Ln x-ln(x-5)=ln2 Help in this problem please having problems on my homework

F(x)=x 3−9xf, left parenthesis, x, right parenthesis, equals, x, cubed, minus, 9, x What is the average rate of change of f over

mel-nik [20]

Answer:

$A(x) = 243$

Step-by-step explanation:

Given

$f(x) = x^3 - 9x$

$Interval: (12,6)$

Required

Determine the average rate of change

Average rate is calculated as thus;

$A(x) = \frac{f(b) - f(a)}{b - a}$

In this case; b = 12 and a = 6

Calculating f(12)

$f(12) = 12^3 - 9 * 12$

$f(12) = 1728 - 108$

$f(12) = 1620$

Calculating f(6)

$f(6) = 6^3 - 9 * 6$

$f(6) = 216 - 54$

$f(6) = 162$

Substitute 12 for b and 6 for a in $A(x) = \frac{f(b) - f(a)}{b - a}$

$A(x) = \frac{f(12) - f(6)}{12 - 6}$

Substitute values for f(6) and f(12)

$A(x) = \frac{1620 - 162}{12 - 6}$

$A(x) = \frac{1458}{ 6}$

$A(x) = 243$

4 0

3 years ago

1. What is the perimeter of the figure below. Simplify. 4x^3-5x 2x^3+6x 6x^3+x

____ [38]

Answer:

$12x^3+2x$

Step-by-step explanation:

The perimeter of a polygon is equal to the sum of its sides.

The sides in the triangle shown have lengths $2x^3+6x$ , $4x^3-5x$ , and $6x^3+x$ in no specific order.

Since its perimeter is given by the sum of its sides, the perimeter is equal to:

$2x^3+6x+4x^3-5x+6x^3+x$

Combine like terms:

$\boxed{12x^3+2x}$

6 0

3 years ago

Determine the area bounded by the curves f(x) = 4x and g(x) = 3x + 1.

ANEK [815]

Answer: 12x^2+4

Step-by-step explanation:

7 0

3 years ago

A random sample of 11 fields of rye has a mean yield of 20.1 bushels per acre and standard deviation of 7.66 bushels per acre. D

Lady bird [3.3K]

Answer:

17.1≤x≤23.1

Step-by-step explanation:

The formula for calculating the confidence interval is expressed as;

CI = x ± z*s/√n

x is the mean yield = 20.1

z is the 80% z-score = 1.282

s is the standard deviation = 7.66

n is the sample size = 11

Substitute

CI = 20.1 ± 1.282*7.66/√11

CI = 20.1 ± 1.282*7.66/3.3166

CI = 20.1 ± 1.282*2.3095

CI = 20.1 ±2.9609

CI = (20.1-2.9609, 20.1+2.9609)

CI = (17.139, 23.0609)

hence the required confidence interval to 1dp is 17.1≤x≤23.1

8 0

3 years ago

Write the equation of the line that passes through the points

sesenic [268]

Answer:

$y+5=2(x-3)$ or $y+9=2(x-1)$

Step-by-step explanation:

step 1

Find the slope of the line

The formula to calculate the slope between two points is equal to

$m=\frac{y2-y1}{x2-x1}$

we have the ordered pairs

(3,-5) and (1,-9)

substitute the values

$m=\frac{-9+5}{1-3}$

$m=\frac{-4}{-2}$

$m=2$

step 2

Find the equation in point slope form

$y-y1=m(x-x1)$

Analyze two cases

First case

we have

$m=2$

$point\ (3,-5)$

substitute

$y+5=2(x-3)$

Second case

we have

$m=2$

$point\ (1,-9)$

substitute

$y+9=2(x-1)$

Note: The equation of the line in point slope form varies according to the point you choose, in contrast to the slope-intercept form

6 0

3 years ago