1) The solution for m² - 5m - 14 = 0 are x=7 and x=-2.
2)The solution for b² - 4b + 4 = 0 is x=2.
<u>Step-by-step explanation</u>:
The general form of quadratic equation is ax²+bx+c = 0
where
- a is the coefficient of x².
- b is the coefficient of x.
- c is the constant term.
<u>To find the roots :</u>
- Sum of the roots = b
- Product of the roots = c
1) The given quadratic equation is m² - 5m - 14 = 0.
From the above equation, it can be determined that b = -5 and c = -14
The roots are -7 and 2.
- Sum of the roots = -7+2 = -5
- Product of the roots = -7
2 = -14
The solution is given by (x-7) (x+2) = 0.
Therefore, the solutions are x=7 and x= -2.
2) The given quadratic equation is b² - 4b + 4 = 0.
From the above equation, it can be determined that b = -4 and c = 4
The roots are -2 and -2.
- Sum of the roots = -2-2 = -4
- Product of the roots = -2-2 = 4
The solution is given by (x-2) (x-2) = 0.
Therefore, the solution is x=2.
Answer:
65 feet below sea level.
Step-by-step explanation:
With the information provided, we can create the following equation for the position of the sea lion (p)
p = 3x - 10
In this equation, x would be the final position of the seal when it caught the fish. Since we are told that the seal's position is 25 feet below sea level then we can plug in this value as x and solve for p...
p = (3 * 25) - 10
p = 75 - 10
p = 65
Finally, we can see that the sea lion's position is 65 feet below sea level.
Answer:
A) A[p(t)] = 36πt²
B) 7234.56 square units
Step-by-step explanation:
<u>Given functions</u>:
<u>Part A</u>
To find the area of the circle of spilled paint as a function of time, substitute the function p(t) into the given function A(p):
![\begin{aligned}A(p) & = \pi p^2\\\\ \implies A[p(t)] & = \pi [p(t)]^2\\& = \pi (6t)^2\\& = \pi 6^2 t^2\\& = 36\pi t^2\end{aligned}](https://tex.z-dn.net/?f=%5Cbegin%7Baligned%7DA%28p%29%20%26%20%3D%20%5Cpi%20p%5E2%5C%5C%5C%5C%20%5Cimplies%20A%5Bp%28t%29%5D%20%26%20%3D%20%5Cpi%20%5Bp%28t%29%5D%5E2%5C%5C%26%20%3D%20%5Cpi%20%286t%29%5E2%5C%5C%26%20%3D%20%5Cpi%206%5E2%20t%5E2%5C%5C%26%20%3D%2036%5Cpi%20t%5E2%5Cend%7Baligned%7D)
<u>Part B</u>
Given
Substitute the given values into the equation for A[p(t)} found in part A:
![\begin{aligned}A[p(8)] & = 36\pi t^2\\& = 36 \cdot 3.14 \cdot 8^2\\& = 36 \cdot 3.14 \cdot 64\\& = 113.04 \cdot 64\\& = 7234.56\:\: \sf square\:units\end{aligned}](https://tex.z-dn.net/?f=%5Cbegin%7Baligned%7DA%5Bp%288%29%5D%20%26%20%3D%2036%5Cpi%20t%5E2%5C%5C%26%20%3D%2036%20%5Ccdot%203.14%20%5Ccdot%208%5E2%5C%5C%26%20%3D%2036%20%5Ccdot%203.14%20%5Ccdot%2064%5C%5C%26%20%3D%20113.04%20%5Ccdot%2064%5C%5C%26%20%3D%207234.56%5C%3A%5C%3A%20%5Csf%20square%5C%3Aunits%5Cend%7Baligned%7D)
Therefore, the area of spilled paint after 8 minutes if 7234.56 square units.
I would say the amount used would be at least 50 gallons because it makes most sense. Hope I helped :))
