Workout to the simplest:[tex] \int \: {x}^{2} ln( {x}^{3} ) dx[/tex]

Answer:[tex]\rm \displaystyle \ln(x) { {x}^{3} } - \frac{ {x}^{3} }{3} + \rm C[/tex]Step-by-step explanation:we would like to integrate the following integration[tex] \displaystyle \int {x}^{2} \ln( {x}^{3} ) dx[/tex]before doing so we can use logarithm exponent rule in order to get rid of the exponent of ln(x)[tex] \displaystyle \int 3 {x}^{2} \ln( {x}^{} ) dx[/tex]now notice that the integrand is in the mutilation of two different functions thus we can use integration by parts given by[tex] \rm\displaystyle \int u \cdot \: vdx = u \int vdx - \int u' \bigg( \int vdx \bigg)dx[/tex]where u' can be defined by the differentiation of ufirst we need to choose our u and v in that case we'll choose u which comes first in the guideline ILATE which full from is Inverse trig, Logarithm, Algebraic expression, Trigonometry, Exponent.since Logarithms come first our [tex] \displaystyle u = \ln(x) \quad \text{and} \quad v = {3x}^{2} [/tex]and u' is [tex]\frac{1}{x}[/tex]altogether substitute:[tex] \rm \displaystyle \ln(x) \int 3{x}^{2} dx - \int \frac{1}{x} \left( \int 3 {x}^{2} dx \right)dx[/tex]use exponent integration rule to integrate exponent:[tex] \rm \displaystyle \ln(x) \int 3{x}^{2} dx - \int \frac{1}{x} \left( 3\frac{ {x}^{3} }{3} \right)dx[/tex]once again exponent integration rule:[tex] \rm \displaystyle \ln(x) 3\frac{ {x}^{3} }{3} - \int \frac{1}{x} \left( 3\frac{ {x}^{3} }{3} \right)dx[/tex]simplify integrand:[tex] \rm \displaystyle \ln(x) 3\frac{ {x}^{3} }{3} - \int \frac{ 3{x}^{3} }{3x} dx[/tex]use law of exponent to simplify exponent:[tex] \rm \displaystyle \ln(x) \frac{ 3{x}^{3} }{3} - \int \frac{ 3\cancel{ {x}^{3}} }{3 \cancel{x}} dx[/tex][tex] \rm \displaystyle \ln(x) \frac{ 3{x}^{3} }{3} - \int \frac{ 3{x}^{3} }{3} dx[/tex]use constant integration rule to get rid of constant:[tex]\rm \displaystyle \ln(x) \frac{3 {x}^{3} }{3} - 1 \int {x}^{2}dx[/tex]use exponent integration rule:[tex]\rm \displaystyle \ln(x) \frac{3 {x}^{3} }{3} - \frac{ {x}^{3} }{3} [/tex][tex]\rm \displaystyle \ln(x) { {x}^{3} } - \frac{ {x}^{3} }{3} [/tex]and finally we of course have to add the constant of integration:[tex]\rm \displaystyle \ln(x) { {x}^{3} } - \frac{ {x}^{3} }{3} + \rm C[/tex]and we are done!

Mathematics College

Workout to the simplest:
$ \int \: {x}^{2} ln( {x}^{3} ) dx$

Answers

Answer 1

Answer:

$\rm \displaystyle \ln(x) { {x}^{3} } - \frac{ {x}^{3} }{3} + \rm C$

Step-by-step explanation:

we would like to integrate the following integration

$ \displaystyle \int {x}^{2} \ln( {x}^{3} ) dx$

before doing so we can use logarithm exponent rule in order to get rid of the exponent of ln(x³)

$ \displaystyle \int 3 {x}^{2} \ln( {x}^{} ) dx$

now notice that the integrand is in the mutilation of two different functions thus we can use integration by parts given by

$ \rm\displaystyle \int u \cdot \: vdx = u \int vdx - \int u' \bigg( \int vdx \bigg)dx$

where u' can be defined by the differentiation of u

first we need to choose our u and v in that case we'll choose u which comes first in the guideline ILATE which full from is Inverse trig, Logarithm, Algebraic expression, Trigonometry, Exponent.

since Logarithms come first our

$ \displaystyle u = \ln(x) \quad \text{and} \quad v = {3x}^{2} $

and u' is $\frac{1}{x}$

altogether substitute:

