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andreyandreev [35.5K]
2 years ago
15

Evaluate the difference quotient for the given function. Simplify your answer.

Mathematics
1 answer:
nasty-shy [4]2 years ago
4 0

I suppose you mean

f(x) = \dfrac{x+5}{x+1}

Then

f(3) = \dfrac{3+5}{3+1} = \dfrac84 = 2

and the difference quotient is

\dfrac{f(x)-f(3)}{x-3} = \dfrac{\frac{x+5}{x+1}-2}{x-3} \\\\ \dfrac{f(x)-f(3)}{x-3} = \dfrac{\frac{x+5-2(x+1)}{x+1}}{x-3} \\\\ \dfrac{f(x)-f(3)}{x-3} = \dfrac{-x+3}{(x+1)(x-3)} \\\\ \dfrac{f(x)-f(3)}{x-3} = \boxed{-\dfrac{x-3}{(x+1)(x-3)}}

If it's the case that <em>x</em> ≠ 3, then (<em>x</em> - 3)/(<em>x</em> - 3) reduces to 1, and you would be left with

\dfrac{f(x)-f(3)}{x-3}\bigg|_{x\neq3} = -\dfrac1{x+1}

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A cooling tower for a nuclear reactor is to be constructed in the shape of a hyperboloid of one sheet. The diameter at the base
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Answer:

Step-by-step explanation:

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(x/a)²  +  (y/b)²    =  (k/c)² + 1

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we have

(x/a)²  +  (y/b)²   = 1      

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(x/a)²  +  (y/b)²    =  (z/c)² + 1        

(1/a)² [ x² + y² ]  = (z/c)² + 1  

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(250)²/(150)²   =  (z/c)² + 1    ⇒ (62500/ 22500)  =  (200/c)² + 1

2,78  =  40000/c² + 1

2.78c²  =  40000  + c²

1.78c² = 40000

c²  =  40000/1.78

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c = 149,91

Then we finally have the equation:

x²/(150)²   + y² /(150)² - z²/149,91  = 1

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