OUR ASSIGNMENT: Wildlife Sanctuary

You are designing a path for traveling to one of the animal habitats in the wildlife sanctuary. Which of the following regions did you choose?



Lion Habitat Hippo Habitat Elephant Habitat

Answers

Answer 1

Lion habitats are often designed to mimic their natural environment, with rocky outcroppings, grassy plains, and trees for shade.,

Hippos  spend most of their time in the water, and their habitats often include large ponds or rivers, Elephant habitats often include areas for grazing, watering holes, and shaded areas for rest.

what is habitat?

A habitat is a specific environment or place where a particular species of plant or animal lives and thrives. A habitat provides all the essential needs for a species to survive, such as food, water, shelter, and space. The physical characteristics of a habitat, such as temperature, humidity, soil type, and vegetation, determine which species can live there and how they interact with each other.

Habitats can be very diverse, ranging from deserts and forests to wetlands and coral reefs. Different species have different habitat requirements, and some species can adapt to different habitats while others are very specific in their requirements.

The study of habitats is an essential part of ecology, as understanding the habitat requirements of different species is crucial for their conservation and management.

To know more about Habitat visit:

https://brainly.com/question/28815163

#SPJ1


Related Questions

PLEASE HELP ME ASAP PLEASE.

PLEASE HELP ME ASAP PLEASE.

Answers

Answer:

See below

Step-by-step explanation:

g (h(6))   :

   h (6) =  3 ( 6^2) + 2 = 110

   then g (110) =   sqrt (110)

h (g(5))

    g(5) = sqrt 5

        then h( sqrt5) = 3 ( sqrt5)^2 + 2 = 17

Two ships, one sailing at 20mi/h and the other at 35mi/h, left port at the same time. Three hours later they were
110mi apart. If you had to find the angle between their courses an equation that could be used to solve this problem is:

Two ships, one sailing at 20mi/h and the other at 35mi/h, left port at the same time. Three hours later

Answers

Answer:

Step-by-step explanation:

Two ships, one sailing at 20mi/h and the other at 35mi/h, left port at the same time. Three hours later
Two ships, one sailing at 20mi/h and the other at 35mi/h, left port at the same time. Three hours later

Please work this out or I get a detention

Please work this out or I get a detention

Answers

Answer:

a = 11 , b = 2

Step-by-step explanation:

\(\frac{(4-\sqrt{5})(4+\sqrt{5}) }{2\sqrt{11}} = \frac{ \sqrt{a}}{y} \\Hence,\\\frac{4^2-(\sqrt{5})^2 }{2\sqrt{11}} = \frac{ \sqrt{a}}{y}\\\frac{16-5}{2\sqrt{11} } = \frac{ \sqrt{a}}{y}\\\frac{11}{2\sqrt{11}} = \frac{ \sqrt{a}}{y}\\\frac{\sqrt{11}*\sqrt{11} }{2\sqrt{11}} = \frac{ \sqrt{a}}{y}\\\frac{\sqrt{11} }{2} = \frac{ \sqrt{a}}{y}\\a=11,b =2\)

A= 11 and 6 is 2 this is the coree answer

Jacob kept track of the number of hours that he spent playing soccer each week for several weeks he spent 3, 6, 7, 8, and 11 hours. What is the range of the data set?

Answers

Answer:

8

Step-by-step explanation:

The range of the data set is determined by the maximum - minimum.

The max value is 11

The min value is 3

11-3=8

The range of the data set is 8.

Find the distance between points R and W.

Find the distance between points R and W.

Answers

Answer:

9

Step-by-step explanation:

Distance between W and R = |-3 - 6| = |-9| = 9

What is the measure of circumscribed O 45°
O 50°
O 90°
O 95°

What is the measure of circumscribed O 45O 50O 90O 95

Answers

The measure of the inscribed angle is equal to 90 degrees

What is an inscribed angle

The inscribed angle theorem mentions that the angle inscribed inside a circle is always half the measure of the central angle or the intercepted arc that shares the endpoints of the inscribed angle's sides. In a circle, the angle formed by two chords with the common endpoints of a circle is called an inscribed angle and the common endpoint is considered as the vertex of the angle.