$ \rm \displaystyle \ln(x) \int 3{x}^{2} dx - \int \frac{1}{x} \left( \int 3 {x}^{2} dx \right)dx$

use exponent integration rule to integrate exponent:

$ \rm \displaystyle \ln(x) \int 3{x}^{2} dx - \int \frac{1}{x} \left( 3\frac{ {x}^{3} }{3} \right)dx$

once again exponent integration rule:

$ \rm \displaystyle \ln(x) 3\frac{ {x}^{3} }{3} - \int \frac{1}{x} \left( 3\frac{ {x}^{3} }{3} \right)dx$

simplify integrand:

$ \rm \displaystyle \ln(x) 3\frac{ {x}^{3} }{3} - \int \frac{ 3{x}^{3} }{3x} dx$

use law of exponent to simplify exponent:

$ \rm \displaystyle \ln(x) \frac{ 3{x}^{3} }{3} - \int \frac{ 3\cancel{ {x}^{3}} }{3 \cancel{x}} dx$

$ \rm \displaystyle \ln(x) \frac{ 3{x}^{3} }{3} - \int \frac{ 3{x}^{3} }{3} dx$

use constant integration rule to get rid of constant:

$\rm \displaystyle \ln(x) \frac{3 {x}^{3} }{3} - 1 \int {x}^{2}dx$

use exponent integration rule:

$\rm \displaystyle \ln(x) \frac{3 {x}^{3} }{3} - \frac{ {x}^{3} }{3} $

$\rm \displaystyle \ln(x) { {x}^{3} } - \frac{ {x}^{3} }{3} $

and finally we of course have to add the constant of integration:

$\rm \displaystyle \ln(x) { {x}^{3} } - \frac{ {x}^{3} }{3} + \rm C$

and we are done!

Related Questions

PLEASEEEEEE IM BEGGING SOMEONE PLEASEEEE HELPPPP PLEASEEEEE PLEASEEEEE SOEMONE HELPPPP PLEASEEEEEEEEEEEEEEEEEEEE

Answers

Answer:

8 nachos and 5 hot dogs

Step-by-step explanation:

Let x equal number of nachos

let y equal number of how dogs

1.5x + 2y = 22

x + y = 13

y = 13 - x

1.5x + 2(13 - x) = 22

1.5x + 26 - 2x = 22

1.5x - 2x = 22 - 26

-0.5x = - 4

x = -4/-0.5

x = 8

y = 13 - x

y = 13 - 8

y = 5

What is the value of h in the diagram below? If necessary, round your answer
to the nearest tenth of a unit.

Answers

Answer:

what's the diagram??

Step-by-step explanation:

what's the diagram??

Name: Salem A
Score:
Unit # 12 - Lesson #4 Exit Ticket: The spinner shown below has
three sections. If the pointer is spun one time, which number is it
most likely to land on? Explain your choice.
3
1
2

Answers

The number the spinner is most likely to land on is 2

Which number is it most likely to land on?

From the question, we have the following parameters that can be used in our computation:

The spinner

From the spinner, we have the number that covers the largest area to be 2

i.e.

Largest area = 2

This means that the number it is most likely to land on is 2 and it has the highest probability

Answers

Answer:

A triangle

Step-by-step explanation:

The plane which cuts a corner intersects the polyhedron in n faces that depend on the specific polyhedron as seen in the attachment

And here's a cube, and three faces intersect. Because the intersection of two planes is a line, and that there are three planes with which to intersect, the polygon has three sides.

Therefore in the given situation, the polygon is a triangle

Please PLease PLEASE HELP ME!!!!!!!!!!!!!! Consider what would happen if you were to slice a face at

who want crown things

Answers

Answer:

meeee plzzzzzzz even thow i have no idea whta that ios

Step-by-step explanation:

identify the 3D shape :)thank you

Answers

Answer: Triangular prism

If you folded the figure up, you would have a prism where the parallel bases are right triangles. Each lateral face is a rectangle.

It might help to imagine a room where the floor and ceiling are triangles (they are identical or congruent triangles). Each wall of this room is one of the rectangles shown.

Solve the system of equations using elimination.

−2x + 3y = 15x + y = 10

A (2, 8)
B (3, 7)
C (6, 9)
D (9, 11)

Answers

The solution of the linear equations −2x + 3y = 15 and x + y = 10 will be (3. 7). Then the correct option is B.

