Answer: ![\$10,\ \$5](https://tex.z-dn.net/?f=%5C%2410%2C%5C%20%5C%245)
Step-by-step explanation:
(a) Given
Sam charge $5 for each dog for a thirty minute walk
For an hour which is double the thirty minutes, it must be double of the same charge.
![\Rightarrow 2\times 5=\$10](https://tex.z-dn.net/?f=%5CRightarrow%202%5Ctimes%205%3D%5C%2410)
(b)Given
With $20, Christie sells 100 cups of lemonade with a quarter per cup charge
For 100 cup, she generate a revenue of
![\Rightarrow \dfrac{1}{4}\times 100\\\\\Rightarrow \$25](https://tex.z-dn.net/?f=%5CRightarrow%20%5Cdfrac%7B1%7D%7B4%7D%5Ctimes%20100%5C%5C%5C%5C%5CRightarrow%20%5C%2425)
So, she earns
that is , her profit is ![\$5](https://tex.z-dn.net/?f=%5C%245)
Answer:
4c^2+7c-5=0
4c^2+7c=5
4c^2+7c=5
4c^2+7c-5=0\quad :\quad c=\frac{-7+\sqrt{129}}{8},\:c=\frac{-7-\sqrt{129}}{8}\quad \left(\mathrm{Decimal}:\quad c=0.54472\dots ,\:c=-2.29472\dots \right)
Hope This Helps!!!
Answer:
x= ![-\frac{277}{18}](https://tex.z-dn.net/?f=-%5Cfrac%7B277%7D%7B18%7D)
Step-by-step explanation:
Using the critical point concept, it is found that a = -3 and b = 7.
<h3>What are the critical points of a function?</h3>
- The critical points of a function are the values of x for which:
![f^{\prime}(x) = 0](https://tex.z-dn.net/?f=f%5E%7B%5Cprime%7D%28x%29%20%3D%200)
In this problem, the function is:
![f(x) = x^3 + ax^2 + b](https://tex.z-dn.net/?f=f%28x%29%20%3D%20x%5E3%20%2B%20ax%5E2%20%2B%20b)
Hence, the derivative is:
![f^{\prime}(x) = 3x^2 + 2ax](https://tex.z-dn.net/?f=f%5E%7B%5Cprime%7D%28x%29%20%3D%203x%5E2%20%2B%202ax)
Then:
![f^{\prime}(x) = 0](https://tex.z-dn.net/?f=f%5E%7B%5Cprime%7D%28x%29%20%3D%200)
![3x^2 + 2ax = 0](https://tex.z-dn.net/?f=3x%5E2%20%2B%202ax%20%3D%200)
![x(3x + 2a) = 0](https://tex.z-dn.net/?f=x%283x%20%2B%202a%29%20%3D%200)
![x = 0](https://tex.z-dn.net/?f=x%20%3D%200)
![3x + 2a = 0](https://tex.z-dn.net/?f=3x%20%2B%202a%20%3D%200)
![3x = -2a](https://tex.z-dn.net/?f=3x%20%3D%20-2a)
![x = -\frac{2a}{3}](https://tex.z-dn.net/?f=x%20%3D%20-%5Cfrac%7B2a%7D%7B3%7D)
Since the critical point is at x = 2, we have that:
![-\frac{2a}{3} = 2](https://tex.z-dn.net/?f=-%5Cfrac%7B2a%7D%7B3%7D%20%3D%202)
![-2a = 6](https://tex.z-dn.net/?f=-2a%20%3D%206)
![2a = -6](https://tex.z-dn.net/?f=2a%20%3D%20-6)
![a = -3](https://tex.z-dn.net/?f=a%20%3D%20-3)
Then:
![f(x) = x^3 - 3x^2 + b](https://tex.z-dn.net/?f=f%28x%29%20%3D%20x%5E3%20-%203x%5E2%20%2B%20b)
Critical point at (2,3) means that when
, then:
![3 = 2^3 - 3(2)^2 + b](https://tex.z-dn.net/?f=3%20%3D%202%5E3%20-%203%282%29%5E2%20%2B%20b)
![8 - 12 + b = 3](https://tex.z-dn.net/?f=8%20-%2012%20%2B%20b%20%3D%203)
![b = 7](https://tex.z-dn.net/?f=b%20%3D%207)
You can learn more about the critical point concept at brainly.com/question/2256078