In this problem, the side length of the square is 5 which forms 90 degrees to all the other sides.

The measure of the circumscribed angle is 90 degree

Learn more on inscribed angle here;

https://brainly.com/question/3538263

#SPJ1

you've just read an article that makes claims and provides statistics you would like to use in your report. why is it important to determine if other sources are making the same claims and citing the same statistics?

Answers

Overall, consulting multiple sources is an important part of conducting research and ensuring the accuracy and credibility of the information you use in your reports.

What is probability?

Probability is a measure of the likelihood or chance of an event occurring. It is expressed as a number between 0 and 1, where 0 indicates that the event is impossible and 1 indicates that the event is certain to occur. In between 0 and 1, probabilities are often expressed as fractions, decimals, or percentages. Probability theory is widely used in fields such as mathematics, statistics, physics, engineering, finance, and more to analyze and understand random events and phenomena.

Here,

It is important to determine if other sources are making the same claims and citing the same statistics for several reasons:

Ensuring accuracy: By consulting multiple sources, you can verify the accuracy of the claims and statistics provided in the original article. This can help you avoid relying on potentially biased or misleading information.

Assessing credibility: If other reputable sources are also making similar claims and citing the same statistics, it can increase the credibility of the information. On the other hand, if other sources are not making the same claims or are citing conflicting statistics, it may indicate that the original article is unreliable.

Providing context: By consulting multiple sources, you can gain a broader understanding of the topic at hand and the various factors that may be influencing the claims and statistics. This can help you provide more nuanced and accurate information in your report.

To know more about probability,

https://brainly.com/question/30034780

#SPJ4

Betsy participates in a scavenger hunt that requires her to retrieve items from 4 locations. The locations are on a map with the coordinates as given:

Location 1 is at (−4, −1).

Location 2 is at ​​(−4, 4).

Location 3 is at (3, 4).

Location 4 is at (3, −1).

The paths from one location to another are straight lines. One unit on the coordinate grid equals 10 yd. Betsy starts at location 1 and goes to location 2, then location 3, and then location 4, and then returns back to location 1.

What is the total distance Betsy has traveled?

Answers

Answer:

240 yd

Step-by-step explanation:

Let A, B, C, and D represent location 1, location 2, location 3, and location 4 respectively.

Consider the figure in the attached file.

We need to find the total distance traveled by Betsy.

The distance covered by Betsy is

length of segment AB length of segment BC length of segment CD length of segment DA.

To find the distance AB, we need to find the distance from A to B on y-axis.

So, length of segment AB units

To find the distance BC, we need to find the distance from B to C on x-axis.

So, length of segment BC units

To find the distance CD, we need to find the distance from C to D on y-axis.

So, length of segment CD units

To find the distance DA, we need to find the distance from D to A on x-axis.

So, length of segment DA units

Hence, the total distance covered is units

It is given that 1 unit equals 10 yd, so distance traveled by Besty is yd

Consider functions fand g.
f(x) = -23
g(x) = |x − 1
What is the value of (go f)(4)?

A. 9
B. - 1/8
C. -9
D. 1/8

Answers

The value of (gof)(4) is 9 if the function f(x) is f(x) =\(-x^3\), and function g(x) is g(x) = |1/8x-1| option (A) is correct.

What is a function?

It is described as a particular kind of relationship, and each value in the domain is associated with exactly one value in the range according to the function. They have a predefined domain and range.

from the question:

We have a function:

f(x) = -x³

Plug x = 4 in the f(x)

f(4) = -4³ = -64

Plug the above value in the g(x)

g(f(4)) = |-8-1| = |-9| = 9

Thus, the value of (gof)(4) is 9 if the function f(x) is f(x) = -x³, and function g(x) is g(x) = |1/8x-1| option (a) is correct.

to know more about the function visit:

https://brainly.com/question/12431044

#SPJ1

complete and correct questions

f(x) = -x3

g(x) = |1/8x-1|

What is the value of (gof)(4)?.

