Answer:
4.
Step-by-step explanation:
We are asked to find the value of expression
at
.
First of all, we will find the derivative of the given expression using "Quotient Rule of Derivatives" as shown below:
![(\frac{f(x)}{g(x)})'=\frac{f'(x)\cdot g(x)-f(x)\cdot g'(x)}{(g(x))^2}](https://tex.z-dn.net/?f=%28%5Cfrac%7Bf%28x%29%7D%7Bg%28x%29%7D%29%27%3D%5Cfrac%7Bf%27%28x%29%5Ccdot%20g%28x%29-f%28x%29%5Ccdot%20g%27%28x%29%7D%7B%28g%28x%29%29%5E2%7D)
![\frac{d}{dx}(\frac{2x+3}{3x^2-4})](https://tex.z-dn.net/?f=%5Cfrac%7Bd%7D%7Bdx%7D%28%5Cfrac%7B2x%2B3%7D%7B3x%5E2-4%7D%29)
![\frac{\frac{d}{dx}(2x+3)*(3x^2-4)-(2x+3)*\frac{d}{dx}(3x^2-4)}{(3x^2-4)^2}](https://tex.z-dn.net/?f=%5Cfrac%7B%5Cfrac%7Bd%7D%7Bdx%7D%282x%2B3%29%2A%283x%5E2-4%29-%282x%2B3%29%2A%5Cfrac%7Bd%7D%7Bdx%7D%283x%5E2-4%29%7D%7B%283x%5E2-4%29%5E2%7D)
![\frac{2*(3x^2-4)-(2x+3)*(6x)}{(3x^2-4)^2}](https://tex.z-dn.net/?f=%5Cfrac%7B2%2A%283x%5E2-4%29-%282x%2B3%29%2A%286x%29%7D%7B%283x%5E2-4%29%5E2%7D)
![\frac{6x^2-8-12x^2-18x}{(3x^2-4)^2}](https://tex.z-dn.net/?f=%5Cfrac%7B6x%5E2-8-12x%5E2-18x%7D%7B%283x%5E2-4%29%5E2%7D)
![\frac{-6x^2-18x-8}{(3x^2-4)^2}](https://tex.z-dn.net/?f=%5Cfrac%7B-6x%5E2-18x-8%7D%7B%283x%5E2-4%29%5E2%7D)
Therefore, our required derivative is
.
Now, we will substitute
in our derivative to find the required value as:
![\frac{-6(-1)^2-18(-1)-8}{(3(-1)^2-4)^2}](https://tex.z-dn.net/?f=%5Cfrac%7B-6%28-1%29%5E2-18%28-1%29-8%7D%7B%283%28-1%29%5E2-4%29%5E2%7D)
![\frac{-6(1)+18-8}{(3(1)-4)^2}](https://tex.z-dn.net/?f=%5Cfrac%7B-6%281%29%2B18-8%7D%7B%283%281%29-4%29%5E2%7D)
![\frac{-6+18-8}{(3-4)^2}](https://tex.z-dn.net/?f=%5Cfrac%7B-6%2B18-8%7D%7B%283-4%29%5E2%7D)
![\frac{4}{(-1)^2}](https://tex.z-dn.net/?f=%5Cfrac%7B4%7D%7B%28-1%29%5E2%7D)
![\frac{4}{1}](https://tex.z-dn.net/?f=%5Cfrac%7B4%7D%7B1%7D)
![4](https://tex.z-dn.net/?f=4)
Therefore, the value of expression
at
is 4.
Answer: 1.905
Step-by-step explanation:
75 percent *2.54
= (75/100)*2.54
= (75*2.54)/100
= 190.5/100 = 1.905
Answer:
Step-by-step explanation:
-x(4x^2 -6x + 1)...distribute thru the parenthesis
-4x^3 + 6x^2 - x <====
Answer:
m<CDE=66 degrees.
Step-by-step explanation:
(1) Extend the segment DC so it intersects with line BA. Call the intersection F.
(2) Consider triangle BCF. In here, we are given m<ABC=24 deg. Since m<BCD = 90 deg, we known that m<BCF = 90 deg. Knowing two angles in the triangle BCF lets us determine the rhird angle m<BFC = 180-90-24 = 66 deg.
(3) Because of the fact that AB || DE and the fact that line DF intersects AB and DE, the angles <BFC and <CDE are congruent. Therefore m<CDE=66 deg.