Answer: ![f(x)=2x^2+5](https://tex.z-dn.net/?f=f%28x%29%3D2x%5E2%2B5)
Step-by-step explanation:
First integrate f'(x) so we can find the funtion f(x):
![4\int\limits {x} \, dx =4[\frac{1}{2} x^2]=2x^2+C=f(x)](https://tex.z-dn.net/?f=4%5Cint%5Climits%20%7Bx%7D%20%5C%2C%20dx%20%3D4%5B%5Cfrac%7B1%7D%7B2%7D%20x%5E2%5D%3D2x%5E2%2BC%3Df%28x%29)
The initial conditions say that when x = 0, the function equals 5. Let's write that down:
![f(0)=5=2(0^2)+C=C](https://tex.z-dn.net/?f=f%280%29%3D5%3D2%280%5E2%29%2BC%3DC)
Therefore, the integration constant 'C' must equal 5. This means that our function is:
![f(x)=2x^2+5](https://tex.z-dn.net/?f=f%28x%29%3D2x%5E2%2B5)
Answer:
see the explanation
Step-by-step explanation:
we have the quadratic equation
![y=-16x^{2} +32x-10](https://tex.z-dn.net/?f=y%3D-16x%5E%7B2%7D%20%2B32x-10)
This is a vertical parabola open downward
The vertex is a maximum
Find the x-intercepts of the quadratic equation
The x-intercepts are the values of x when the value of y is equal to zero
so
For y=0
![-16x^{2} +32x-10=0](https://tex.z-dn.net/?f=-16x%5E%7B2%7D%20%2B32x-10%3D0)
Solve the quadratic equation
The formula to solve a quadratic equation of the form
is equal to
![x=\frac{-b(+/-)\sqrt{b^{2}-4ac}} {2a}](https://tex.z-dn.net/?f=x%3D%5Cfrac%7B-b%28%2B%2F-%29%5Csqrt%7Bb%5E%7B2%7D-4ac%7D%7D%20%7B2a%7D)
in this problem we have
so
![a=-16\\b=32\\c=-10](https://tex.z-dn.net/?f=a%3D-16%5C%5Cb%3D32%5C%5Cc%3D-10)
substitute in the formula
![x=\frac{-32(+/-)\sqrt{32^{2}-4(-16)(-10)}} {2(-16)}](https://tex.z-dn.net/?f=x%3D%5Cfrac%7B-32%28%2B%2F-%29%5Csqrt%7B32%5E%7B2%7D-4%28-16%29%28-10%29%7D%7D%20%7B2%28-16%29%7D)
![x=\frac{-32(+/-)\sqrt{384}} {-32}](https://tex.z-dn.net/?f=x%3D%5Cfrac%7B-32%28%2B%2F-%29%5Csqrt%7B384%7D%7D%20%7B-32%7D)
![x=\frac{-32(+/-)8\sqrt{6}}{-32}](https://tex.z-dn.net/?f=x%3D%5Cfrac%7B-32%28%2B%2F-%298%5Csqrt%7B6%7D%7D%7B-32%7D)
![x=\frac{-32(+)8\sqrt{6}}{-32}=\frac{32(-)8\sqrt{6}}{32}=0.39\ sec](https://tex.z-dn.net/?f=x%3D%5Cfrac%7B-32%28%2B%298%5Csqrt%7B6%7D%7D%7B-32%7D%3D%5Cfrac%7B32%28-%298%5Csqrt%7B6%7D%7D%7B32%7D%3D0.39%5C%20sec)
![x=\frac{-32(-)8\sqrt{6}}{-32}=\frac{32(+)8\sqrt{6}}{32}=1.61\ sec](https://tex.z-dn.net/?f=x%3D%5Cfrac%7B-32%28-%298%5Csqrt%7B6%7D%7D%7B-32%7D%3D%5Cfrac%7B32%28%2B%298%5Csqrt%7B6%7D%7D%7B32%7D%3D1.61%5C%20sec)
therefore
This parabola has two x-intercepts representing the times when the dolphin's height above water is zero feet
Answer:
The correct answer is 27
Step-by-step explanation:
- 5a - b
- 5(-6) - 3
30 - 3
= 27
Hopes this can help
<span>Two equations that have the same solution are called equivalent equations e.g. 5 +3 = 2 + 6. And this as we learned in a previous section is shown by the equality sign =. An inverse operation are two operations that undo each other e.g. addition and subtraction or multiplication and division. You can perform the same inverse operation on each side of an equivalent equation without changing the equality.</span>
Answer:
1.1,2,5,8
2.2,3,4,5
3.-7,10,15
Step-by-step explanation:
hope help