anonymous
  • anonymous
Been stuck for hours The function H(t) = −16t2 + 90t + 50 shows the height H(t), in feet, of a projectile after t seconds. A second object moves in the air along a path represented by g(t) = 28 + 48.8t, where g(t) is the height, in feet, of the object from the ground at time t seconds. Part A: Create a table using integers 1 through 4 for the 2 functions. Between what 2 seconds is the solution to H(t) = g(t) located? How do you know? (6 points) Part B: Explain what the solution from Part A means in the context of the problem. (4 points)
Mathematics
  • Stacey Warren - Expert brainly.com
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SOLVED
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katieb
  • katieb
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anonymous
  • anonymous
@mathstudent55
anonymous
  • anonymous
Anybody got an idea? I'm basically just needing help on part A.
mathstudent55
  • mathstudent55
Start by evaluating both functions at t = 1, t = 2, t = 3, t = 4

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anonymous
  • anonymous
16 90 28 48?
anonymous
  • anonymous
@mathstudent55
mathstudent55
  • mathstudent55
How did you get 16?
mathstudent55
  • mathstudent55
H(t) = −16t2 + 90t + 50 Let t = 1. What do you get for H(1) ?
anonymous
  • anonymous
I just found it, idk how i got it, I guessed on it
anonymous
  • anonymous
How do i find h(1)
anonymous
  • anonymous
Like, i'm 100% lost on how I make these, I found some functions but idk how to graph them, can you explain?
mathstudent55
  • mathstudent55
H(t) = −16t2 + 90t + 50 To find H(1) you replace t with 1, and you evaluate the expression. H(1) = -16(1)^2 + 90(1) + 50
mathstudent55
  • mathstudent55
H(1) = -16 + 90 + 50 = 124 Now you need H(2). Replace t with 2 in the H(t) function and evaluate the right side. H(2) = -16(2^2) + 90(2) + 50
anonymous
  • anonymous
How do I evaluate it? Like how'd you get that
anonymous
  • anonymous
1 is H(1) = -16 + 90 + 50 = 124, I need to solve for 2,3, and 4?
anonymous
  • anonymous
@mathstudent55
anonymous
  • anonymous
I need to find 2,3,4 but how?
mathstudent55
  • mathstudent55
Evaluating an expression is just using arithmetic to calculate what it is equal to.
mathstudent55
  • mathstudent55
For t = 2, you get H(2) = -16(2^2) + 90(2) + 50 What is the right side equal to?
anonymous
  • anonymous
H(2) = -16(2v2) + 180 + 50?
mathstudent55
  • mathstudent55
If I asked you what is 2 + 2, would you answer 2 + 2, or would you answer 4?
anonymous
  • anonymous
H(2) -16^4 + 230?
mathstudent55
  • mathstudent55
good, keep going
anonymous
  • anonymous
H(2) - 64 + 230?
mathstudent55
  • mathstudent55
good
mathstudent55
  • mathstudent55
H(2) = - 64 + 230?
anonymous
  • anonymous
So it'd be H(2) = 294, or since 64 is negative would it be H(2) = 166?
mathstudent55
  • mathstudent55
H(2) = 166
mathstudent55
  • mathstudent55
So far we have: H(1) = 124 H(2) = 166 Now we still need H(3) and H(4) for function H(t) H(t) = −16t2 + 90t + 50 H(3) = -16(3)^2 + 90(3) + 50
anonymous
  • anonymous
H(3) = -96 + 320
anonymous
  • anonymous
H(3) = 224?
mathstudent55
  • mathstudent55
No. First do 3^2
anonymous
  • anonymous
9
mathstudent55
  • mathstudent55
H(3) = -16(3)^2 + 90(3) + 50 H(3) = -16(9) + 90(3) + 50 Now do -16 * 9. You already have 90(3) + 50 = 320
anonymous
  • anonymous
-144
anonymous
  • anonymous
-144 + 270 + 50 right?
mathstudent55
  • mathstudent55
yes
anonymous
  • anonymous
H(3)=176?
mathstudent55
  • mathstudent55
Correct. Now we need H(4) H(4) = -16(4)^2 + 90(4) + 50 Remember to start with 4^2 then multiply that by -16
anonymous
  • anonymous
156?
mathstudent55
  • mathstudent55
I got 154 H(4) = -16(4)^2 + 90(4) + 50 = -256 + 360 + 50 =
mathstudent55
  • mathstudent55
Ok. We have now function H(t) evaluated at t = 1, t = 2, t = 3, t = 4. Now we need to do the same for function g(t)
anonymous
  • anonymous
Four more for g(t)?
anonymous
  • anonymous
Alright, what's the functions?
anonymous
  • anonymous
You there math?
mathstudent55
  • mathstudent55
The g(t) function is simpler. Just multiply the number (1, 2, 3, 4) by 48.8, then add to 28. g(t) = 28 + 48.8t g(1) = 28 + 48.8(1) = g(1) = 28 + 48.8(2) = g(1) = 28 + 48.8(3) = g(1) = 28 + 48.8(4) =
anonymous
  • anonymous
g(1) =76.8 g(2)=125.6 g(3)= 174.4 g(4)= 223.2
mathstudent55
  • mathstudent55
Correct. Great job on function g(t). Now we place all values in a table like part A asks for. |dw:1437421534524:dw|
anonymous
  • anonymous
Great, now that the graph's done what now? It says something about what 2 seconds match, or something
mathstudent55
  • mathstudent55
Part A asks to look at the table and see between which two times the functions H and g have the same value.
mathstudent55
  • mathstudent55
|dw:1437421963065:dw|
mathstudent55
  • mathstudent55
Notice that at t = 3, H = 176 and g = 174.4, H is higher, but at t = 4, H = 154, and g = 223.2, g is higher. That means at some time between 3 and 4, the functions must have the same value.
anonymous
  • anonymous
I noticed, so that's the answer it requires?
mathstudent55
  • mathstudent55
The answer to part A is that the objects are at the same height sometime between 3 and 4 seconds.
mathstudent55
  • mathstudent55
Then the answer to part B is that the objects hit each other at that time between 3 and 4 seconds when their paths cross in the air.
anonymous
  • anonymous
Thank you so much, I honestly would've never figured out how to work this problem. Thanks for the help :))
mathstudent55
  • mathstudent55
You are welcome.

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