Find the equation of the tangent line to the graph of y = x^3 – 3x^2 + x at the point (2,-2)
need solution with derivatives(a-e)

Answer:

\(\frac{5x-11}{\left(2x-3\right)\left(x+2\right)}\)

Step-by-step explanation:

\(\frac{5x-11}{2x^2+x-6}\)

Factor the denominator.

\(\frac{5x-11}{\left(2x-3\right)\left(x+2\right)}\)

The fraction cannot be simplified further.

Answer:

solution,

\( \frac{5x - 11}{2 {x}^{2} + x - 6} \\ = \frac{5x - 11}{2 {x}^{2} + (4 - 3)x - 6} \\ = \frac{5x - 11}{2 {x}^{2} + 4x - 3x - 6 } \\ = \frac{5x - 11}{2x(x + 2) - 3(x + 2)} \\ = \frac{5x - 11}{(x + 2)(2x - 3)} \)

Hope this helps..

Another point on the line is (-9, 7). Ultimately, the choice of which point to use depends on the context or specific requirements of the problem you are solving.

To determine which point to use from the equation y - 7 = 3(x + 9), we need more information.

The equation provided represents a linear equation in the form y - y1 = m(x - x1), where (x1, y1) is a point on the line and m is the slope.

Without additional context or specific instructions, we can choose any point that satisfies the equation to use as a reference.

For example, if we let x = 0, we can solve the equation for y:

y - 7 = 3(0 + 9)

y - 7 = 3(9)

y - 7 = 27

y = 27 + 7

y = 34

So, one point on the line is (0, 34).

Alternatively, if we let x = -9, we can solve the equation for y:

y - 7 = 3(-9 + 9)

y - 7 = 3(0)

y - 7 = 0

y = 7

So, another point on the line is (-9, 7).

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The value of x is -3 when value of y = 15 by using the property proportion as x and y are directly related to each other.

What is direct relation?

Two variables x and y are directly related to each other if x increases or decreases the value of y also increases or decreases proportionally.

We are given that value of y is -50 then value of x is 10

We have to find the value of x when y is 15

We solve it using proportion

we have,

10/x = -50/15

On separating the variable from the constant and then simplifying we get,

x=-3

Hence the value of x is -3 when y is 15

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The group of people who participated in the study's sample survey was chosen at random to participate in it by the national grocery store chain. In this instance, the sample comprises the 1,000 customers from throughout the nation that participated in the survey. They are a segment of the total consumer base that frequents the chain's retail outlets.

The chain randomly surveyed 1,000 customers from around the country. It concluded from the study that 80% of all customers who hopped into the chain's stores were interested in the service. The nationwide grocery store chain randomly selected the participants in the study's sample survey from the general public.

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Answer:

3/2 is not a interger a interger is any number that does not have a decmil point if we convert 3/2 to a decmil point you get 1.5 which has a desmil point

no

Hope This Helps!!!

I don't know if there is supposed to be a picture, but 3/2 is not an integer, simplified it would be 1 and 1/2 which isn't a integer

Answer:

See Diagram below

Explanation:

In order to draw a rhombus, recall some of the properties below:

• All sides of a rhombus are equal.

• The opposite sides of a rhombus are parallel.

The rhombus is drawn and attached below:

• The red single lines show that all the sides are equal.

• The arrow and double-arrow shows that opposite sides are parallel.

Solve the system using substitutions:

x has a value of 1. Use this value to find the value of y.

y has a value of 1.

x=1

y=1

Answer:

thats the answer

Step-by-step explanation:

Answer: 12 in each

Step-by-step explanation: To solve this you'd divide the number of donuts by boxes.

Answer:

12 Donuts Per Box

Step-by-step explanation:

24/2=12

The function with the steepest slope is \(y = 7x - 3\).

The correct answer is C.

The linear function with the steepest slope is the one with the highest absolute value for the coefficient of x.