A. 9

B. - 1/8

C. -9

D. 1/8

UNIT RATE TRUE OR FALSE HELP ME!!!

UNIT RATE TRUE OR FALSE HELP ME!!!

Answers

Answer:

False

Step-by-step explanation:

     This is not a unit rate because neither of the rates are equal to 1. A unit rate, for example, could be 25 ft per second.

Have a nice day!

     I hope this is what you are looking for, but if not - comment! I will edit and update my answer accordingly. (ノ^∇^)

- Heather



Write an absolute value inequality and a compound inequality for each length x with the given tolerance.

A length of 100 yd with a tolerance of 4 in .

Answers

To write an absolute value inequality for the length x with a tolerance of 4 inches, we can use the formula:  

 \(| x - 100 | ≤ 4.\)

This inequality states that the absolute value of the difference between x and 100 yards should be less than or equal to 4 inches.

To write a compound inequality, we can break down the absolute value inequality into two separate inequalities:

\(-4 ≤ x - 100 ≤ 4 .\)

This compound inequality states that x minus 100 yards should be greater than or equal to -4 inches and less than or equal to 4 inches.

Therefore, the absolute value inequality is | x - 100 | ≤ 4 and the compound inequality is\(-4 ≤ x - 100 ≤ 4.\)

To know more about tolerance visit:

https://brainly.com/question/30478622

#SPJ11

18. Jameson and Quincy each deposit $7,000 into accounts that earn 6%
interest, but Jameson earns annual simple interest while Quincy earns
annual compound interest. Assuming neither one of them makes any
deposits or withdrawals for 60 months, which of the following is a true
statement?

Answers

Answer:

Jameson will have about $267.58 less in his account than Quincy

Step-by-step explanation:

Find the probability that a randomly chosen customer ordered a burger given that they ordered fries.

Answers

The probability that a randomly chosen customer ordered a burger given that they ordered fries is 0.5.

The probability that a randomly chosen customer ordered a burger given that they ordered fries can be found using conditional probability. Conditional probability is the probability of an event A occurring given that another event B has already occurred. Here, event B is that the customer ordered fries, and event A is that the customer ordered a burger.

Let P(A) be the probability that a customer orders a burger, and P(B) be the probability that a customer orders fries. Let P(A and B) be the probability that a customer orders both a burger and fries. Then, the conditional probability of A given B is given by:
P(A | B) = P(A and B) / P(B)
We are given that the customer ordered fries. Let's assume that P(B) = 0.6, i.e., 60% of the customers order fries. We are also given that 50% of the customers who ordered fries also ordered a burger. Thus, P(A and B) = 0.5 x 0.6 = 0.3. Therefore,
P(A | B) = P(A and B) / P(B) = 0.3 / 0.6 = 0.5
Hence, the probability that a randomly chosen customer ordered a burger given that they ordered fries is 0.5.

To know more about probability visit:-

https://brainly.com/question/31828911

#SPJ11

A biased coin is tossed 10 times and the probability of obtaining heads is 0. 6. Find the probability of obtaining the following. Round answers to the nearest ten-thousandth.

Answers

When a biased coin is tossed ten times, the likelihood of getting at least nine heads is 0.0463.

Explain the term Binomial distribution?This binomial probability distribution makes the assumption that there are two possible outcomes for each trial and that the number of tests is independently distributed.

The binomial distribution's PMF is;

P(X = x) = ⁿCₓ . pˣ . qⁿ⁻ˣ

There were 10 trials.0.6 percent chance of receiving a head

Following are the results of a calculation using a binomial distribution to determine the likelihood of receiving at least 9 heads.

