I am pretty sure it is (c). I used a formula, ( 25.00+(2.50*n))
substitute the variable "n" for the number of deliveries made.
Answer:
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Step-by-step explanation:
Answer:
f = xy²-2x² satisfies that F = ∇f.
Step-by-step explanation:
F(x,y) = (y² - 4x) i + 2xy j
We want f(x,y) such that
![f_x(x,y) = y^2 -4x\\f_y(x,y) = 2xy](https://tex.z-dn.net/?f=f_x%28x%2Cy%29%20%3D%20y%5E2%20-4x%5C%5Cf_y%28x%2Cy%29%20%3D%202xy)
Lets find a primitive of y²-4x respect to the variable x. We need to think y (and y²) as constants here, so a primitive of y² would be xy² the same way that a primitive of k is xk (because we treat y² as constant). A primitive of x is x²/2, thus a primitive of 4x is 2x². Thus, a primitive of y²-4x is xy² - 2x². We can obtain any other primitive by summing a constant, however since we treated y as constant, then we have that
![f(x,y) = xy^2 - 2x^2 + c(y)](https://tex.z-dn.net/?f=f%28x%2Cy%29%20%3D%20xy%5E2%20-%202x%5E2%20%2B%20c%28y%29)
where c(y) only depends on y (thus, it is constant repsect with x).
We will derivate the expression in terms of y to obtain information about c(y)
![2xy = f_y(x,y) = \frac{d}{dy} (xy^2 - 2x^2 + c(y) ) = 2xy -0 + \frac{d}{dy} c(y) = 2xy + \frac{d}{dy} c(y)](https://tex.z-dn.net/?f=2xy%20%3D%20f_y%28x%2Cy%29%20%3D%20%5Cfrac%7Bd%7D%7Bdy%7D%20%28xy%5E2%20-%202x%5E2%20%2B%20c%28y%29%20%29%20%3D%202xy%20-0%20%2B%20%5Cfrac%7Bd%7D%7Bdy%7D%20c%28y%29%20%3D%202xy%20%2B%20%5Cfrac%7Bd%7D%7Bdy%7D%20c%28y%29)
Thus,
is constant. We can take f(x,y) = xy²-2x². This function f satisfies that F = ∇f.
Answer:
![5^{th} term = 126a^5b^4](https://tex.z-dn.net/?f=5%5E%7Bth%7D%20term%20%20%3D%20126a%5E5b%5E4)
Step-by-step explanation:
![\left(a+b\right)^n=\sum _{i=0}^n\binom{n}{i}a^{\left(n-i\right)}b^i\\\\(a + b)^9 =\sum _{i=0}^9\binom{9}{i}a^{\left(9-i\right)}b^i\\\\](https://tex.z-dn.net/?f=%5Cleft%28a%2Bb%5Cright%29%5En%3D%5Csum%20_%7Bi%3D0%7D%5En%5Cbinom%7Bn%7D%7Bi%7Da%5E%7B%5Cleft%28n-i%5Cright%29%7Db%5Ei%5C%5C%5C%5C%28a%20%2B%20b%29%5E9%20%3D%5Csum%20_%7Bi%3D0%7D%5E9%5Cbinom%7B9%7D%7Bi%7Da%5E%7B%5Cleft%289-i%5Cright%29%7Db%5Ei%5C%5C%5C%5C)
![=a^9 + 9a^8b + 36a^7b^2 + 84a^6 b^3 + 126a^5b^4+ 126a^4b^5+84a^3b^6+ 36a^2b^7+ 9ab^8+b^9](https://tex.z-dn.net/?f=%3Da%5E9%20%2B%209a%5E8b%20%2B%2036a%5E7b%5E2%20%2B%2084a%5E6%20b%5E3%20%2B%20126a%5E5b%5E4%2B%20126a%5E4b%5E5%2B84a%5E3b%5E6%2B%2036a%5E2b%5E7%2B%209ab%5E8%2Bb%5E9)
![5^{th} term = 126a^5b^4](https://tex.z-dn.net/?f=5%5E%7Bth%7D%20term%20%20%3D%20126a%5E5b%5E4)