Answer:
9 minutes
Step-by-step explanation:
Answer:
Step-by-step explanation:
a. Since the parabola is compressed by a factor of 1/3 we can state:
- a parabola is written this way : y=(x-h)²+k
- h stands for the translation to the left ⇒ 2*3=6
- k for the units down ⇒4*3=12
So the equation is : y=(x-6)²+12
b.Here the parabola is stretched by a factor of 2 so we must multiply by 1/2
- We khow that a parabola is written this way : y=(x-h)²+k
- (h,k) are the coordinates of the vertex
- the maximum value is 7*0.5=3.5
- we khow tha the derivative of a quadratic function is null in the maximum value
- so let's derivate (x-h)²+k= x²+h²-2xh+k
- f'(x)= 2x-2h h is 1 since the axe of simmetry is x=1
- f'(x)=2x-2 ⇒2x-2=0⇒ x= 1
- Now we khow that 1 is the point where the derivative is null
- f(1)=3.5
- 3.5=(x-1)²+k
- 3.5= (1-1)²+k⇒ k=3.5
So the equation is : y=(x-1)²+3.5
7.
the maximum height is where the derivative equals 0
- h= -5.25(t-4)²+86
- h= -5.25(t²-8t+16)+86
- h=-5.25t²+42t-84+86
- h=-5.25t²+42t+2
Let's derivate it :
- f(x)= -10.5t+42
- -10.5t+42=0
- 42=10.5t
- t= 42/10.5=4
When the height was at max t=4s
- h(max)= -5.25(4-4)²+86 = 86 m
h was 86m
We will find out 7% of 25.
7/100*25
=1.75 %
Therefore, 1.75% of Janie's class has blue eyes.
HARRY POTTER FOREVER! : P
Answer:
8g = 12 + 28
g = 5 packs
Step-by-step explanation:
Share of the sticks of gum
Manuela = 12 sticks
Sinah = 28 sticks
There are 8 sticks in each pack
g = number of packs of gum that sinah bought?
g × 8 sticks = 12 sticks + 28 sticks
8g = 40
Divide both sides by 8
g = 40 / 8
g = 5 packs
So you want to make it: total distance (d) = rate (r) × total time (t), solving for r: r = d / t
r = (420mi) / (3h+214h), r = 420mi / 217h
r = 1.935mi/h = 1.94mi/h
