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Drupady [299]
3 years ago
12

Find the derivative of x2/8-8x

Mathematics
1 answer:
-Dominant- [34]3 years ago
6 0

h(x)=\dfrac{x^2}{8-8x}\\\\h'(x)=\left(\dfrac{x^2}{8-8x}\right)'\\\\\text{use}\ \left(\dfrac{f(x)}{g(x)}\right'=\dfrac{f'(x)g(x)-f(x)g'(x)}{[g(x)]^2}\\\\f(x)=x^2\to f'(x)=(x^2)'=2x\\\\g(x)=8-8x\to g'(x)=(8-8x)'=-8\\\\\text{substitute}\\\\h'(x)=\dfrac{2x(8-8x)-x^2(-8)}{(8-8x)^2}=\dfrac{16x-16x^2+8x^2}{(8-8x)^2}=\dfrac{16x-8x^2}{(8-8x)^2}

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Identify the situation that involves opposite quantities adding up to zero Climbing up 6 feet and climbing down 4 feet Hiking 10
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Answer:

  (b)  Hiking 10 feet due north, then hiking 10 feet due south

Step-by-step explanation:

Any pair of numbers that totals zero will be a pair of opposites. The offered choices are ...

  +6 -4 = 2 . . . not zero

  +10 -10 = 0

  +2 -3 = -1 . . . not zero

  +5 -3 = 2 . . . not zero

Hiking 10 feet due north, then hiking 10 feet due south is a situation involving opposite numbers adding up to zero.

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Step-by-step explanation:

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Solve the system of linear equations.
sweet-ann [11.9K]

Answer:

  • dependent system
  • x = 2 -a
  • y = 1 +a
  • z = a

Step-by-step explanation:

Let's solve this by eliminating z, then we'll go from there.

Add 6 times the second equation to the first.

  (3x -3y +6z) +6(x +2y -z) = (3) +6(4)

  9x +9y = 27 . . . simplify

  x + y = 3 . . . . . . divide by 9 [eq4]

Add 13 times the second equation to the third.

  (5x -8y +13z) +13(x +2y -z) = (2) +13(4)

  18x +18y = 54

  x + y = 3 . . . . . . divide by 18 [eq5]

Equations [eq4] and [eq5] are identical. This tells us the system is dependent, and has an infinite number of solutions. We can find them in terms of z:

  y = 3 -x . . . . solve eq5 for y

  x +2(3 -x) -z = 4 . . . . substitute into the second equation

  -x +6 -z = 4

  x = 2 - z . . . . . . add x-4

  y = 3 -(2 -z)

  y = z +1

So far, we have written the solutions in terms of z. If we use the parameter "a", we can write the solutions as ...

  x = 2 -a

  y = 1 +a

  z = a

_____

<em>Check</em>

First equation:

  3(2-a) -3(a+1) +6a = 3

  6 -3a -3a -3 +6a = 3 . . . true

Second equation:

  (2-a) +2(a+1) -a = 4

  2 -a +2a +2 -a = 4 . . . true

Third equation:

  5(2-a) -8(a+1) +13a = 2

  10 -5a -8a -8 +13a = 2 . . . true

Our solution checks algebraically.

6 0
3 years ago
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