T = 5, so after 5 years
p(t) = t^3 - 14t^2 + 20t + 120
Take derivative to find minimum:
p’(t) = 3t^2 - 28t + 10
Factor to solve for t:
p’(t) = (3t - 2)(t - 5)
0 = (3t - 2)(t - 5)
0 = 3t - 2
2 = 3t
2/3 = t
Plug 2/3 into original equation, this is a maximum. We want the minimum:
0 = t - 5
5 = t
Plug back into original:
5^3 - 14(5)^2 + 20(5) + 120
125 - 14(25) + 100 + 120
125 - 350 + 220
- 225 + 220
p(5) = -5
➡3x - ( 7 over 12)
➡ [12 (3x ) - 7 ] over 12
➡ ( 36x - 7 ) over 12
The missing word for this sentence is common
Have A Good Day :)
Answer:
Yes. The girls to boys ration is the same
Step-by-step explanation:
For skating
Girls to boys ratio = 12:14 = 6:7
For birthday party
Girls to boys ratio = 18:21 = 6:7
Answer:
x=1
Step-by-step explanation:
1. Complete the square on the right side of the equation.
5
(
x
−
1
)2
−
18
2. Use the vertex form, y
=
a
(
x
−
h
)
2
+
k
, to determine the values of a
, h
, and k
.
a=
5
h
=
1
k
=
−
18
3. Since the value of a is positive, the parabola opens up.
Opens Up
4. Find the vertex (
h
,
k
)
.
(
1
,
−
18
)
5. Find p
, the distance from the vertex to the focus.
1
/20
6. Find the focus.
7. (
1
,
−
359/
20
)
8. Find the axis of symmetry by finding the line that passes through the vertex and the focus.
ANSWER: x
=
1
