Since x term is squared, solve for form (x-h)^2=4p(y-k)
x term is squraed so it opens down or up
vertex is (h,k)
p is distance from vertex to focus and from vertex to directix
if p>0, then dirextix is below vertex
if p<0, directix is above vertex
complete the square
y=(-1/6x^2+7x)-80
y=(-1/6)(x^2-42x)-80
take 1/2 of linear coefient and squer it and add negative and positive inside
-42/2=-21, (-21)^2=441
y=(-1/6)(x^2-42+441-441)-80
factor perfect square the square
y=(-1/6)((x-21)^2-411)-80
expand
y=(-1/6)(x-21)^2+73.5-80
y=(-1/6)(x-21)^2-6.5
add 6.5 to both sid
y+6.5=(-1/6)(x-21)^2
times both sides by -6
-6(y+6.5)=(x-21)^2
(x-21)^2=-6(y+6.5)
(y-21)^2=4(-3/2)(y-(-6.5))
vertex is
-3/2<0 so directix is above
it is -3/2 or 1.5 units above the vertex
up is y so
-6.5+1.5=-5
the directix is y=-5
Answer:
4π
Step-by-step explanation:
The period represents the distance, horizontally, between two matching points on the curve, such as two peaks. We can see that one peak is at π, and another at 5π, with the difference being 5π-π = 4π as our period
For the first brackets, You can subtract 4 from 8 and that makes 4. For the second bracket, you can add -8 and 4 which gets you 4. You have simplified what is inside the brackets, now you can add them together. 4 and 4 equals 8. So the answer is 8. You can figure it out other ways also
His average speed during his sprints would be 2.12 minutes.
I got this answer by adding all of the minutes for each sprint and then dividing them by the number of total sprints.
Answer:
Step-by-step explanation:
Total number of students = 15
Time given to each student to present their item= 3 minutes
So, total time for the show can be calculated as minutes