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
Answer:
128 students in total
Step-by-step explanation:
25/100 = 1/4
1/4 = 32/ x
1 x 32
Answer:
The property that was used in step 1 was the distributive property.
The property that was used in step 2 was the subtraction property of equality.
The property that was used in step 3 was the division property of equality.
Step-by-step explanation:
Answer:the equation is 200 + 10x
Step-by-step explanation:
The formula for simple interest is expressed as
I = PRT/100
Where
P represents the principal or initial amount deposited into the account.
R represents interest rate on the principal
T represents time in years
I = interest after t years
From the information given
T = x years
P = $200
R = 5%
Therefore
I = (200 × 5 × x)/100
I = 1000x/100
I = 10x
Therefore, the equation representing the total amount of money that would be in the account after x years would be
200 + 10x
