I don't know how to solve these. please help. show work please.​

(1) f(x) = (1 - x³) / (x - 1)

(a) The domain is the set of values that this function can take on. If x = 1, the denominator becomes 0 and the function is undefined. Any other value of x is okay, though, since for x ≠ 1, we have

f(x) = (1 - x³) / (x - 1) = - (1 - x³) / (1 - x) = -(x² + x + 1)

which is defined for all x. This also tells us that the plot of f(x) is a parabola with a hole at x = 1. So, the domain is the interval (-∞, 1) ∪ (1, ∞).

(b) The range is the set of values that the function actually does take on. Taking the simplified version of f(x), we can complete the square to write

-(x² + x + 1) = -(x² + x + 1/4 - 1/4) - 1 = -(x + 1/2)² - 3/4

which is represented by a parabola that opens downward, with a maximum value of -3/4. So the range is the interval (-∞, -3/4).

(c) Judging by the plot of f, the limits at both negative and positive infinity are -∞.

(d) Same answer as part (a).

(2) f(x) = x³ - x

(a) The derivative of f at x = 3, and hence the slope of the tangent line to this point, is

[tex]f'(3)=\displaystyle\lim_{h\to0}\frac{f(3+h)-f(3)}h[/tex]

[tex]f'(3)\displaystyle=\lim_{h\to0}\frac{((3+h)^3-(3+h))-24}h[/tex]

[tex]f'(3)=\displaystyle\lim_{h\to0}\frac{(27+27h+9h^2+h^3)-(3+h)-24}h[/tex]

[tex]f'(3)=\displaystyle\lim_{h\to0}\frac{26h+9h^2+h^3}h[/tex]

[tex]f'(3)=\displaystyle\lim_{h\to0}(26+9h+h^2)=\boxed{26}[/tex]

(b) The tangent line at x = 3 has equation

y - f (3) = f ' (3) (x - 3)

y - 24 = 26 (x - 3)

y = 26 x - 54

We also want to find any other tangent lines parallel to this one, which requires finding all x for which f '(x) = 26. We could use the same limit definition as in part (a), but to save time, we exploit the power rule to get

f '(x) = 3 x² - 1

Then solve for when this is equal to 26:

3 x² - 1 = 26   ==>   x² = 9   ==>   x = ±3

The other tangent line occurs at x = -3, for which we have f (-3) = -24, and so the equation for the tangent is

y - f (-3) = 26 (x - (-3))

y + 24 = 26 (x + 3)

y = 26 x + 54

Answer:

3.2

Step-by-step explanation:

Imagine a straight line from the top of the pyramid to the base, the point where the line will meet the base will be half the side of the pyramid. This will form a right angles triangle.

Slope is given by

[tex]\text{Slope}=\dfrac{\Delta y}{\Delta x}\\\Rightarrow \text{Slope}=\dfrac{8.9}{\dfrac{5.6}{2}}=3.17857\\\Rightarrow \text{Slope}\approx3.2[/tex]

The slope of the face of the pyramid is 3.2

Answer:

yes

Step-by-step explanation:

Answer:

yes? That's right. ummmm lol

Answer:

W>16

Step-by-step explanation:

The formula for calculating the perimeter of a rectangle:

P = 2L+2W

L is the length of the rectangle

W is the width of the rectangle:

Given

P = 96m

If the length of a rectangle is 2 times the width, then L = 2W

Substitute into the formula:

Since the perimeter is less than 96m

96 < 2(2W)+2W

96 < 4W+2W

96 < 6W

Divide both sides by 6:

96/6 < 6W/6

16 < W

W>16

Hence the possible values of the width are all values greater than 16.

Answer:

The answer is The first one -10/27

Answer:

A

Step-by-step explanation:

Answer:

-8

Step-by-step explanation:

A triangle is always 180 degrees

(btw I'm not sure if this is addition or multiplication so sorry if i'm wrong!)

65 + 40 = 105

180 - 105 = 75

75 - 83 = -8

Answer:

the angle itself is 75 degrees so x=-8

Step-by-step explanation:

Answer:

First, let's write our equation in a general way.

We know that:

1 cubic foot weighs 80 pounds.

The container weighs 40 pounds.

Then, if i put n cubic feet of sand in the container, the total mass will be one time the mass of the container plus n times the mass of one cubic foot of sand.

We can write this as:

w(n) = 40lb + n*80lb

This is a linear equation, where the y-axis will represent the mass in pounds and the x-axis will be the number of cubic feet of sand in the container in units, a graph of this is shown below.

You can see that it is really steep, this is because for really small increments in n, the weight increases a lot.

Answer

ok, Just plot the points at (0,40) and (2,200) :))

Answer:

The probability that the fisher chosen from Clearwater did not have a license and the fisher chosen from Mountain View had a license is 0.32.

Step-by-step explanation:

Denote the events as follows:

X = a fisher at Clearwater Park had a fishing license

Y = a fisher at Mountain View Park had a fishing license

The two events are independent.