P(X ≥ 9) = P(X = 9) + P(X = 10)

P(X ≥ 9) = ¹⁰C₉. (0.6)⁹ (1 - 0.6)¹ + ¹⁰C₁₀. (0.6)¹⁰ (1 - 0.6)⁹

P(X ≥ 9) = 0.0403 + 0.0060

P(X ≥ 9) = 0.0463

Thus, when a biased coin is tossed ten times, the likelihood of getting at least nine heads is 0.0463.

To know more about the Binomial distribution, here

https://brainly.com/question/9325204

#SPJ4

The complete question is-

A biased coin is tossed 10 times and the probability of obtaining heads is 0.6.

Find the probability of obtaining at least 9 heads. Round answer to the nearest ten-thousandth.

Tekan-Tekan Sdn. Bhd. has order for 200 Model AS-120 calculator for delivery on day 200. The calculator consists of three parts. Components 2 and 3 form subassembly 1 . Sub-assembly 1 and component 4 form the final assembly. Following are the work centers and times of each operation. Table Q3(a) shows routine file of the operation. Assuming: - Only one machine is assigned to each operation - The factory works on 8-hour shift, 5 days a week - All parts move in one lot of 200. (a) Illustrate the backward schedule based on the information given above. (12 marks) (b) Identify when component 3 must be started to meet the delivery date. (2 marks)

Answers

Component 3 must be started on day 197 to meet the delivery date of day 200.

To illustrate the backward schedule, we need to start from the delivery date (day 200) and work our way backward, taking into account the lead times and dependencies of each operation.

(a) Backward schedule:

Operation    |  Work Center  |  Time (hours)  |  Start Day

--------------------------------------------------------

Final Assembly |   Work Center 1  |        1       |     200

Sub-assembly 1 |   Work Center 2  |        2       |     199

Component 4     |   Work Center 3  |        3       |     197

Component 2     |   Work Center 4  |        4       |     196

Component 3     |   Work Center 5  |        3       |     ????

(b) To identify when component 3 must be started to meet the delivery date, we need to consider its dependencies and lead times.

From the backward schedule, we see that component 3 is required for sub-assembly 1, which is scheduled to start on day 199. The time required for sub-assembly 1 is 2 hours, which means it should be completed by the end of day 199.

Since component 3 is needed for sub-assembly 1, we can conclude that component 3 must be started at least 2 hours before the start of sub-assembly 1. Therefore, component 3 should be started on day 199 - 2 = 197 to ensure it is completed and ready for sub-assembly 1.

Hence, component 3 must be started on day 197 to meet the delivery date of day 200.

Learn more about Scheduling here:

brainly.com/question/30012511

#SPJ4

Tori received $28.50 for 2 hours of work. How
much did she earn if she worked 15 hours?

Answers

Answer:

Hey! I hope this helps. I used ratio, I divided $28.50 by 2 to find out how much she worked for in an hour then I multiplied by 15.

Tori received $28.50 for 2 hours of work. Howmuch did she earn if she worked 15 hours?

I NEED HELP ASAPPP NO LINKS PLSS​

I NEED HELP ASAPPP NO LINKS PLSS

Answers

Answer:

heyy! im reaaally sorry if its wrong but I think its c, f, d

brainliest? :)

Step-by-step explanation:

Answer:

7= D

8= F

9= C

Step-by-step explanation:

7. x - 3 \(\leq\) 7

     +3     +3

x \(\leq\) 10

8. 3b < 18

   /3       /3

    b < 6

9. \(\frac{y}{3}\) > 9

  *3    *3

 y > 27

10- 12 I am so sorry, but I don't understand these functions lol

Determine whether the planes are parallel, perpendicular, or neither. x−y−9z=1,9x+y−z=4 parallel perpendicular neither If neither, find the angle between them

Answers

Therefore, the angle between the two planes is given by θ = arccos(17 / 83), which can be calculated using inverse cosine function. To determine whether the planes are parallel, perpendicular, or neither, we can examine the normal vectors of the planes.

