Answer:
The maximum height of the projectile is 90 ft
Step-by-step explanation:
Here, we want to get the maximum height reached by the projectile
The answer here will be the y-coordinate value of the vertex form of the given equation
so firstly, we have to write the equation in the vertex form
We have this as;
y = -16t^2 + 64t + 26
That will be;
y = a(x-h)^2 + k
y = -16(x-2)^2 + 90
where the vertex of the equation is;
(-h,k)
K
in this case is 90 and thus, that is the maximum height of the projectile
(x-h)^2=4P(y-k), vertex is (h,k)
P is distance from vertex to directix
remember to subtract P from the y value of the vertex (p-k) and that y value is the directix, y=p-k
nut
ok so one way is to just graph them on a graphing utility
remember if the graph opens up, then the directix is below that
or we can convert to 4P(y-k)=(x-h)^2 form where P is distance from directix
I will only convert the 1st one fully, you should be able to do the rest
1. y=-x^2+3x+8
multiply both sides by -1 since we don't like the x^2 term negative
-y=x^2-3x-8
add8 to both sides
-y+8=x^2-3x
take 1/2 of linear coeficient and square it and add to both sides
-3/2=-1.5
(-1.5)^2=2.25
-y+10.25=x^2-3x+2.25
factor perfect square
-y+10.25=(x-1.5)^2
force undistribute -1 in left side
(-1)(y-10.25)=something, we don't care anymore for now
factor out a 4 in -1
4(-1/4)(y-10.25)
k=10.25
p=-1/4=-0.25
directix=k-p=10.25-(-0.25)=10.5
directix is y=10.5
basically completee the square with x and find P by force factoring a 4 out
2. directix: y=-1.75
3. directix: y=1.5
4. directix: y=17.25
5. d: -37.5
6. d: 9.25
7. d=2.625
order them yourself
Answer:
Did you find the answer?
Step-by-step explanation:
<span> -k - (-8k) = -k + 8k = 7k</span>
Answer:
$43.20
Step-by-step explanation:
If each family member buys one ticket and one lunch, then for ticket price t we have the total expenditure as ...
5(t +6.50) = 248.50
t +6.50 = 49.70 . . . . . divide by 5
t = 43.20 . . . . . . . . . . subtract 6.50
The price of each train ticket is $43.20.
