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Lina20 [59]
3 years ago
11

Compute the difference​ quotient, StartFraction f (x plus h )minus f (x )Over h EndFraction f(x+h)−f(x) h​, for the function f (

x )equals 3 x squaredf(x)=3x2​, and simplify.
Mathematics
1 answer:
lawyer [7]3 years ago
4 0

Answer:

The difference quotient for f(x)=3x^2 is 3 h + 6 x.

Step-by-step explanation:

The difference quotient is a formula that computes the slope of the secant line through two points on the graph of <em>f</em>. These are the points with x-coordinates x and x + h. The difference quotient is used in the definition the derivative and it is given by

\frac{f(x+h)-f(x)}{h}

So, for the function f(x)=3x^2 the difference quotient is:

To find f(x+h), plug x+h instead of x

f\left(x+h\right)=3 \left(h + x\right)^{2}

Finally,

\frac{f\left(x+h\right)-f\left(x\right)}{h}=\frac{\left(3 \left(h + x\right)^{2}\right)-\left(3 x^{2}\right)}{h}

\frac{3\left(\left(h+x\right)^2-x^2\right)}{h} \\\\\frac{3(h^2+2hx+x^2-x^2)}{h} \\\\\frac{3h\left(h+2x\right)}{h}\\\\3h+6x

The difference quotient for f(x)=3x^2 is 3 h + 6 x.

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A rental car agency charges $30.00 per day
lutik1710 [3]
<h2>Answer:</h2><h2>They should travel 120 mils in one day for both rental agencies  to cost the same amount to rent</h2>

Step-by-step explanation:

A rental car agency charges $30.00 per day  plus per mile $0.15.

Let x be the number of miles travelled by car

Their total cost = 30 + (0.15x)   ... (1)

Another rental car  agency charges $36.00 per day plus $0.10  per mile

Their total cost = 36 + (0.10x)   ... (2)

Equating (1) and (2), we get

30 + (0.15x) = 36 + (0.10x)

36 - 30 = 0.15x - 0.10x

6 = 0.05x

x = 120 miles

They should travel 120 mils in one day for both rental agencies  to cost the same amount to rent

5 0
3 years ago
Y +
Usimov [2.4K]

Question:

What is the common denominator of $y+\frac{y-3}{3}$ in the complex fraction $\frac{y+\frac{y-3}{3}}{\frac{5}{y}+\frac{2}{3 y}}$

A) $3 y(y-3)$

B) $y(y-3)$

C) 3y

D) 3

Answer:

Option D : 3 is the common denominator

Explanation:

It is given that the complex fraction $\frac{y+\frac{y-3}{3}}{\frac{5}{y}+\frac{2}{3 y}}$

We need to determine the common denominator of $y+\frac{y-3}{3}$ from the complex fraction.

Let us consider the fraction $y+\frac{y-3}{3}$

To find the common denominator, let us take LCM.

Thus, rewriting the above fraction as,

\frac{y}{1} +\frac{y-3}{3}$

The LCM can be determined by multiplying the denominators.

Thus, we get,

1\times3=3

Thus, the common denominator is 3.

Hence, Option D is the correct answer.

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3 years ago
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3 years ago
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Kruka [31]

Answer:

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Step-by-step explanation:

To evaluate this, start by turning each into improper fractions.

3 1/2 - 4 2/3

7/2 - 14/3

Now give both common denominators and complete the operation.

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answer:

to my knowledge it's, 65

5 0
3 years ago
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