Answer:
The final depth of Melissa is 14 meters below the surface
Step-by-step explanation:
In this kind of problems, involving directions, etc, usually one position is the positive direction and the other position is the negative direction.
In our problem, we suppose that the surface is the positivo zero, above the surface is the positive position(positive depth) and below the surface is the negative directions(negative depth).
The problem states that Melissa is 29 meters below the surface. So, her initial position is 29 meters in the negative direction, so it is equal to -29.
Then, the problem states that Melissa rises upward 15 meters. Upward is the positive direction, so she moved to the positive direction. It means that we are going to do -29+15 = -14 meters.
It means that the final depth of Melissa is 14 meters below the surface
When it doesn’t look like a U anymore and is upside down
Looking at an equation than when x is negative
The input is the hours and the out put is the cost.
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
If i read this correctly then the answer would be
57-12= 45
45/9= 5
The answer is 5