What is the solution to the equation?

The allocation of weights to the important variables that produce the calculation's optimum is referred to as a direct consequence.

The system of linear equations is given below.

−2x + 3y = 15 ....1

x + y = 10

2x + 2y = 20 ...2

Add equations 1 and 2, then we have

5y = 35

y = 7

Then the value of the variable 'x' is given as,

x + 7 = 10

x = 3

The solution of the linear equations −2x + 3y = 15 and x + y = 10 will be (3. 7). Then the correct option is B.

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Two cylinders, a and b, each started with different amounts of water. The graph shows how the height of the water changed as the volume of water increased in each cylinder. Match the graphs of a and b to Cylinders P and Q. Explain your reasoning. height in centimeters b volume in milliliters P

Answers

To match the graphs of cylinders a and b to cylinders P and Q, we need to analyze the relationship between the height of the water and the volume of water in each cylinder.

Cylinder P would correspond to graph b, while Cylinder Q would correspond to graph a.

The reasoning behind this is as follows:

Cylinder P, corresponding to graph b, shows a steeper increase in height with increasing volume. This indicates that the water level rises quickly as more volume is added, suggesting that the cylinder has a smaller cross-sectional area. Since height is directly proportional to volume for a cylinder, a smaller cross-sectional area would result in a higher rise in height for the same volume of water.

Cylinder Q, corresponding to graph a, shows a slower increase in height with increasing volume. This implies that the water level rises more gradually as more volume is added, indicating a larger cross-sectional area. A larger cross-sectional area would result in a smaller increase in height for the same volume of water.

In summary, the steeper graph b matches Cylinder P with a smaller cross-sectional area, while the gentler graph a matches Cylinder Q with a larger cross-sectional area.

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Please help . Determine the type of triangle that is drawn below.

Answers

Scalene obtuse

Hope this helps, brainliest? :))

Scalene obtuse first person who answered is correct

1/2 + 1/2 =

answer
quick

Answers

Answer:

1/4

Step-by-step explanation:

just add the demoniator!

Answer: 1

Step-by-step explanation:

1/2 + 1/2 only add the top numbers using the same denominator, you end with this

2/2 then divide

2/2 = 1

Bella is deciding between two parking garages. Garage A charges an initial fee of $7 to
park plus $3 per hour. Garage B charges an initial fee of $3 to park plus $4 per hour.
Let A represent the amount Garage A would charge if Bella parks for t hours, and let
B represent the amount Garage B would charge if Bella parks for t hours. Write an
equation for each situation, in terms of t, and determine the hours parked, t, that
would make the cost of each garage the same.

Answers

Answer:

Step-by-step explanation:

The equation for the cost of parking in Garage A for t hours is:

A = 3t + 7

The equation for the cost of parking in Garage B for t hours is:

B = 4t + 3

To find the number of hours parked, t, that would make the cost of each garage the same, we can set the two equations equal to each other and solve for t:

3t + 7 = 4t + 3

Subtracting 3t from both sides, we get:

7 = t + 3

Subtracting 3 from both sides, we get:

4 = t

Therefore, if Bella parks for 4 hours, the cost of parking in Garage A and Garage B will be the same.

To verify, we can substitute t = 4 into the two equations:

A = 3(4) + 7 = 19

B = 4(4) + 3 = 19

So, if Bella parks for 4 hours, the cost of parking in Garage A and Garage B will be $19.

Answer:

Bella is deciding between two parking garages. Garage A charges an initial fee of $7 to

park plus $3 per hour. Garage B charges an initial fee of $3 to park plus $4 per hour.

Let A represent the amount Garage A would charge if Bella parks for t hours, and let

B represent the amount Garage B would charge if Bella parks for t hours. Write an

equation for each situation, in terms of t, and determine the hours parked, t, that

would make the cost of each garage the same.

A = $7 + $3

B = $3 + $4

Select the correct answer
Vector v has its initial point at (7.-9) and its terminal point at (-17,4), Which unit vector is in the same direction as v?