The normal vector of the plane with equation x - y - 9z = 1 is [1, -1, -9].

The normal vector of the plane with equation 9x + y - z = 4 is [9, 1, -1].

If the dot product of the two normal vectors is 0, then the planes are perpendicular. If the dot product is non-zero, we can use the dot product formula to find the angle between the planes.

The dot product of the normal vectors is:

[1, -1, -9] · [9, 1, -1] = (1)(9) + (-1)(1) + (-9)(-1) = 9 - 1 + 9 = 17.

Since the dot product is non-zero, the planes are neither parallel nor perpendicular.

To find the angle between the planes, we can use the dot product formula:

cos(θ) = (n1 · n2) / (||n1|| ||n2||),

where n1 and n2 are the normal vectors of the planes, and ||n1|| and ||n2|| are their magnitudes.

The magnitude of [1, -1, -9] is ||n1|| = sqrt(1^2 + (-1)^2 + (-9)^2) = sqrt(1 + 1 + 81) = sqrt(83),

and the magnitude of [9, 1, -1] is ||n2|| = sqrt(9^2 + 1^2 + (-1)^2) = sqrt(81 + 1 + 1) = sqrt(83).

Plugging in the values, we have:

cos(θ) = (17) / (sqrt(83) * sqrt(83)) = 17 / 83.

Thus, the angle between the planes is given by θ = arccos(17 / 83).

Learn more about vectors here:

https://brainly.com/question/30958460

#SPJ11

.............................

.............................

Answers

2/3 <=======3

i think,,,, if not sorry i suck at math

cosine of theta would be sqrt 33/7

you’d enter 33 on top and 7 on bottom

100 points and brainly for whoever gets this right

1. A cylinder and a cone have the same diameter: 8 inches. The height of the cylinder is 3 inches. The height of the cone is 18 inches.

Use π = 3.14.

What is the relationship between the volume of this cylinder and this cone? Explain your answer by determining the volume of each and comparing them. Show all your work.

Answers

I hope that helps

Stay safe

100 points and brainly for whoever gets this right1. A cylinder and a cone have the same diameter: 8

Need this QUICK!! Evaluate without using a calculator (x2y-3)0+x1/3-(4x)1/2 when x = 64 and y = 27.Show work

Answers

Answer:

-11

Step-by-step explanation:

Given the expression

(x²y-3)⁰+x^1/3-(4x)^1/2 when x = 64 and y = 27.Show work

Note that anything raise to power of zero is 1, hence (x²y-3)⁰ =  1

x^1/3

= 64^1/3

= ∛64

= 4

(4x)^1/2

=  (4* 64)^1/2

= 4^1/2 * 64^1/2

= 2 * 8

= 16

Substitute;

(x²y-3)⁰+x^1/3-(4x)^1/2

=  1 + 4 - 16

= 5 - 16

= -11

Hence the required value is -11

8. Expand, then simplify: (2 Points) (2a – 3) (a2 + 3a - 5) ​

Answers

Hello

just a second

people reading this please complete because you will help me a lot.

I am an Indian girl my name is Lamer and am 13 years old.

I Just got this new device after working at a farm for 2 years.

I used to use brainly at my friend device she had money to buy brainly plus.

I cant please help me get points so I can get good marks and my dad let me complete my education instead of getting married.  

2,914 rounded to the thousand and to nearest hundred

Answers

Answer: 2194.00 and 2194.000

Step-by-step explanation: rounded to the nearest 1000= 2194.000

rounded to the nearest 100 = 2194.00

for each function, find f(-1), f(1), and f(3)

f(x) = 4

f(x) = 3x - 4

Answers

Answer:

f

(

x

)

=

3

x

4

becomes:

f

(

1

)

=

(

3

×

1

)

4

f

(

1

)

=

3

4

f

(

1

)

=

7

Step-by-step explanation:

What is the probability of landing on a number greater then 5 and then landing on a number greater then 4

What is the probability of landing on a number greater then 5 and then landing on a number greater then

Answers

SOLUTION

Given the question in the image, the following are the solution steps to answer the question.