The information provided is:

n (X) = 48

n (X') = 32

n (Y) = 72

n (Y') = 18

Then,

N (X) = n (X) + n (X')

        = 48 + 32

        = 80

N (Y) = n (Y) + n (Y')

        = 72 + 18

        = 90

Compute the probability that the fisher chosen from Clearwater did not have a license and the fisher chosen from Mountain View had a license as follows:

[tex]P(X'\cap Y)=P(X')\times P(Y)[/tex]

                 [tex]=\frac{n(X')}{N(X)}\times \frac{n(Y)}{N(Y)} \\\\=\frac{32}{80}\times\frac{72}{90}\\\\=0.32[/tex]

Thus, the probability that the fisher chosen from Clearwater did not have a license and the fisher chosen from Mountain View had a license is 0.32.

Answer:

y  =  − 2 /3 x  + 4

Step-by-step explanation:

Answer: y=-2/3x + 4

Step-by-step explanation:

Answer:

she uses 72 gallons

Step-by-step explanation:

just do 144/2 and the answer is 72

if you wanna check your answer just do 72x2 and it equals 144

Answer:

jessie: 14.5

ben: 10.5

Answer:

No it is the ticked one........

Hope it helps.......

Answer: is it a function-yes

why: none of the y values are the same

Step-by-step explanation:

Answer:

[tex]22[/tex]

Step-by-step explanation:

If FG= 8

and GH=14

G is a midpoint

To find FH you would add 8 and 14.

[tex]8 + 14 = 22[/tex]

Answer:

add it FH +GH

=8+14

=22 ans.....

Answer: Can u post a question?

Step-by-step explanation:

Answer:

|0.05|

Step-by-step explanation:

no absolute value can be negative

Answer:

0.05

Step-by-step explanation:

The lines outside the number mean absolute value. The absolute value of a number is how far it is from 0, so it's always positive. Basically, you just swap the sign of whatever number you are looking at. In this case, absolute value of -0.05 would simply be 0.05. Hope this helped!

Answer:1

Step-by-step explanation:6-5/3-2=1/1

Answer:

[tex]-8,+735[/tex]

Step-by-step explanation:

The lowest point in New Orleans is 8 feet below sea  level.

This can be represented numerically using [tex]-8[/tex]

(negative sign denotes below sea level)

The highest point in Chicago is 735 feet above sea  level.

This can be represented numerically using [tex]+735[/tex]

(positive sign denotes above sea level)

Answer:

This is correct but if some people are confused it’s a negative integer and a positive integer

Step-by-step explanation:

Answer:

The vertex is (-5, -1)

Step-by-step explanation:

Standard vertex form is a(x - b)^2 + c where (b, c) is the vertex.

Answer:

AB, BC, AC

Step-by-step explanation:

Hopefully I helped!! :)

Answer:

35

Step-by-step explanation:

Comman knowlege. Also there is a fancy name for them because thay are the same way... Corresponding Angles

Answer:

35 degrees

Step-by-step explanation:

It is congruent to 8 and lined up so it is also 35 degrees.

Answer:

39pounds 6oz

Step-by-step explanation:

15x2=30

1x30=30pounds

5x30=150oz

30p+150oz=39.37500

37500p=6oz

39pounds and 6 oz

Answer:

Situation 3 is not functional

Step-by-step explanation:

Here, we want to determine if there exists a functional relationship between the properties in each situation.

For there to exist a functional relationship, then one of the factors in the situation must be dependent on the other factor in the situation.

Let us consider the situations individually now;

Situation 1

There exists a functional relationship here. This is because the higher the minutes used, the higher the cell phone bill and the lower the minutes used, the lower the cell phone bill. This is because there exists a fixed rate of charge per minute

Situation 2

There exists a functional relationship here too.

This is because, the we cannot find the perimeter of the square without knowing the measure of the sides of the square. That is why there is a mathematical formula that links the perimeter of the square to the sides of the square.

In a case where we have the perimeter as P and the sides as L

Then the functional equation linking both is;

P(l ) = 4 L

Situation 3;

There is no functional relationship here. The amount owed per each credit card is tied to the credit card in question.

There is no way the total amount owed by a person is distributed across the number of credit cards the person have. Each credit card has its own money charged on it monthly due to the activities on it which is independent on the activities of the other credit cards

Answer:

2 1/4

Step-by-step explanation:

Answer:

the answer is 0.4 The reason is because 0.4 x8=0.32

Step-by-step explanation:

Answer:

50 minutes

Step-by-step explanation:

First set up an inequality to find you answer like

800 - 6x = 1000 - 10x

then subtract 800 from both sides leaving you with

-6x = 200 - 10 x

Then add 10 x to both sides giving you

4x = 200

The simplify from here by dividing 200 by 4

200/4 = 50 giving you your answer

Answer:

$16.65

Step-by-step explanation:

333.00 divided by 0.20