Answers

Answer:

option c

Step-by-step explanation:

does anyone know the answer to this? 5x-(4+3x)

Answers

Answer:

2x-4

Step-by-step explanation:

5x-(4+3x)

5x-4-3x

5x-3x-4

2x-4

Give a recursive definition for the following set of ordered pairs of positive integers ($a|b$ means that a is a factor of b): $S=${$(a,b)|a \in Z^+, b \in Z^+, a|b$}

Answers

A recursive definition for the set S can be given as follows:

What is recursion?

Recursion is a programming technique where a function calls itself to solve a problem.

Base case: (1, n) is in S for all positive integers n, since 1 is a factor of all positive integers.

Recursive case: If (a, b) is in S, then (a', b) is in S for all positive integers a' that are factors of a, and (a, b') is in S for all positive integers b' that are multiples of b.

In other words, the set S contains all pairs (a,b) where a is a positive integer that divides b, and b can be obtained by multiplying any such a with another positive integer. The base case includes all pairs where a=1 and b is any positive integer.

The recursive case states that if (a,b) is in S, then all pairs where a' is a factor of a and b is a positive integer such that b=a'b are also in S, as well as all pairs where b' is a multiple of b and a is a positive integer that divides b'.

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what is the value of k?

Answers

Answer:

(4k+5)+ (6k+10) = 115

Exterior angle of a triangle is equal to the sum of two opposite interior angles

10k=15=115

10k= 100

k = 100/10

k = 10

Step-by-step explanation:

Answer:

k = 10

Step-by-step explanation:

The 3rd angle that's not defined in the equation is supplementary to 115, so the angle is 180-115 = 65.

We can solve for the equation 65+(4k+5)+(6k+10)=180 -> 65+4k+5+6k+10=180 -> 10k+80 = 180 -> 10k = 100 -> k = 10.

To double-check(optional), we can plug k back into the equation, so 65 + 4*10 + 5 + 6*10 + 10 = 180 -> 100 + 65 + 5 + 10 = 180 -> 180 = 180, so we can confirm that k = 10.

3
a =
b =
5
Work out a-2b as a column vector.

Answers

Answer:

Please see attached photo.

Step-by-step explanation:

Step 1:

Analyze what was given

Step 2:

Calculate 2b.

Step 3:

Carryout the operation a – 2b

Please attached photo for explanation

Differentiate the function with respect to x. Shot steps

Answers

The given function y = sec⁻¹(x³) is differentiated as dy/dx = 3x/√(x² - 1).

What is differentiation?

The differentiation of a function is defined as rate of change of its value at a point. It can be written as f'(x) = Lim h --> 0 (f(x + h) - f(x)) /(x + h - x).

Its geometric meaning is the slope of tangent of the function at a given point.

The given function is as below,

y = sec⁻¹(x³)

The given function is a composite function of sec⁻¹x and x³.

In order to differentiate it, first differentiate x³ and then sec⁻¹x as follows,

dx³/dx = 3x²

And, dsec⁻¹x /dx = 1/x√(x² - 1)

Now, differentiation of sec⁻¹(x³) is given as,

d sec⁻¹(x³)/dx = 3x²/(x√(x² - 1))

= 3x/√(x² - 1)

Hence, the differentiation of the given function is 3x/√(x² - 1).

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Keller Construction is considering two new investments. Project E calls for the purchase of earthmoving equipment. Project H represents an investment in a hydraulic lift. Keller wishes to use a net present value profile in comparing the projects. The investment and cash flow patterns are as follows: Use Appendix B for an approximate answer but calculate your final answer using the formula and financial calculator methods.

Answers

Based on the net present value profile, Project H has a higher NPV than Project E.

To compare the net present value (NPV) of Project E and Project H, we need to calculate the present value of cash flows for each project and determine which one has a higher NPV. The cash flow patterns for the two projects are as follows:

Project E:

Initial investment: -$100,000

Cash flows for Year 1: $40,000

Cash flows for Year 2: $50,000

Cash flows for Year 3: $60,000

Project H:

Initial investment: -$120,000

Cash flows for Year 1: $60,000

Cash flows for Year 2: $50,000

Cash flows for Year 3: $40,000

To calculate the present value of cash flows, we need to discount them using an appropriate discount rate. The discount rate represents the required rate of return or the cost of capital for the company. Let's assume a discount rate of 10%.

