Answer: f(x) = -0.016x² + 1.6x
Step-by-step explanation:
If the lenght of the road over the arch is 100m, we can consider a coordinate plane and say that the road starts at point (0,0) and finishes at (100,0). The vertice of the parabola is at point (50,40), because the maximum height is 40 and it is always in the middle point of the roots.
So, we have
(0,0) (50,40) (100,0)
A quadratic function is always on the form: f(x) = ax² + bx + c
0 = a0² + b0 + c
40 = a50² + b50 + c
0 = a100² + b100 + c
0 = a0² + b0 + c → c = 0 ∴
40 = a50² + b50
0 = a100² + b100
_________________________
2500a + 50b = 40 (*2)
10000a + 100b = 0
_________________________
5000a + 100b = 80
10000a + 100b = 0 (-)
__________________________
-5000a = 80
-a=80/5000
a=-0.016
∴
2500a + 50b = 40
2500.(-0.016) + 50b = 40
-40 + 50b = 40
50b = 80
b = 80/50
b = 1.6
This way f(x) = -0.016x² + 1.6x
Answer:
Definetely, it is reasonable. You may assume that a pet as a companionship will help the elderly feel more comfortable and therefore, happy. There are a few problems tough:
- There is no practical way of meassuring 'happiness'.
- Sometimes, the correlations of two factors may be a coincidence. Scientist should always consider this when they try to claim something byusing some backup logic, like we did.
- Even tough the statement makes some sense, you need to be aware that maybe is not completly positively correlated. Maybe having 20 more pets does not make an elderly happy if it alredy had 1 or 2.
D, because there are several students that are in your school. There would be many different answers.
Answer:
a. $45.86
b. $43.87
c. Percentage change = -4.40%)
Step-by-step explanation:
a. Let the price of share at the beginning of first year be represented with X
Now, Price of company's share dropped by 3.50% at the end of first year.
So, Price of share at the end of first year = x - 3.5% of x
= x - 0.035x
= 1x - 0.035x
= 0.965x
But it is equal to $44.25
=> 0.965x = 44.25
x = 44.25 / 0.965
x = 45.8549223
x = $45.86
b. During second year price of share decreased by $1.99. Therefore, Price of share at the end of second year = $45.86 - $1.99 = $43.87
c. Percentage change in the price of shares over two years = {(45.86 - 43.87)/45.86} *100
= (1.99/45.86)*100
= 0.04339294 * 100
= 4.40%
Now, as price of shares has dropped, the percentage change will be negative. (Δ% = -4.40%)
