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patriot
3 days ago
15

Write a difference quotient that best approximates the instantaneous rate of change of g at x=0

Mathematics
1 answer:
lawyer [4K]3 days ago
7 0

Step-by-step explanation:

The difference quotient represents the slope of the line connecting two points on a curve. To achieve the most accurate estimate, we need to use points that are nearest to x = 0. For this problem, the relevant points are (-0.001, 1.999) and (0.001, 2.001).

m = (2.001 − 1.999) / (0.001 − (-0.001))

m = 1

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Which are the solutions of x2 = –5x + 8? StartFraction negative 5 minus StartRoot 57 EndRoot Over 2 EndFraction comma StartFract
tester [3938]

Answer:

x=\frac{-5-\sqrt{57} }{2}\ or\ x=\frac{-5+\sqrt{57} }{2}

Detailed solution:

Given:

The problem to solve is:

x^2=-5x+8

Convert the equation into the standard quadratic form ax^2+bx +c =0, where a,\ b,\ and\ c represent constants.

So, by adding 5x-8 to both sides, we get:

x^2+5x-8=0

Note that a=1,b=5,c=-8.

The roots of this quadratic are found by applying the quadratic formula given as:

x=\frac{-b\pm \sqrt{b^2-4ac}}{2a}

Substitute a=1,b=5,c=-8 into the formula and calculate for x.

x=\frac{-5\pm \sqrt{5^2-4(1)(-8)}}{2(1)}\\x=\frac{-5\pm \sqrt{25+32}}{2}\\x=\frac{-5\pm \sqrt{57}}{2}\\\\\\\therefore x=\frac{-5-\sqrt{57} }{2}\ or\ x=\frac{-5+\sqrt{57} }{2}

Hence, the roots are:

x=\frac{-5-\sqrt{57} }{2}\ or\ x=\frac{-5+\sqrt{57} }{2}

4 0
15 days ago
Read 2 more answers
casey bought sandwiches and a bag of chips. Each sandwich cost three times as much as bag of chips. She bought 5 sandwiches for
AnnZ [3900]

Answer:

4

Step-by-step explanation:

Each sandwich costs 6 dollars, while chips sell for 3 dollars. She purchased 5 sandwiches at 6 dollars each, amounting to 30 dollars (5*6=30). This leaves her with 12 dollars to use since her total expenditure was 42 dollars. Given that chips are 3 dollars each, with 12 dollars left, 4 bags could be bought (4 * 3 = 12).

3 0
3 days ago
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Angie baked 100 cookies and 20 brownies. She wants to  split them into equal groups  for the big sale. Each group must have the
zzz [4035]
Avoid repeating the question as it can be perplexing.

Given 100 cookies and 20 brownies,
What is the highest number you can divide them equally by?

To find the greatest common factor,
Factor them:
100 = 2*2*5*5
20 = 2*2*5
Thus, the greatest common factor, which is shared between them, is 2*2*5 or 20.

Calculating further, 100/20=5
20/20=1

This means there are 20 groups, each containing 5 cookies and 1 brownie.


20 groups
7 0
2 days ago
Turkey sandwiches cost $2.50 and veggie wraps cost $3.50 at a snack stand. Ben has sold no more than $30 worth of turkey sandwic
tester [3938]

Answer:

Ben could have sold a maximum of 6 turkey sandwiches.

Step-by-step explanation:

Turkey sandwiches are priced at $2.50, while veggie wraps cost $3.50 at the snack stand.

Our goal is to determine the largest number of turkey sandwiches Ben might have sold.

2. 5 0 x + 3. 5 0 y \leq 3 0

4 veggie wraps were sold (y).

Thus, the inequality is: 2.50x + 3.50(4) < 30

2.50x + 14 < 30

- 14 - 14

2.50x < 16

x

x

Ultimately, Ben could sell a maximum of 6 turkey sandwiches.

4 0
7 days ago
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*TAXES MULTIPLE CHOICE* Zurab works for a salary of $1,986 per month. He has federal income tax withheld at the rate of 15 perce
zzz [4035]
To find the answer, subtract the total percentage of 24.65% and $48 from 1986, resulting in the final value.
8 0
13 days ago
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