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Gemiola [76]
2 years ago
7

Calculate the average rate of change of the function f(x) = 3x2 over the interval 1 ≤ x ≤ 5.

Mathematics
1 answer:
RideAnS [48]2 years ago
5 0

Answer:

18

Step-by-step explanation:

The average rate of change of f(x) in the closed interval [ a, b ] is

\frac{f(b)-f(a)}{b-a}

here [ a, b ] = [ 1, 5 ]

f(b) = f(5) = 3 × 5² = 75

f(a) = f(1) = 3 × 1² = 3, hence

average rate of change = \frac{75-3}{5-1} = \frac{72}{4} = 18

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Tamiku [17]

Answer:

4

Step-by-step explanation:

Go to where it says -8 on the y-axis then rise 4 and run 1

6 0
2 years ago
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Manuel bought 9 pounds of apples. He has eaten three fourths
Diano4ka-milaya [45]

1. So, since Manuel bought 9 pounds and ate 3/4 of 1 pound, he has 8.25 pounds left  (9  - 0.75  = 8.25)

2. Let us call "x" the cost of 1 pound of apples

3. (8.25) * (x) = $15


4. x = $1.81818  rounded to the nearest dollar is $2 / pound

6 0
3 years ago
What is the slope of the line that contains the points (-4,2) and (6,-3)?-
schepotkina [342]

Answer:

c

Step-by-step explanation:

the formula is \frac{y_{2}-y_{1} }{x_{2} -x_{1}}

When we plug that in we get \frac{-3-2}{6- (-4)} = \frac{-5}{10} = -\frac{1}{2}

Hope this helps!

8 0
3 years ago
At 10 percent interest, how long does it take to quadruple your money?
horsena [70]

It takes about 14.55 years for quadruple your money

<em><u>Solution:</u></em>

Given that,

At 10 percent interest, how long does it take to quadruple your money

Rule of 144:

The Rule of 144 will tell you how long it will take an investment to quadruple

Here,

Rate of interest = 10 %

Therefore, number of years to quadruple your money is obtained by dividing 144 by 10

<em><u>Rule of 144 Formula: </u></em>

N = \frac{144}{R}

Where:

N = Number of many years times.

144 = Is the constant variable.

R = Rate of interest.

\rightarrow N =  \frac{144}{10} = 14.4

Thus it takes about 14.4 years for quadruple your money.

<em><u>Another method:</u></em>

If initial amount is $ 1 and it if quadruples it should be $ 4

We have to find the number of years if rate of interest is 10 %

Let "n" be the number of years

Then we can say,

Amount = Principal(1+\frac{R}{100})^n

4 = 1(1+\frac{10}{100})^n

4 = 1(1+0.1)^n\\\\4= 1(1.1)^n\\\\4 = 1.1^n\\\\We\ know\ that,\\\\(1.1)^{14.55} = 1.1^n\\\\We\ know\ that\\\\If\ a^m = a^n\ then\ m = n\\\\Therefore,\\\\14.55 = n\\\\n = 14.55

Thus Option D 14.55 years is correct

7 0
3 years ago
Ricardo ran 160 minutes last week at the park. If he runs 15% more this week, how many
Ilia_Sergeevich [38]

Answer:

4356

Step-by-step explanation:

<u><em>Don't be a baka</em></u>

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