Let's compare the coefficients of x in each of the given functions:

\(y = -8x + 5\)

Slope: -8

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

Simplifying, we get \(y - 9 = -2x - 2\)

Rearranging, we have \(y = -2x + 7\)

Slope: -2

\(y = 7x - 3\)

Slope: 7

\(y + 2 = 6(x + 10)\)

Simplifying, we get \(y + 2 = 6x + 60\)

Rearranging, we have \(y = 6x + 58\)

Slope: 6

Therefore, the steepest slope is the \(y = 7x - 3\).

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Check the picture below.

Answer:

let the the first number X,

second number be 2×(8x) or. 16x

third number be 8x

equation 1 ,

X + 16x + 8x = 84

or. 25x = 84

or. x = 84 ÷ 25 = 3.36

Step-by-step explanation:

there is nothing missing. this is a complete proof.

yes, the various steps are correct.

8

In this pattern, we have 4 12 then 20.

We can see that the difference 4 and 12 is 8.

Since the difference between 12 and 20 is also 8, the common difference of the sequence is 8.

Answer:

a the graph is correct

Step-by-step explanation:

edg 21 ^u^

The graph x² + ( y²/49 )>1 is correct. The correct option is A.

Inequality is the relationship between two expressions that are not equal, employing a sign such as ≠ “not equal to,” > “greater than,” or < “less than.”.

The given inequality is x² + ( y²/49 )>1;. The graph is plotted on the x-y plane. The curves of the graph cut the y-axis at positive 7 and negative 7 and cut the x-axis at positive 1 and negative 1.

Hence, the correct option is A.

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Based on 10% of 82 being 8.2, 60% of 82 can be found to be the sum of 49.2.

First find out what 10% of 82 is:

= 10% x 82

= 8.2

You can then find out what 60% is by using the formula:
= 10% of 82 x 60%/10%

= 8.2 x 6

= 49.2

In conclusion, you can find it by multiplying the 10% by 6.

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Answer:

1/4 miles

Step-by-step explanation:

Hey there!

Well starting at Campbell and going to Morristown it is 1/4 miles.

Going from Campbell to Clarksville it is 2/4 miles.

So to find the difference we’ll subtract.

2/4 - 1/4

= 1/4 miles

Hope this helps :)

s3+5s2+8s+4

Step-by-step explanation:

Answer:

(1-e^(-2t))*u(t) - (1-e^(-t))*u(t)

Where u(t) is the step function

Step-by-step explanation:

use partial fraction decomposition. This involves expressing the rational function as the sum of simpler fractions, each with a pole at a different point in the complex plane. Once we have done this, we can use the formula for the inverse Laplace transform of a simple pole to find the inverse Laplace transform of the original function.

In 2.5 liters we have 84.535 fluid ounces.

(1 liter is equal to 33.814 fluid ounces)

A unitary method is a mathematical way of obtaining the value of a single unit and then deriving any no. of given units by multiplying it with the single unit.

We know, 1 liter is equal to 33.814 fluid ounces.

Now, To convert liters to fluid ounces we have multiply the number of liters by the unit value of fluid ounces which is,

= 2.5×33.814 fluid ounces.

= 84.535 fluid ounces.

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Given: Which geometric figure has 60 rotational symmetry?

As the total angle of rotation = 360

So, 360/60 = 6

This means the regular hexagon has 60 rotational symmetry.

So, the answer will be option A. regular hexagon.

Answer:

\(Probability =0.1744\)

Step-by-step explanation:

Given

Total

\(American = 11\)

\(Canadian = 18\)

Selection

\(American = 0\)

\(Canadian = 4\)

Required

Determine the probability of selecting a 4 committee member that are Canadian.

First, we calculate total possible selection.