Using the formula method, we can calculate the present value (PV) of each cash flow and sum them up to obtain the NPV for each project:

For Project E:

PV = $40,000/(1 + 0.10)^1 + $50,000/(1 + 0.10)^2 + $60,000/(1 + 0.10)^3

PV = $36,363.64 + $41,322.31 + $45,454.55

PV = $123,140.50

For Project H:

PV = $60,000/(1 + 0.10)^1 + $50,000/(1 + 0.10)^2 + $40,000/(1 + 0.10)^3

PV = $54,545.45 + $41,322.31 + $30,251.14

PV = $126,118.90

Using the financial calculator method, we can input the cash flows and the discount rate to calculate the NPV directly. By entering the cash flows for each project and the discount rate of 10%, we find that the NPV for Project E is approximately $123,140.50 and the NPV for Project H is approximately $126,118.90.

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The volume of a sphere is 4500cm. What is the surface area of the sphere to the nearest whole number?

Answers

The surface area of the sphere, to the nearest whole number, is 1318 cm².

How to determine the surface area of a sphere?

A sphere is simply a three-dimensional geometric object that is perfectly symmetrical in all directions.

The volume of a sphere is expressed as:

Volume = (4/3)πr³

The surface area of a sphere is expressed as:

SA = 4πr²

Where r is the radius of the sphere and π is the mathematical constant pi.

Given that the volume V is 4500 cm³.

First, we solve for the radius:

Volume = (4/3)πr³

4500 = (4/3)πr³

4500 × 3 = 4πr³

13500 = 4πr³

r³ = 13500/4π

r = ∛( 13500/4π )

Now that we have the radius, we can calculate the surface area of the sphere using the formula:

SA = 4πr²

Substituting the radius we found:

SA = 4 × π × ∛( 13500/4π )²

SA = 1318 cm²

Therefore, the surface area is approximately 1318 cm².

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A 6 inch pizza has 610 calories, with 249 of those from fat. A 16 inch pizza is cut into 8 slices . Estimate the number of calories in one slice of 16 inch pizza.

Answers

Answer:

Step-by-step explanation:

.In this case (16)2 / (6)2 or 7.1111The larger pizza has (7.1111)(610) calores

Answer:

To solve this problem, we first need to understand that the number of calories in a pizza doesn't depend on its diameter but on its area. The reason is simple: the more pizza there is, the more calories it contains. And the area of a pizza (or any circle) increases with the square of the radius.

The area of a circle is given by the formula πr^2, where r is the radius.

The 6-inch pizza has a radius of 3 inches, so its area is π(3^2) = 9π square inches.

The 16-inch pizza has a radius of 8 inches, so its area is π(8^2) = 64π square inches.

The 16-inch pizza is 64π/9π = 64/9 ≈ 7.11 times the area of the 6-inch pizza, and therefore should have roughly 7.11 times the calories, assuming the pizzas are made with the same proportions of ingredients.

So, the 16-inch pizza should have approximately 610 calories * 7.11 = 4337.1 calories.

If the 16-inch pizza is cut into 8 slices, each slice would have approximately 4337.1 calories / 8 = 542.14 calories.

Keep in mind this is an estimate as it assumes that the distribution of ingredients (and therefore the distribution of calories) is uniform across the pizza, which might not be the case in reality. But it gives a good first approximation.

For the past month, Irene kept a record of the prices at which she purchased gas for her car. She bought 33 litres at $0.94 per litre; 50 litres at $1.05 per litre; 26 litres at $0.95 per litre; and 33 litres at $0.83 per litre. What is the average price-per-litre that Irene paid for gas over the past month?

Answers

Answer:

$0.95 per litre

Step-by-step explanation:

To find the average price-per-litre that Irene paid for gas over the past month, we need to first find the total amount of money that she spent on gas, and the total number of litres that she purchased. Then we can divide the total amount spent by the total number of litres to get the average price-per-litre.

To calculate the total amount of money that Irene spent on gas, we need to multiply the number of litres by the price per litre for each purchase, and then add up the results:

Total spent = (33 litres x $0.94 per litre) + (50 litres x $1.05 per litre) + (26 litres x $0.95 per litre) + (33 litres x $0.83 per litre) =>

=> Total spent = $30.42 + $52.50 + $24.70 + $27.39 =>

=> Total spent = $135.01

So Irene spent a total of $135.01 on gas over the past month.

