F(x)=3x-8--------
6x

Find and simplify

f(3)-f(1)
------------
3-1

I have no idea what this question is, any ideas?

Answers

Answer 1

Answer: What this is asking is for you to plug values into the following function: $f(x)=(3x-8)/(6x)$

Since the question is asking you to find $f(3)-f(1)$ , this is how you work it out:
You take the function;
$f(x)=(3x-8)/(6x)$
And plug the numbers indicated in for x;
$f(x)=(3x-8)/(6x)\nf(3)=(3(3)-8)/(6(3))\nf(3)=(9-8)/(18)\nf(3)=(1)/(18)\n\nf(1)=(3(1)-8)/(6(1))\nf(1)=(3-8)/(6)\nf(1)=(-5)/(6)\n\nNow\ what\ you\ do\ is\ you\ subract\ f(3)\ and\ f(1).\nf(3)-f(1)\nf(3)-f(1)=(1)/(18)-(-5)/(6)\nf(3)-f(1)=(1)/(18)-(-15)/(18)\nf(3)-f(1)=(1+15)/(18)\nf(3)-f(1)=(16)/(18)=(8)/(9)$
So the answer to f(3) - f(1) = $(8)/(9)$

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DO NOT ANSWER W/O EXPLANATION PLEASE! NEED WRITTEN SOLUTION.In triangle ABC, an altitude is drawn from vertex C to the line containing AB. The length of this altitude is h and h=AB. Which of the following is true?
I. Triangle ABC could be a right triangle.
II. Angle C cannot be a right angle.
III. Angle C could be less than 45 degrees.

Answers

We have altitude h to side AB and AB=h, i.e. the altitude is congruent to the side it goes to.

That's all kinds of triangles. One way to see them is using two horizontal parallel lines h apart, the bottom one with a base AB=h somewhere on it. Then any C on the top line makes a triangle ABC with altitude h=AB.

Let's go through the choices.

I. ABC could be a right triangle. That's TRUE.

We could have the isoscleles right triangle, C directly above B, so AC is the leg and an altitude, AB=AC and B is the right angle.

II. Angle C cannot be a right angle. That's TRUE.

The biggest angle C can be is when it's over the midpoint of AB, so if AB=2, h=2, and

$AC=√(2^2+1^2)=√(5)$

$C_{\textrm{max}} = 2 \arctan(1/2) \approx 53.13^\circ$

III. Angle C could be less than 45 degrees. That's TRUE.

As long as C stays on our top parallel, we can make it as acute as we like by going farther away from AB.

All true. Hmmm.

In the standard (x,y) coordinate plane below, the points ( 0,2), (8,2), (3,6), and (11,6) are the vertices of a parallelogram. What is the area, in square units, of the parallelogram

Answers

The area of the parallelogram is 32 square units.

What is a parallelogram?

Parallelogram is a quadrilateral that has two pairs of parallel sides.

In a parallelogram, opposite sides and angles are equal.

The adjacent angles add up to 180 degrees.

We have,

First, we can plot the points on the coordinate plane to get a better visual understanding of the parallelogram:

| (3,6) (11,6)

| *-----------*

| / /

| *-----------*

| (0,2) (8,2)

Now,

We can see that the base of the parallelogram is the line segment connecting (0,2) and (8,2), which has a length of 8 units.

To find the height of the parallelogram, we can observe that the line segment connecting (0,2) and (3,6) is perpendicular to the base, and has a length of 4 units.

Therefore,

The height of the parallelogram is 4 units.

Now,

The area of a parallelogram is given by the formula:

Area = base x height

Plugging in the values we found, we get:

Area = 8 x 4

Area = 32

Therefore,

The area of the parallelogram is 32 square units.

Learn more about parallelograms here:

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Your area would be 32, 8 by 4 is what the formula is

Find the area.
4 cm
6 cm
6 cm

Answers

Answer:

30 cm²

Step-by-step explanation:

6*(4+6)/2=30 cm²

The hours since a person has eaten and the strength of hunger they feel. what is the independent and dependent variable?

Answers

The hours are independent, time keeps flowing. but the hunger depends on hours. If time itself stopped, so would all matter, and thus, you would never be hungry.

Find the exact values of the numbers c that satisfy the conclusion of the Mean Value Theorem for the interval [−2, 2]. (Enter your answers as a comma-separated list.)

Answers

Answer:

The answer is " $\bold{c= \pm (2)/(√(3))}$ "

Step-by-step explanation:

If the function is:

$\to f'(x) = 3x^2-2 \n\n\to f'(c) = 3c^2-2$

points are:

$\to -2 \leq x \leq2$

use the mean value theorem:

$\to f'(c) = ( f(b)- f(a))/(b-a)$

$= ( f(2)- f(-2))/(2-(-2))\n\n= (4-(-4) )/(4)\n\n= (8)/(4)\n\n= 2$

$\to 3c^2-2=2 \n\n\to 3c^2=4 \n\n\to c^2=(4)/(3) \n\nc= \pm (2)/(√(3))$

Final answer:

The Mean Value Theorem states that for a continuous and differentiable function on a closed interval, there exists at least one 'c' within that interval where the average change rate equals the instantaneous rate at 'c'. In the given case of interval [-2,2], to find 'c', first calculate the average slope between the points (f(2)-f(-2))/4. Then equate this average slope to the derivative 'f'(c). The solution(s) to this equation are the c values for this problem.

Explanation:

The subject of this question pertains to the Mean Value Theorem in Calculus. According to this theorem, if a function f is continuous on a closed interval [a, b] and differentiable on the open interval (a, b), then there exists at least one number c in the open interval (a, b) such that the average rate of change over the interval equals the instantaneous rate of change at c.

In the given case, we're trying to find the 'c' value for the interval [-2,2]. First, we need to find the average slope between the two points. Assuming f is your function, that would be (f(2)-f(-2))/ (2 - -2). Subtract the function values of the two points and divide by the total interval length. Next, we need to see where this average slope equals the instantaneous slope 'f'(c), this entails solving the equation 'f'(c) = (f(2)-f(-2))/4. The solution to this equation will be the c values that satisfy the Mean value theorem within the provided interval.

Learn more about Mean Value Theorem here:

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An angelfish was 1 1/2 inches long when it was bought. Now it is 2 1/3 inches long.a. How much has the angelfish grown?

b. An inch is 1/12 of a foot. How much has the angelfish grown in feet?

40 points!