\(Total = American + Canadian\)

\(Total = 11 + 18\)

\(Total = 27\)

Number of ways to select 4 from 27 is:

\(^{27}C_4 = \frac{27!}{(27-4)!4!}\)

\(^{27}C_4 = \frac{27!}{23!4!}\)

\(^{27}C_4 = \frac{27*26*25*24*23!}{23!4!}\)

\(^{27}C_4 = \frac{27*26*25*24}{4!}\)

\(^{27}C_4 = \frac{27*26*25*24}{4*3*2*1}\)

\(^{27}C_4 = \frac{421200}{24}\)

\(^{27}C_4 = 17550\)

Next, we calculate ways of selecting 4 Canadians from 18 is:

\(^{18}C_4 = \frac{18!}{(18-4)!4!}\)

\(^{18}C_4 = \frac{18!}{14!4!}\)

\(^{18}C_4 = \frac{18*17*16*15*14!}{14!4!}\)

\(^{18}C_4 = \frac{18*17*16*15}{4!}\)

\(^{18}C_4 = \frac{18*17*16*15}{4*3*2*1}\)

\(^{18}C_4 = \frac{73440}{24}\)

\(^{18}C_4 = 3060\)

The required probability is:

\(Probability =\frac{3060}{17550}\)

\(Probability =0.1744\)

According to the labeling on the attached graph, the size of the inflationary gap is equal to: Y1 – YP. The correct answer is option B.

Although part of your question is missing, you might be referring to this full question: (Figure: Short-Run Equilibrium) Look at the figure Short-Run Equilibrium. It reflects a short-run inflationary gap. According to the labeling on the graph, the size of the inflationary gap is equal to:

A) P2 - P1.

B) Y1 - YP.

C) P2 - P0.

D) P1 - P0.

An inflationary gap is a macroeconomic concept that measures the difference between the current level of real gross domestic product (GDP) and the GDP which would exist if an economy was operating at full employment. For the gap to be considered inflationary, the current real GDP have to be higher than the potential GDP. It is called inflationary because it leads to inflation (continuous rise in prices). An inflationary gap refers to the positive difference among real GDP and potential GDP at full employment.

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Answer:

To find the volume of the shipping box in cubic feet, we need to convert the dimensions from inches to feet and then calculate the volume.

Given:

Length = 36 inches

Width = 24 inches

Height = 18 inches

Converting the dimensions to feet:

Length = 36 inches / 12 inches/foot = 3 feet

Width = 24 inches / 12 inches/foot = 2 feet

Height = 18 inches / 12 inches/foot = 1.5 feet

Now, we can calculate the volume of the box by multiplying the length, width, and height:

Volume = Length * Width * Height

Volume = 3 feet * 2 feet * 1.5 feet

Volume = 9 cubic feet

Therefore, the shipping box can hold 9 cubic feet.

Step-by-step explanation:

First convert the units because it's asking for the cubic feet but they give us the measurements in inches.

To convert inches to feet we divide the number by 12.

36 ÷  12 = 3

24 ÷  12 = 2

18 ÷ 12 = 1.5

Now to find the volume, we multiply it all together.

3 × 2 × 1.5 = 9

It can hold 9 cubic feet.

Hope this helped!

Step-by-step explanation:

I'm not sure if I'm using substitution method but I guess it's x = 12.4

Answer:

Yes, because while the total number of professors increases, the number of pure math professors decreases.

Step-by-step explanation:

Using Hamilton's method:

pure math 4/28 = 0.142857

applied math 12/28 = 0.42857

statistics = 12/28 = 0.42857

10 × 0.142857 = 1.42857

10 × 0.42857 = 4.2857

10 × 0.42857 = 4.2857

numbers of professors:

pure math 1

applied math 4

statistics 4

total 9

Add 1 to pure math

Final original numbers of professors using Hamilton's method

pure math 2

applied math 4

statistics 4

total 10

Add 1 professor to department.

11 × 0.142857 = 1.5714

11 × 0.42857 = 4.71428

11 × 0.42857 = 4.71428

numbers of professors:

pure math 1

applied math 4

statistics 4

total 9

Add 1 to applied math and 1 to statistics

Final new numbers of professors using Hamilton's method

pure math 1

applied math 5

statistics 5

total 11

Despite the addition of 1 professor to the department, the field of pure mathematics went from 2 professors to 1 professor. This is an example of the Alabama paradox.

Answer: Yes, because while the total number of professors increases, the number of pure math professors decreases.