To find the total number of litres that Irene purchased, we simply need to add up the number of litres for each purchase:

Total litres = 33 litres + 50 litres + 26 litres + 33 litres =>

=> Total litres = 142 litres

So Irene purchased a total of 142 litres of gas over the past month.

Finally, to find the average price-per-litre that Irene paid for gas, we need to divide the total amount spent by the total number of litres purchased:

Average price-per-litre = Total spent / Total litres =>

=> Average price-per-litre = $135.01 / 142 litres =>

=> Average price-per-litre = $0.95 per litre

Therefore, the average price-per-litre that Irene paid for gas over the past month was $0.95 per litre.

(I would appreciate a Brainliest rating if this helped you)

Can you guys help me solve this problem

Answers

Answer:

528

Step-by-step explanation:

First we have to find the price per case.

We can do this by dividing 408 by 17, because we know that 17 cases cost 408 and each case will cost the same.

408/17= 24

Now we can find the price of the five cases they want to add.

24 X 5 = 120

Now we just add that price back to original order price.

408 + 120 = 528

Which table shows a linear function linear functions?

Answers

A linear table can represent the linear function.

In the given question, we have to explain which table shows a linear functions.

As we know that,

We can generate a table of values for any line since every linear equation represents a relationship between the x and y values.

So a linear table can represent the linear function.

Check to see whether there is a consistent rate of change to determine if a table of numbers represents a linear function. If so, you are examining a linear function.

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A sphere and its dimension are shown in the diagram 15 inches

Answers

The measurement that is closest to the volume of the sphere is given as follows:

1,767.1 in³.

What is the volume of an sphere?

The volume of an sphere of radius r is given by the multiplication of 4π by the radius cubed and divided by 3, hence the equation is presented as follows:

$V = \frac{4\pi r^3}{3}$

From the image given at the end of the answer, we have that the diameter is of 15 units, hence the radius of the sphere, which is half the diameter, is given as follows:

r = 0.5 x 15

r = 7.5 units.

Then the volume of the sphere is given as follows:

V = 4/3 x π x 7.5³

V = 1,767.1 in³.

Missing Information

The sphere is given by the image presented at the end of the answer.

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A sphere and its dimension are shown in the diagram 15 inches

Five less than twice the value of a number is equal to three times the quantity of 4 more than 1/2 the number what is the number let x be the number right and solve an equation to find x show your work.

Answers

The value of the number is x = 34.

Let's break down the problem and solve it step by step.

1. "Five less than twice the value of a number": This can be represented as 2x - 5, where x is the number.

2. "Three times the quantity of 4 more than 1/2 the number": This can be represented as 3 * (x/2 + 4).

According to the problem statement, the two expressions are equal. We can set up the equation as follows:

2x - 5 = 3 * (x/2 + 4)

Now, let's solve the equation:

2x - 5 = 3 * (x/2 + 4)

Distribute the 3 to both terms inside the parentheses:

2x - 5 = (3/2)x + 12

Multiply through by 2 to eliminate the fraction:

2(2x - 5) = 2((3/2)x + 12)

4x - 10 = 3x + 24

Next, let's isolate the x term by moving the constant terms to the other side of the equation:

4x - 3x = 24 + 10

Simplify:

x = 34

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2^{51} mod 22 in words, two to the power of fifty-one mod twenty-two

Answers

Since 2⁵ = 32, and

2⁵ ≡ 32 ≡ 10 (mod 22),

we have

2⁵¹ ≡ 2 • 2⁵⁰ ≡ 2 • (2⁵)¹⁰ ≡ 2 • 10¹⁰ (mod 22)

Now consider 10¹⁰ (mod 22):

10 = 2 • 5

10¹⁰ ≡ 2¹⁰ • 5¹⁰ ≡ (2⁵)² • 5¹⁰ ≡ 10² • 5¹⁰ ≡ 2² • 5¹² (mod 22)

so that

2⁵¹ ≡ 2³ • 5¹² (mod 22)

Now consider 5¹² (mod 22):

5 and 22 are coprime, and ɸ(22) = 10 (where ɸ(n) is the Euler totient function). By Euler's theorem,

5¹² ≡ 5² • 5¹⁰ ≡ 5² • 1 ≡ 25 ≡ 3 (mod 22)

and so

2⁵¹ ≡ 2³ • 3 ≡ 24 ≡ 2 (mod 22)

Another, more tedious method: Start with smaller powers of 2 and look for a pattern.

