y = a (x – h)2 + k.
Show graph here.
Explanation of graphing.
d) In your own words, describe how this graph compares to the graph of y = x2?
Answer:
Click here to see answer by venugopalramana(3286) |
Question 31911: 2) For the function y = x2 - 4x - 5, perform the following tasks:
a) Put the function in the form y = a(x - h)2 + k.
b) What is the line of symmetry?
c) Graph the function using the equation in part a. Explain why it is not necessary to plot points to graph when using y = a (x – h)2 + k.
Show graph here.
Explanation of graphing.
d) In your own words, describe how this graph compares to the graph of y = x2?
Answer:
Click here to see answer by venugopalramana(3286) |
Question 32212: This is the problem that I have trouble solving. I have an idea of how to solve it but I am not sure where to beign to find the x cooridinates.
You are riding on a roller coaster whose path can be modeled by
y=.005x2(squared)-2x+200
where x and y are measured in feet. When t=0 sec, you are at the point (0,200) going downhill.
a. when t=4 sec, the y coordinate of your locations is 32. What is the x coordinate?
b. when t=4.23sec, the y coordinate of your location is 18. What is the y coordinate?
c.Use pythagorean theorem to approximate the lenght of the track between the two points.
d. what was the average speed betweem the two points?
Thanks.
Click here to see answer by stanbon(75887) |
Question 32267: 3) Suppose you throw a baseball straight up at a velocity of 64 feet per second. A function can be created by expressing distance above the ground, s, as a function of time, t. This function is s = -16t2 + v0t + s0
• 16 represents 1/2g, the gravitational pull due to gravity (measured in feet per second2).
• v0 is the initial velocity (how hard do you throw the object, measured in feet per second).
• s0 is the initial distance above ground (in feet). If you are standing on the ground, then s0 = 0.
a) What is the function that describes this problem?
Answer:
b)The ball will be how high above the ground after 1 second?
Answer:
Show work in this space.
c)How long will it take to hit the ground?
Answer:
Show work in this space.
d)What is the maximum height of the ball? What time will the maximum height be attained?
Answer:
Show work in this space.
Click here to see answer by venugopalramana(3286) |
Question 32268: When using the quadratic formula to solve a quadratic equation (ax2 + bx + c = 0), the discriminant is b2 - 4ac. This discriminant can be positive, zero, or negative.
Create three unique equations where the discriminant is positive, zero, or negative. For each case, explain what this value means to the graph of y = ax2 + bx + c.
Click here to see answer by venugopalramana(3286) |
Question 32509: Three peices of string measure 20 cm, 41 cm and 44 cm. if the same amount is cut off all three peices, the remaining peices can be formed into a right-angled triangle. What length should be cut from each peice of string?
Click here to see answer by stanbon(75887) |
Question 32563: A company determines that the cost C, in dollars of producing x tennis rackets is C= 32x+120,000. the revenue R in dollars, from selling all of the tennis racquets is R = x(200-0.01x).
How many rackets should the company manufacture and sell if the company wishes to earn a profit of at least $550.000?
Solution:
-0.01x^2+168x-670,000is >or= to 0
It says use the quadratic formula to find the approximate values of the inequality, but I keep coming up with a -under the radical sign and can't solve it. Can someone write out what I am doing wrong w/ finding the approximate values? The approximate critical values are supposed to be 6513.2 and 10,286.8, so the company should manufacture at least 6514 racquets but not more than 10,286 to produce the desired proffit. I am lost on how they are getting this answer.
Click here to see answer by stanbon(75887) |
Question 32495: The Empire State Bldg is 1250 ft tall. If an object thrown upward from the top of the building at an initial velocity of 35 ft per second, its height after "t" seconds after it is thrown is given by the
function h(t)= -16t^2+35t+1250. How long will it be before the oject hits the ground?
Click here to see answer by Fermat(136)  |
Question 32754: How would you solve the following using the quadratic formula - showing step by step? I know the book says the answer is 2 +- sqrt(2) /2.
However, I can't seem to come up with that. Here is the problem:
(3y-1)(2y-3)=y
Here's what I have so far:
= -(-12) +- sqrt((-12)^2 -4(6)(3) / 2(6)
= 12 +- sqrt(144-72) / 12
= 12 +- sqrt(72) / 12
= 12+- sqrt(36 *2) / 12
= 12 +- 6 sqrt(2) / 12
then what would follow? Thank you.
Click here to see answer by mukhopadhyay(490) |
Question 32740: Please ;') A right triangle is a triangle with one angle measuring 90°. In a right triangle, the sides are related by Pythagorean Theorem, where c is the hypotenuse (the side opposite the 90° angle). Find the hypotenuse when the other 2 sides’ measurements are 3 feet and 4 feet.
Click here to see answer by sarah_adam(201) |
Question 32675: This is my question:express each of the following in the form y = a(x - h)^2 + k.
Hence state the coordinate of the turning point and sketch the graph in each case:
a)x^2 - 2x + 3
b)x^2 - 8x +12
c)- x^2 + 4x + 1
d)x^2 +4x + 1
Can you show me the solution of these exercise.
Click here to see answer by kietra(57) |
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