Step-by-step explanation:
Given ![g'(x) = g^{-2}, x> 0\ g(1) = 0 \ and \ g(2) = 0](https://tex.z-dn.net/?f=g%27%28x%29%20%3D%20g%5E%7B-2%7D%2C%20x%3E%200%5C%20g%281%29%20%3D%200%20%5C%20and%20%5C%20g%282%29%20%3D%200)
To get g(x), we will have to integrate g'(x)
![g(x) = \int\limits {x^{-2}} \, dx\\ g(x) = \frac{x^{-2+1}}{-2+1} + C\\ g(x) = -x^{-1} + C\\g(x) = -x^{-1} + C\\](https://tex.z-dn.net/?f=g%28x%29%20%20%3D%20%5Cint%5Climits%20%7Bx%5E%7B-2%7D%7D%20%5C%2C%20dx%5C%5C%20g%28x%29%20%20%3D%20%5Cfrac%7Bx%5E%7B-2%2B1%7D%7D%7B-2%2B1%7D%20%2B%20C%5C%5C%20g%28x%29%20%3D%20-x%5E%7B-1%7D%20%2B%20C%5C%5Cg%28x%29%20%3D%20-x%5E%7B-1%7D%20%2B%20C%5C%5C)
If g(1) = 0, this means at x = 1, g(x) = 0
0 = -1⁻¹ + C
C= 1
Substitute C = 1 into the function
g(x) = -x⁻¹ + 1
If g(2) = 0, this means at x = 2, g(x) = 0
0 = -2⁻¹ + C
C= 2⁻¹
C = 1/2
Substitute C = 2 into the function
g(x) = -x⁻¹ + 1/2
Answer:
x intercept: (3, 0), (7, 0)
y-intercept: (0, -21)
vertex : (5,4)
the graph points down
Step-by-step explanation:
f(x) = - (x - 3)(x - 7)
f(x) = - (x^2 - 7x - 3x + 21)
f(x) = - (x^2 - 10x + 21)
f(x) = -x^2 + 10x - 21
x-intercept when f(x) = 0 so
x - 3 = 0; x = 3
x - 7 = 0; x = 7
x intercept: (3, 0), (7, 0)
y-intercept when x = 0 so y = -21
y-intercept: (0, -21)
vertex:
x = -b/2a
x = -10/ 2(-1)
x = 5
plug in x = 5 into the equation to find y
y = -(5)^2 + 10(5) - 21
y = -25 + 50 - 21
y = 4
so vertex : (5,4)
Since a = - 1<0, the graph is going downward and has maximum
Answer:
Step-by-step explanation:
both represent the same line .
Hence it has infinite solutions as there are infinite points on aline.
9514 1404 393
Answer:
3000 kL
Step-by-step explanation:
(2500 cows)(40 L/day/cow)(30 day/mo)(1 kL/(1000 L)) = 2.5×40×30 kL/mo
= 3000 kL/mo
About 3000 kL of manure would be produced in one month.
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That's about 3 cubic meters.