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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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Answer:

original price $75

discount $18.75

sale price $56.25

Step-by-step explanation:

I found a pair of dress pants for $75.

Since the discount is 25%, then the discount is

25% of $75 = 0.25 × $75 = $18.75

The sale price is the original price, $75, minus the discount, $18.75.

$75 - $18.75 = $56.25

5 0
1 year ago
I have 30 ones 2thousands 4hundred thousands , 60 tens and 100 hundreds what number am I ?
viva [34]

Answer:

Step-by-step explanation:

Units = 30

Thousands = 2,000

Hundreds of Thousands = 400,000

Tens = 60

Hundreds = 100

HTHHTU

400,000

    2,000

       100

         60

<u>          30</u>

<u>402,190</u>

7 0
3 years ago
Read 2 more answers
A crawling tractor sprinkler is located as pictured below, 100 feet South of a sidewalk. Once the water is turned on, the sprink
deff fn [24]

Answer:

  a) see below

  b) 32 minutes after turn-on

  c) 52 minutes after turn-on

  d) 20 minutes

  e) 6856.6 ft²

Step-by-step explanation:

a) We have elected to put the origin at the point where the hose crosses the south edge of the sidewalk. Units are feet. Then the sprinkler starts at (0, -100). After 1 hour, 3600 seconds, the sprinkler is 1800 inches, or 150 ft north of where it started, so stops at (0, 50).

The lines forming the sidewalk boundaries are y=0 and y=10.

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b) Water will first strike the sidewalk when the sprinkler is 20 feet south of it, or 80 feet north of where it started. The sprinkler travels that distance in ...

  (80 ft)(12 in/ft)/(1/2 in/s)(1 min/(60 s)) = 32 min . . . time to start sprinkling sidewalk

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c) The sprinkler has to travel to a point 130 ft north of its starting position for the water to fall north of the sidewalk. That distance is traveled in ...

  (130 ft)(2/5 min/ft) = 52 min . . . time until end of sprinkling sidewalk

Note that we have combined the scale factors in the expression of part b into one scale factor of (2/5 min/ft).

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d) The difference of times in parts b and c is the time water falls on the sidewalk: 20 minutes.

__

e) In one hour, the sprinkler travels a distance of ...

  (60 min)(5/2 ft/min) = 150 ft

Of that distance, 10 feet is sidewalk. So, the sprinkler covers an area of grass that is a 140 ft by 40 ft rectangle and a circle of 20 ft radius. The total area of that is ...

  A = LW + πr² = (140 ft)(40 ft) +π(20 ft)² = (14+π)(400) ft² ≈ 6856.6 ft²

The area of grass watered in 1 hour is about 6856.6 ft².

5 0
3 years ago
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5 0
2 years ago
The CDC reported in 2012 that 1 in 88 American children had been diagnosed with an autism spectrum disorder (ASD).
gladu [14]

Answer:

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sample space, n = 300

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probability of not diagnosed with ASD, q = 1 - p = 0.9886

Mean, m is given as np = 300 * 0.0114 = 3.42

variance, v = npq = 300 * 0.0114 * 0.9886 = 3.38101

standard deviation, s = square root of variance = 3.38101^(0.5) = 1.83875

This binomial distribution can be approximated as Poisson Distribution since

n > 20 and p < 0.05

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b) x = 2

P(X < 2) = P(X = 0) + P(X = 1)

using the z score table and evaluating, we obtain

P(x<2) = 0.1446

4 0
3 years ago
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