SOLUTION: Hello, I can someone help me with these problems. 1. Find the x and y intercepts, if any, if none exist, state F(x)=x^2-4x-18 2. Use formula 4.9t^2+vot=s to answer th

Algebra ->  Equations -> SOLUTION: Hello, I can someone help me with these problems. 1. Find the x and y intercepts, if any, if none exist, state F(x)=x^2-4x-18 2. Use formula 4.9t^2+vot=s to answer th      Log On


   

Question 247721: Hello,
I can someone help me with these problems.
1. Find the x and y intercepts, if any, if none exist, state
F(x)=x^2-4x-18

2. Use formula 4.9t^2+vot=s to answer the question;
A coin was tossed downward with an initial velocity of 30 meters per second (v0) at an altitude of 402 meters (s). Approximately how long does it take the coin to reach the ground
This is what I got no sure?
use 4.9t^2 + vot = s
a coin is tossed downward with an initial velocity of 30 meters per second(v0)at an altitude of 402 meters(s). approximately how long does it take the coin to reach the ground?
-4.9t^2-30t = -402 meters
4.9t^2 + 30t -402 = 0
Use Quadratic formula:
t = [-30 +- sqrt(900 - 4*4.9*-402)]/(9.8)
t = [-30 +- sqrt(8779.2)]/9.8
Positive solution:
t = [-30+93.7]/9.2
t = 6.924 seconds


3. Not sure of this one
Translate the problem into a pair of linear equations in 2 variables. Solve the equations using either elimination or substitution. State your answer for the specified variable.
Roberto invested some money at 7% and then invested $2000 more than twice this amount at 9%. His total annual income from the two investments was $2930. How much did he invest at 9%?
Thank you so much, I know you guys are great, I glad you are here to people like me that have been out of school for 15 years.
Tammy
Answer by Alan3354(69443) About Me  (Show Source):
You can put this solution on YOUR website!
1. Find the x and y intercepts, if any, if none exist, state
F(x)=x^2-4x-18
For the y-intercept, set x=0
y = -18 is the y-int.
For x, set y=0:
x^2-4x-18 = 0
Solved by pluggable solver: SOLVE quadratic equation (work shown, graph etc)
Quadratic equation ax%5E2%2Bbx%2Bc=0 (in our case 1x%5E2%2B-4x%2B-18+=+0) has the following solutons:

x%5B12%5D+=+%28b%2B-sqrt%28+b%5E2-4ac+%29%29%2F2%5Ca

For these solutions to exist, the discriminant b%5E2-4ac should not be a negative number.

First, we need to compute the discriminant b%5E2-4ac: b%5E2-4ac=%28-4%29%5E2-4%2A1%2A-18=88.

Discriminant d=88 is greater than zero. That means that there are two solutions: +x%5B12%5D+=+%28--4%2B-sqrt%28+88+%29%29%2F2%5Ca.

x%5B1%5D+=+%28-%28-4%29%2Bsqrt%28+88+%29%29%2F2%5C1+=+6.69041575982343
x%5B2%5D+=+%28-%28-4%29-sqrt%28+88+%29%29%2F2%5C1+=+-2.69041575982343

Quadratic expression 1x%5E2%2B-4x%2B-18 can be factored:
1x%5E2%2B-4x%2B-18+=+%28x-6.69041575982343%29%2A%28x--2.69041575982343%29
Again, the answer is: 6.69041575982343, -2.69041575982343. Here's your graph:
graph%28+500%2C+500%2C+-10%2C+10%2C+-20%2C+20%2C+1%2Ax%5E2%2B-4%2Ax%2B-18+%29


x = 2 + sqrt(22)
x = 2 - sqrt(22)
--------------------
2. Use formula 4.9t^2+vot=s to answer the question;
A coin was tossed downward with an initial velocity of 30 meters per second (v0) at an altitude of 402 meters (s). Approximately how long does it take the coin to reach the ground
This is what I got no sure?
use 4.9t^2 + vot = s
-----------------
s = -4.9t^2 - 30t + 402 takes it all into account
--------------------
Set s = 0 to find when it hits the ground.
-4.9t^2 - 30t + 402 = 0
Solved by pluggable solver: SOLVE quadratic equation (work shown, graph etc)
Quadratic equation ax%5E2%2Bbx%2Bc=0 (in our case -4.9x%5E2%2B-30x%2B402+=+0) has the following solutons:

x%5B12%5D+=+%28b%2B-sqrt%28+b%5E2-4ac+%29%29%2F2%5Ca

For these solutions to exist, the discriminant b%5E2-4ac should not be a negative number.

First, we need to compute the discriminant b%5E2-4ac: b%5E2-4ac=%28-30%29%5E2-4%2A-4.9%2A402=8779.2.

Discriminant d=8779.2 is greater than zero. That means that there are two solutions: +x%5B12%5D+=+%28--30%2B-sqrt%28+8779.2+%29%29%2F2%5Ca.

x%5B1%5D+=+%28-%28-30%29%2Bsqrt%28+8779.2+%29%29%2F2%5C-4.9+=+-12.6221821669043
x%5B2%5D+=+%28-%28-30%29-sqrt%28+8779.2+%29%29%2F2%5C-4.9+=+6.49973318731242

Quadratic expression -4.9x%5E2%2B-30x%2B402 can be factored:
-4.9x%5E2%2B-30x%2B402+=+%28x--12.6221821669043%29%2A%28x-6.49973318731242%29
Again, the answer is: -12.6221821669043, 6.49973318731242. Here's your graph:
graph%28+500%2C+500%2C+-10%2C+10%2C+-20%2C+20%2C+-4.9%2Ax%5E2%2B-30%2Ax%2B402+%29



a coin is tossed downward with an initial velocity of 30 meters per second(v0)at an altitude of 402 meters(s). approximately how long does it take the coin to reach the ground?
-4.9t^2-30t = -402 meters
4.9t^2 + 30t -402 = 0
Use Quadratic formula:
t = [-30 +- sqrt(900 - 4*4.9*-402)]/(9.8)
t = [-30 +- sqrt(8779.2)]/9.8
Positive solution:
t = [-30+93.7]/9.2
t = 6.924 seconds
------------------
The same method you used, ~0.4 seconds difference somewhere.
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3. Not sure of this one
Translate the problem into a pair of linear equations in 2 variables. Solve the equations using either elimination or substitution. State your answer for the specified variable.
Roberto invested some money at 7% and then invested $2000 more than twice this amount at 9%. His total annual income from the two investments was $2930. How much did he invest at 9%?
x = amount at 7%
y = amount at 9%
------------------
y = 2x + 2000
0.07x + 0.09y = 2930
---------------------
Sub for y
0.07x + 0.09*(2x+2000) = 2930
7x + 18x + 18000 = 293000
25x = 275000
x = $11,000
y = $24,000