STEP 1: Write the formula for calculating probability

\(Probability=\frac{number\text{ of required outcomes}}{number\text{ of total possible outcomes}}\)

STEP 2: Find the probability of landing on a number greater than 5

\(\begin{gathered} Pr(greater\text{ than 5\rparen}=Pr(6\text{ and above\rparen} \\ Pr(greater\text{ than 5\rparen}=Pr(6)=\frac{1}{4} \end{gathered}\)

STEP 3: Find the probability of landing on a number

In the following set of numbers (18, 26, 29, 18, 44) what is the median?

A) 26
B) 27
C) 18
D) 24

Answers

The median of the following set of numbers  (18, 26, 29, 18, 44) is 26. The correct option to this question is option A

To find median of the following sequence (18, 26, 29, 18, 44) we will arrange them in ascending order

                            18 , 18 , 26 , 29 , 44   . . . . . .  . . . .(1)

Since the number of terms is odd we will apply the formula

                     Median  = \(\frac{(n+1)}{2} th\) term . . . . . . .(2)

       Here n = number of terms

As per question the n = 5

Therefore putting in equation 2 we get

                      Median = \(\frac{(5+1)}{2} th\) term

                      Median = \(\frac{6}{2} th \\\)  term

                      Median = 3 term

Hence the third term from the sequence ( shown in 1 ) we get the median that is 26

Hence the median of the following set of numbers (18, 26, 29, 18, 44) is 26 .

To learn more about median

https://brainly.com/question/26177250

The median is:

26

Explanation:

First, we will arrange the numbers from least to greatest.

18, 26, 29, 18, 44

Rearrange

18, 18, 26, 29, 44.

Now, the median is the number in the middle, which is 26.

∴ Median = 26

[infinity] (cos(15))k k = 1 Determine whether the series is convergent or divergent. convergent divergent

Answers

The series Σ(cos(15)k) from k=1 to infinity is convergent.



Σ\((cos(15)k)\) from k=1 to infinity

To determine if this series converges or diverges, we can use the Ratio Test. The Ratio Test states that if the limit as n approaches infinity of the absolute value of the ratio of consecutive terms is less than 1, then the series converges. If it's greater than 1, it diverges. If it's equal to 1, the test is inconclusive.

Step 1: Find the ratio of consecutive terms, a(k+1)/a(k)

a(k+1) = cos(15)(k+1)
a(k) = cos(15)k

Ratio: |a(k+1)/a(k)| = |cos(15)(k+1) / cos(15)k|

Step 2: Simplify the ratio

|cos(15)(k+1) / cos(15)k| = |cos(15)|

Since the ratio doesn't depend on k, the limit will just be the absolute value of the ratio itself.

Step 3: Compare the limit to 1

|cos(15)| < 1, since 0 < cos(15) < 1

According to the Ratio Test, since the limit of the absolute value of the ratio of consecutive terms is less than 1, the series converges.

Your answer: The series Σ(cos(15)k) from k=1 to infinity is convergent.

To know more about series converges. refer here:

https://brainly.com/question/15415793

#SPJ11

the question is in the picture. will give brainilist.​

the question is in the picture. will give brainilist.

Answers

Step-by-step explanation:

They are perpendicular

TIME REMAINING
01:38:18
The function rule T–4, 6(x, y) could be used to describe which translation?

a parallelogram on a coordinate plane that is translated 4 units down and 6 units to the right
a trapezoid on a coordinate plane that is translated 4 units to the left and 6 units up
a rhombus on a coordinate plane that is translated 4 units down and 6 units to the left
a rectangle on a coordinate plane that is translated 4 units to the right and 6 units up

Answers

The translation that represents T–4, 6(x, y) is (b) a trapezoid on a coordinate plane that is translated 4 units to the left and 6 units up

How to determine the translation?

