<span>Simplifying
2d + -5 = 17
Reorder the terms:
-5 + 2d = 17
Solving
-5 + 2d = 17
Solving for variable 'd'.
Move all terms containing d to the left, all other terms to the right.
Add '5' to each side of the equation.
-5 + 5 + 2d = 17 + 5
Combine like terms: -5 + 5 = 0
0 + 2d = 17 + 5
2d = 17 + 5
Combine like terms: 17 + 5 = 22
2d = 22
Divide each side by '2'.
d = 11
Simplifying
d = 11 </span>
Answer:
C=-3t+30
Step-by-step explanation:
C=-3t+30
Answer:
See below ↓
Step-by-step explanation:
We need to check the different time intervals to find the max. height
- t = 0 or 1 [both give same result]
- f(1) = -16(1) + 16(1) + 12 = 12 feet
2. t = 2
- f(2) = -16(2)² + 16(2) + 12 = -20 feet
⇒ Clearly as she is diving, her maximum height will be her initial height which is <u>12 feet</u>
⇒ To achieve this, it takes her <u>0 seconds</u> [initial height = no time needed]
<u>Taking f(x) = 0 [surface of water → just touching/hit the water]</u>
- 0 = -16x² + 16x + 12
- 4x² - 4x - 3 = 0
- 4x² - 6x + 2x - 3 = 0
- 2x(2x - 3) + 1(2x - 3) = 0
- (2x + 1)(2x - 3) = 0
- x is positive
- x = 3/2 = <u>1.5 seconds</u>
<u></u>
⇒ After 1 second, she is <u>12 feet</u> above the water
⇒ The diving board is <u>12 feet</u> above the water
In QUADRANT IV is the where ( 1 , -7 ) are located
Answer:
a. x = 1 b. 36 c. 36
Step-by-step explanation:
a. At the equilibrium point, D(x) = S(x)
(x - 7)² = x² + 4x + 31
Expanding, we ave
x² - 14x + 49 = x² + 4x + 31
collecting like terms
14x + 4x = 49 - 31
18x = 18
x = 18/18 = 1
b. Substituting x = 1 into D(x), we have
D(1) = (1 - 7)² = (-6)² = 36
c. Substituting x = 1 into S(x), we have
S(1) = 1² + 4(1) + 31 = 1 + 4 + 31 = 36
