The answer would be r = -2.
7r + 7 - 2r = -3
5r + 7 = -3
5r = -3 - 7
5r = -10
r = 10/-5
r = -2.
By the product rule,
![\dfrac{dy}{dx} = \dfrac{x-1}{x+1} \dfrac{d(7x^7-x^2)}{dx} + \dfrac{7x^7-x^2}{x+1} \dfrac{d(x-1)}{x+1} + (7x^7-x^2)(x-1) \dfrac{d\left(\frac1{x+1}\right)}{dx}](https://tex.z-dn.net/?f=%5Cdfrac%7Bdy%7D%7Bdx%7D%20%3D%20%5Cdfrac%7Bx-1%7D%7Bx%2B1%7D%20%5Cdfrac%7Bd%287x%5E7-x%5E2%29%7D%7Bdx%7D%20%2B%20%5Cdfrac%7B7x%5E7-x%5E2%7D%7Bx%2B1%7D%20%5Cdfrac%7Bd%28x-1%29%7D%7Bx%2B1%7D%20%2B%20%287x%5E7-x%5E2%29%28x-1%29%20%5Cdfrac%7Bd%5Cleft%28%5Cfrac1%7Bx%2B1%7D%5Cright%29%7D%7Bdx%7D)
By the power and chain rules,
![\dfrac{dy}{dx} = \dfrac{(x-1)(49x^6-2x)}{x+1} + \dfrac{7x^7-x^2}{x+1} - \dfrac{(7x^7-x^2)(x-1)}{(x+1)^2}](https://tex.z-dn.net/?f=%5Cdfrac%7Bdy%7D%7Bdx%7D%20%3D%20%5Cdfrac%7B%28x-1%29%2849x%5E6-2x%29%7D%7Bx%2B1%7D%20%2B%20%5Cdfrac%7B7x%5E7-x%5E2%7D%7Bx%2B1%7D%20-%20%5Cdfrac%7B%287x%5E7-x%5E2%29%28x-1%29%7D%7B%28x%2B1%29%5E2%7D)
When
, the first and last term vanish, and we're left with
![\dfrac{dy}{dx}\bigg|_{x=1} = \dfrac{7 - 1}{1 + 1} = \dfrac62 = \boxed{3}](https://tex.z-dn.net/?f=%5Cdfrac%7Bdy%7D%7Bdx%7D%5Cbigg%7C_%7Bx%3D1%7D%20%3D%20%5Cdfrac%7B7%20-%201%7D%7B1%20%2B%201%7D%20%3D%20%5Cdfrac62%20%3D%20%5Cboxed%7B3%7D)
Answer:
f(x) = a(x - 1) + 20
Step-by-step explanation:
Vertex form is written in this format: f(x) = a(x - h) + k. The vertex point is written in the form (h,k). To write the vertex in the equation, fill in the digits where they belong.
Hope it helps!
If we find the square root of 13 ans 14 we get
sqrt(13) = 3.60555 <span>
sqrt(14) = 3.74166</span>
All Real numbers can be rational number and
irrational number.
<span>We can write 3.7 as 37/10, which is the easy
rational number and an irrational number within the range is sqrt (27/2)</span>
<span>Real number system is used in mathematics and statistics.</span>