The translation rule is given as:

T–4, 6(x, y)

This can be rewritten as

T(x- 4, y + 6)

The above represents a translation 4 units left and 6 units up

Hence, the translation that represents T–4, 6(x, y) is (b) a trapezoid on a coordinate plane that is translated 4 units to the left and 6 units up

Read more about transformation translation at:

https://brainly.com/question/8797028

#SPJ1

Convert this document and share it as an image DO DO Tools Mobile View 83% 11:15 pm X Share 00 Problem 6 (10 pts) Let T: P₂ > F3 be the function defined by T(abrer²) = ar $r² $²³. Prove rigorously that I is a linear transformation, and then write its matrix with respect to the basis (1, 1, 2) of P2 and the basis (1, r,²,a of Ps. Hint: Be careful with the size of the matrix. It should be of size 4 x 3.

Answers

The matrix of T with respect to the given bases is:[0 r² r³][r r² 0][1 r 0][0 0 0]

To prove that T is a linear transformation, we need to show that T satisfies the two properties of a linear transformation. Let T : P₂ -> F₃ be defined by T(abr²) = ar $r² $²³, where F₃ is the field of integers modulo 3.

Then, we have to check whether T satisfies the two properties of a linear transformation:

Additivity: T(u + v) = T(u) + T(v) for all u, v in P₂.

Homogeneity: T(cu) = c

T(u) for all u in P₂ and all scalars c in F₃.

1. Additivity To show that T satisfies additivity, let u and v be arbitrary elements of P₂.

Then, we have: u = a₁ + b₁r + c₁r²v = a₂ + b₂r + c₂r²where a₁, b₁, c₁, a₂, b₂, and c₂ are elements of F₃.

We need to show that:T(u + v) = T(u) + T(v)

This means that we need to show that:T(u + v) = ar $r² $²³

                      = (a₁ + a₂)r + (b₁ + b₂)r² + (c₁ + c₂)r⁴T(u) + T(v)

                      = ar $r² $²³ + ar $r² $²³= ar $r² $²³ + ar $r² $²³

                       = ar $r² $²³ = (a₁ + a₂)r + (b₁ + b₂)r² + (c₁ + c₂)r⁴

Therefore, T satisfies additivity.2. Homogeneity

To show that T satisfies homogeneity, let u be an arbitrary element of P₂ and let c be an arbitrary scalar in F₃.

Then, we have:u = a + br + cr²where a, b, and c are elements of F₃.

 We need to show that:T(cu) = cT(u)This means that we need to show that:

                       T(cu) = acr + bcr² + ccr⁴cT(u)

                                 = c(ar $r² $²³) = acr + bcr² + ccr⁴

Therefore, T satisfies homogeneity.Since T satisfies additivity and homogeneity, it is a linear transformation.

Now, we need to find the matrix of T with respect to the given bases.

Let's first find the image of the basis vector (1, 1, 2) under T: T(1, 1, 2) = 1r + 1r² + 2r⁴ = r + r² + 2r⁴

Similarly, we can find the images of the other basis vectors: T(1, 0, 0) = 0T(0, 1, 0) = r²T(0, 0, 1) = r³

Therefore, the matrix of T with respect to the given bases is:[0 r² r³][r r² 0][1 r 0][0 0 0]

