Answer:
Step-by-step explanation:
The Fundamental Theorem of Calculus states that:
![\displaystyle \frac{d}{dx}\left[ \int_a^x f(t)\, dt \right] = f(x)](https://tex.z-dn.net/?f=%5Cdisplaystyle%20%5Cfrac%7Bd%7D%7Bdx%7D%5Cleft%5B%20%5Cint_a%5Ex%20f%28t%29%5C%2C%20dt%20%20%5Cright%5D%20%3D%20f%28x%29)
Where <em>a</em> is some constant.
We can let:
By substitution:
Taking the derivative of both sides results in:
![\displaystyle g'(s) = \frac{d}{ds}\left[ \int_6^s g(t)\, dt\right]](https://tex.z-dn.net/?f=%5Cdisplaystyle%20g%27%28s%29%20%3D%20%5Cfrac%7Bd%7D%7Bds%7D%5Cleft%5B%20%5Cint_6%5Es%20g%28t%29%5C%2C%20dt%5Cright%5D)
Hence, by the Fundamental Theorem:
Problem 3
The constant term is 290. This is the term that stays the same no matter what the value of 'a' happens to be. Contrast this with the variable term 2.50a which changes if 'a' changes (hence the name "variable" for "vary" or "change")
If Mike sold 0 accessories, then a = 0 and the expression would be
2.50*a + 290 = 2.50*0 + 290 = 290
Selling 0 accessories leads to $290. This is the amount he is guaranteed with the 2.50a portion being additional money to motivate him to sell more.
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Answer: Choice (3) 290, amount he is guaranteed
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Problem 4
Plug y = 0 into the equation. Solve for x
9x - 14y = -3
9x - 14*0 = -3 .... replace y with 0
9x - 0 = -3
9x = -3
9x/9 = -3/9 ... divide both sides by 9
x = -3/9
x = -1/3
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Answer: Choice (3) which is -1/3
When two graphs intersect, it means something in real-life:
The baseball's flight path and the bird's flight path intersect.
Therefore, the baseball hits the bird. (Technically, we can see that the baseball would hit the bird twice, but this is not likely.)
