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:
B
Step-by-step explanation:
The closed circle at - 
indicates that x can equal this value
The open circle at 
indicates that x cannot equal this value.
All values of x between - and are valid, thus
- ≤ x < → B
well, we know the common difference is -3, to go from the 4th term to the 8th term, we need to add "d" 4 times or namely 3+4(-3), likewise to go from the 13th term to the 19th term we have to add "d" 6 times, or namely -24 + 6(-3).
Hello,
10*10=100>89
n=89 is prime if it not divisible by all prime less then its square root
0<89<100 ==>0<√89<10
The primes to test are 2,3,5,7.
89 does not end with a even digit ==> 89 is not divisible by 2
8+9=17 if not divisible by 3 ==>89 is not divisible by 3
89 does not end with 0 or 5 ==>89 is not divisible by 5
3*8+1*9=33 is not divisible by 7 ==>89 is not divisible by 7
So: 89 is prime.
Y = 8x + 12
Now, plug in the 60.
60 = 8x + 12
Subtract 12 from both sides.
48 = 8x
Divide both sides by 8.
6 = x
Swap sides.
x = 6
It would take 6 hours for the pool to have 60 inches of water inside it.
