All categories

3 years ago

What is the average rate of change of the function on the interval from x = 0 to x = 5?

Mathematics

2 answers:

bixtya [17]3 years ago

8 0

The average rate is 3^x/2

damaskus [11]3 years ago

6 0

Answer:

Average rate of change = 24.2

Step-by-step explanation:

$f(x)=\frac{1}{2}3^x$

Average rate of change formula is on interval a to b is

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

Given interval is x=0 to x=5

a=0 and b=5

Average rate = $\frac{f(5)-f(0)}{5-0}$

$f(0)=\frac{1}{2}3^0=\fracc{1}{2}=0.5$

$f(5)=\frac{1}{2}3^5=\frac{3^5}(2}=121.5$

Average rate = $\frac{f(5)-f(0)}{5-0}$

Average rate = $\frac{121.5-0.5}{5}=24.2$

Average rate of change = 24.2

You might be interested in

Select all the situations that describe a probability of 1/6 of drawing a red marble out the bag.

konstantin123 [22]

The correct answer is E (6 red, 4 yellow, 8 green, 6 blue, 12 white).

E) 6 + 4 + 8 + 6 + 12 = 36 (total marble count)
6 red/36 total marbles
simplify to find the probability ⬇️
(6/6=1; 36/6=6) = 1/6 chance of picking red

6 0

3 years ago

Without using a calculator convert the decimal into a fraction 0. 75

mojhsa [17]

Step-by-step explanation:

Decimals can always be put over 1, as they're part of a whole number.

$\frac{0.75}{1}$

Multiply both numerator and denominator by 100:

$\frac{0.75 \times 100}{1\times 100} =\frac{75}{100}$

$\frac{0.75}{1} \: and \: \frac{75}{100} \: are \: fractions \: of \: 0.75$

3 0

3 years ago

The sum of 3 consecutive even number is 270 what is thr first number in this sequense

Alenkasestr [34]

Answer:

the first 3 consecutive numbers

x, x +1, x +2 = 270

x+x+1+x+2 =270

3x +3 =270

collect like terms

3x =270 -3

3x =267

divide both sides by 3

x =89

7 0

3 years ago

Use Newton’s Method to find the solution to x^3+1=2x+3 use x_1=2 and find x_4 accurate to six decimal places. Hint use x^3-2x-2=

luda_lava [24]

Let $f(x) = x^3 - 2x - 2$ . Then differentiating, we get

$f'(x) = 3x^2 - 2$

We approximate $f(x)$ at $x_1=2$ with the tangent line,

$f(x) \approx f(x_1) + f'(x_1) (x - x_1) = 10x - 18$

The $x$ -intercept for this approximation will be our next approximation for the root,

$10x - 18 = 0 \implies x_2 = \dfrac95$

Repeat this process. Approximate $f(x)$ at $x_2 = \frac95$ .

$f(x) \approx f(x_2) + f'(x_2) (x-x_2) = \dfrac{193}{25}x - \dfrac{1708}{125}$

Then

$\dfrac{193}{25}x - \dfrac{1708}{125} = 0 \implies x_3 = \dfrac{1708}{965}$

Once more. Approximate $f(x)$ at $x_3$ .

$f(x) \approx f(x_3) + f'(x_3) (x - x_3) = \dfrac{6,889,342}{931,225}x - \dfrac{11,762,638,074}{898,632,125}$

Then

$\dfrac{6,889,342}{931,225}x - \dfrac{11,762,638,074}{898,632,125} = 0 \\\\ \implies x_4 = \dfrac{5,881,319,037}{3,324,107,515} \approx 1.769292663 \approx \boxed{1.769293}$

Compare this to the actual root of $f(x)$ , which is approximately 1.769292354, matching up to the first 5 digits after the decimal place.

4 0

2 years ago

Tim needs 23 3/4 m of wood trim to remodel a room. Wood trim is sold in lengths of 1 1/4 m. What equation can be used to find th

Bumek [7]

I hope this helps you

5 0

3 years ago