Learn more about linear transformation

brainly.com/question/13595405

#SPJ11

Other Questions
37. A woman wants to construct a box whose base length is twice the base width. The material to build the top and bottom is $9/m and the material to build the sides is $6/m. If the woman wants the Find the angles of the triangle whose vertices are A(-6, 8),B(7, 7), C(9, -6). (Standard notation for triangle ABC is usedthroughout. Use a calculator and round off your answers to onedecimal place A company has provided the following data: Sales 3,000 units Sales price $70 per unit Variable cost $50 per unit Fixed cost $25,000 If the sales volume decreases by 25%, the variable cost per unit increases by 15%, and all other factors remain the same, operating profit will: a client comes to the physician's office for treatment of severe sunburn. the nurse takes this opportunity to discuss the importance of protecting the skin from the sun's damaging rays. what is the appropriate teaching by the nurse to prevent skin damage? The bad feelings associated with disappointing news can generally be reduced if the receiver knows the reasons for the rejection, feels that the news was revealed sensitively, and a.understands who caused the problem.b.sees that the message was presented on high-quality company letterhead.c.notices that the direct strategy was used.d.believes that the matter was treated fairly andseriously.d.believes that the matter was treated fairly andseriously. A type of rock that could be used to form tools and weapons is called ____. kara, sammy, liz, and mark each took many samples from the same population of students. the number of students in each sample is shown in the table. which person's sampling distribution was most likely to closely approximate the population distribution? Imagine your friend's cousin writes a rebuttal argument to her claim in favor of teens owning smartphones. Read his argument excerpt and answer the question that follows:Smartphone ownership among teens is certainly on the rise. Yet there is reason for caution. Teens are showing signs of smartphone addiction. A survey by TextPlus found that half of teens "couldn't live without their mobile devices for a week, while 36 percent said they weren't able to go 10 minutes without checking their phones." All this time on the devices creates more chances for problems. Smartphones and social media have been linked to serious cases of cyber bullying. Some students have been hurt or worse. A school superintendent in California, J. Thomas Morton, sent a letter to parents. He asked them to monitor their teens' use of all electronic devices, as cyber bullying incidents are on the rise.Which of the following is true about this argument excerpt?A. It is respectful in tone to the audience and supports its claim with specific, credible evidence.B. It contains specific, credible evidence but uses a disrespectful tone that should be editedC. It fails to support its claim with specific, credible evidence and uses a disrespectful tone.D. It uses a respectful tone but needs specific, credible evidence to support the claim. which of the following is true about language? a. language has both verbal and nonverbal characteristics. b. national languages, dialects, and translation facilitate straightforward communication. c. business jargons are common and easily understood across cultures. d. language does not entail facial expressions and gestures. Question 1: Special order Sales volume in units 110 Revenue $11,000 Variable costs $3,300 Contribution margin $7,700 Fixed costs $1,600 Profit $6,100 Special order: A client wants to buy 10 units at a discounted price of $40 per unit. This is a one-time deal (i.e., a short-term decision). You have enough spare capacity to fulfill this special order without cutting back on your regular sales. a) Use the gross approach to decide whether you should take the special order: status quo (no special order) total amounts after adding the special order Revenue $11,000 Variable costs $3,300 Contribution margin $7,700 Fixed costs $1,600 Profit $6,100 Should you take the special order Which emphasizes interaction between the environment, culture, and how people think?Choose matching termStructuralismHumanistic PsychologyFunctionalismBehaviorism Put these substances in order of density with the most dense first and the least dense last. What is one of the faults of imperialism that becomes clear in Heart ofDarkness? What are the relative clause words? A circle has a diameter of 10 cm. What is the circumference, and what is the area income statement sections during the current year, newtech corporation sold a segment of its business at a loss of $618,750. until it was sold, the segment had a current period operating loss of $550,000. the company had $2,062,500 from continuing operations for the current year. prepare the lower part of the income statement, beginning with the $2,062,500 income from continuing operations. follow tax allocation procedures, assuming that all changes in income are subject to a 30% income tax rate. disregard earnings per share disclosures. (round all calculations to nearest dollar amount.) From the functionalist perspective, the incest taboo helps families to avoidA) emotional overload.B) role confusion.C) looking outside the family for marriage partners.D) Internet dating. Which term refers to changes to the U.S. Constitution?A. clauseB. articleC. amendmentD. ratification Who is Swift using satire in A Modest Proposal? ____ are computers that are physically placed inside the products in which they operate to add very specific features and capabilities.