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sashaice [31]
3 years ago
8

Find the average rate of change of the function over the given intervals. f(x) = 12x3 + 12; [5,7]

Mathematics
1 answer:
AlladinOne [14]3 years ago
7 0
<span>average rate of change = (f(7) - f(5)) / (x7 - x5)
</span>f(7) = <span>12 (7^3) + 12 = 4128
f(5) = </span>12 (5^3) + 12 = 1512

so
average rate of change = (4128 - 1512)/(7-5)
average rate of change = 2616 / 2
average rate of change = 1308

hope it helps
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Usimov [2.4K]

Answer:

r\approx0.03\text{ or about $3\%$}

Step-by-step explanation:

The standard compound interest formula is given by:

\displaystyle A=P(1+\frac{r}{n})^{nt}

Where A is the amount afterwards, P is the principal, r is the rate, n is the times compounded per year, and t is the number of years.

Since we are compounding annually, n=1. Therefore:

\displaystyle  A = P (1+r)^{t}

Lester wants to invest $10,000. So, P=10,000.

He wants to earn $1000 interest. Therefore, our final amount should be 11000. So, A=11000.

And our timeframe is 3.3 years. So, t=3.3. Substituting these values, we get:

11000=10000(1+r)^{3.3}

Let’s solve for our rate r.

Divide both sides by 10000:

1.1=(1+r)^{3.3}

We can raise both sides to 1/3.3. So:

\displaystyle (1.1)^\frac{1}{3.3}=((1+r)^{3.3})^\frac{1}{3.3}

The right side will cancel:

\displaystyle r+1=(1.1)^\frac{1}{3.3}

So:

\displaystyle r=(1.1)^\frac{1}{3.3}-1

Use a calculator:

r\approx0.03

So, the annual rate of interest needs to be about 0.03 or 3% in order for Lester to earn his interest.

5 0
3 years ago
3x squared =118. Solve the equation. Round to the nearest hundredth if necessary.
Anit [1.1K]

Answer:

3.62

Step-by-step explanation:

118 square rooted is 10.86

10.86/3 = 3.62

8 0
2 years ago
Read 2 more answers
Plz help me here I really need it. Please and thanks!
Alik [6]

Answer:

no they are not proportional and the graph would be at points (1, 3) (5, 9)

Step-by-step explanation:

Can i have brainliest Please?

8 0
2 years ago
If f(x)=3x-1 and g(x)=x+5, find (f o g)(x) and (g o f)(x)<br><br> (f o g)(x)=<br><br> (g o f)(x)
Nuetrik [128]

Answer:

(f o g)(x)= 3x + 14

(g o f)(x) = 3x + 4

Step-by-step explanation:

(f o g)(x) = f(g(x)) = f(x + 5) = 3(x + 5) - 1 = 3x + 15 - 1 = 3x + 14

(g o f)(x) = g(f(x)) = g(3x - 1) = 3x - 1 + 5 = 3x + 4

3 0
2 years ago
Justify each step in solving the equation -3(2x-3)=25-8x by writing a reason for each statement.
Mice21 [21]

Answer: x= 8.


Step-by-step explanation: Given equation -3(2x-3)=25-8x.

Step 1: We have -3 in front of (2x-3). We always simplify a parenthesis first.

Therefore, applying Distributive property in first step, we get

-6x +9 = 25-8x.

Step 2:  We need to get rid 9 from left side to get constant numbers on right side.

9 is being added on left side.

So, we would apply reverse operation of addition.

Therefore, applying Subtraction property of equality, we get

-6x +9-9 = 25-8x-9

-6x =16 -8x.

Step 3: We need to get rid 8x from right side.

The reverse operation of subtraction is addition.

Therefore, applying Addition property of equality, we get

-6x+8x =16 -8x+8x

2x = 16.

Step 4: We need to isolate it for x.

So, applying Division property of equality, we get

\frac{2x}{2}=\frac{16}{2}

<h3>x= 8.</h3>
4 0
3 years ago
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