2 ≡ 2 (mod 22)

2² ≡ 4 (mod 22)

2³ ≡ 8 (mod 22)

2⁴ ≡ 16 (mod 22)

2⁵ ≡ 32 ≡ 10 (mod 22)

2⁶ ≡ 2 • 32 ≡ 2 • 10 ≡ 20 (mod 22)

2⁷ ≡ 2 • 20 ≡ 40 ≡ 18 (mod 22)

2⁸ ≡ 2 • 18 ≡ 36 ≡ 14 (mod 22)

2⁹ ≡ 2 • 14 ≡ 28 ≡ 6 (mod 22)

2¹⁰ ≡ 2 • 6 ≡ 12 (mod 22)

2¹¹ ≡ 2 • 12 ≡ 24 ≡ 2 (mod 22)

2¹² ≡ 2 • 2 ≡ 4 (mod 22)

and so on, with a cyclic pattern of length 10. That is, $2^{10k+1}\equiv2\pmod{22}$ for any integer k ≥ 0. So 2⁵¹ ≡ 2 (mod 22).

Which of the following equations are equivalent? Select three options. 2 + x = 5 x + 1 = 4 9 + x = 6 x + (negative 4) = 7 Negative 5 + x = negative 2

Answers

The three equivalent equations are 2 + x = 5, x + 1 = 4 and -5 + x = -2. So, correct options are A, B and E.

Two equations are considered equivalent if they have the same solution set. In other words, if we solve both equations, we should get the same value for the variable.

To determine which of the given equations are equivalent, we need to solve them for x and see if they have the same solution.

Let's start with the first equation:

2 + x = 5

Subtract 2 from both sides:

x = 3

Now let's move on to the second equation:

x + 1 = 4

Subtract 1 from both sides:

x = 3

Notice that we got the same value of x for both equations, so they are equivalent.

Next, let's look at the third equation:

9 + x = 6

Subtract 9 from both sides:

x = -3

Since this value of x is different from the previous two equations, we can conclude that it is not equivalent to them.

Now, let's move on to the fourth equation:

x + (-4) = 7

Add 4 to both sides:

x = 11

This value of x is also different from the first two equations, so it is not equivalent to them.

Finally, let's look at the fifth equation:

-5 + x = -2

Add 5 to both sides:

x = 3

Notice that we got the same value of x as the first two equations, so this equation is also equivalent to them.

So, correct options are A, B and E.

To learn more about equations click on,

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Complete question is:

Which of the following equations are equivalent? Select three options.

2 + x = 5

x + 1 = 4

9 + x = 6

x + (- 4) = 7

- 5 + x = - 2

How long will it take to pay off 47,538 with only 4,782 per month?

Please HELPPPP

Answers

Answer:

9.9 months not counting mortgage or any other factors

Step-by-step explanation:

1/2s=4s-21 please show steps

Answers

Answer:

s = 6

Step-by-step explanation:

Goal is to isolate the variable (s)

1/2s = 4s - 21

Subtract 4s from both sides - this cancels out the 4s on the right side and moves it to the left side

1/2s - 4s = -21

To add or subtract fractions, they must have a common denominator

Convert 4s to a fraction over 2

1/2s - 8/2s = -21

Subtract the numerators and keep the denominators

-7/2s = -21

Remember the goal is to isolate the variable

In order to get rid of the -7/2, we multiply by its reciprocal (which is -2/7)

What we do to one side, we must do to the other (this means multiply by -2/7 on both sides

-7/2s × -2/7 = -21 × -2/7

s = -21 × -2/7

Negative × negative = positive

s = 42/7

Divide 42 by 7

s = 6

ILL GIVE BRAINLY What is the surface area of the cube?

Drag and drop the correct surface area to match the cube.

Answers

Answer:

Below

Step-by-step explanation:

A cube has SIX sides of equal area

each side has area = L x W and L and W are the same = 4.5 m

so: Area = six X ( 4.5 X 4.5) = 6 * 4.5 * 4.5 = 121.5 m^2

Answer:

Hope the picture will help you...

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Workout to the simplest:\( \int \: {x}^{2} ln( {x}^{3} ) dx\)​

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Workout to the simplest:
\( \int \: {x}^{2} ln( {x}^{3} ) dx\)