2.2 In each of the following equations, solve for 8 where 0° 8≤ 90°. Give your answers correct to TWO decimal places. 2.2.1 tan 0 = 2,22. 2.2.2 8 cos(0 +10°) = 5 2.2.3 7 sec 0 -11 = 0
Answers
The solutions to the trigonometric equations are
2.2.1 θ = 26.57
2.2.2 θ = 68.46
22.3 θ = Undefined
How to determine the solutions to the equationsGiven that
2.2.1 tan θ = 1/2
Take the arc tan of both sides
So, we have
θ = tan⁻¹(1/2)
Divide 1 by 2
So, we have
θ = tan⁻¹(0.5)
Evaluate
θ = 26.57
Next, we have
2.2.2. cos(θ +10) = 1/5
Take the arc cos of both sides
So, we have
θ + 10 = cos⁻¹(1/5)
Divide 1 by 5
So, we have
θ + 10 = cos⁻¹(0.2)
Evaluate
θ = 78.46 - 10
So, we have
θ = 68.46
Lastly, we have
2.2.3 7sec(θ -11) = 0
Divide both sides by 7
sec(θ -11) = 0
Rewrite as
1/cos(θ - 11) = 0
So, we have
1 = 0 --- This is false
Hence, 7sec(θ -11) = 0 is undefined
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Question
In each of the following equations, solve for θ where 0° ≤ θ ≤ 90°. Give your answers correct to TWO decimal places.
2.2.1 tan θ = 1/2
2.2.2. cos(θ +10) = 1/5
2.2.3 7sec(θ -11) = 0
Related Questions
Verify the identity. (Simplify at each step.)
7 cos^2 − 7 sin^2 = 14 cos^2 − 7
7 cos^2 = 7 sin^2 -7 ( ? )
=7 cos^2 +7 cos^2 -7
=14 cos^2 -7
Need help asap will give brainliest
Answers
The given identity is verified by simplifying the left-hand side and right-hand side separately and showing that they are equal (7 cos^2(x) − 7 sin^2(x) = 14 cos^2(x) − 7).
To verify the given identity, we start with the left-hand side (LHS) and simplify it using the trigonometric identity cos^2θ + sin^2θ = 1:
LHS = 7cos^2θ − 7sin^2θ
= 7(cos^2θ − sin^2θ)
= 7(cosθ + sinθ)(cosθ − sinθ)
Next, we can use the Pythagorean identity cos^2θ + sin^2θ = 1 to substitute cos^2θ with 1 − sin^2θ:
LHS = 7[(1 − sin^2θ) − sin^2θ]
= 7(1 − 2sin^2θ)
Now, we can simplify the right-hand side (RHS) of the equation:
RHS = 14cos^2θ − 7
= 7(2cos^2θ − 1)
Using the same Pythagorean identity as before, we substitute cos^2θ with 1 − sin^2θ:
RHS = 7[2(1 − sin^2θ) − 1]
= 7(1 − 2sin^2θ)
We can see that the LHS and RHS are equal, which verifies the given identity.
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solve for the value of x. Do the expressions 1/2x+3 and 3/2x-1 have the same value. show or explain for full credit.
Answers
Answer:
Step-by-step explanation:
I am assuming that the equations are typed correctly meaning
x/2+3=3x/2-1
x/2-3x/2=-1-3
-2x/2=-4
-2x=-8
x=4
So the expressions are equal only when x=4
Dr.Osborne has scheduled Anita Blanchette for a spirometry test and wants you to telephone her the day before the test to prepare her so that optimal results are obtained.
1.) What information do you give Anita before her spirometry so that the best test results can be obtained?
2.) How would you explain the rationale for the performance of this procedure?
Answers
To ensure the best test results, Anita should be provided with the following information before her spirometry:
1. Instructions for taking the test: Anita should be thoroughly explained about how the spirometry test works and what steps she needs to follow. This includes taking a deep breath and blowing as hard as she can into the spirometer mouthpiece. It is important to emphasize that she needs to repeat this procedure a few times and take deep breaths between each exhale.
2. Emphasize the importance of taking medication as prescribed: Anita should be reminded of the importance of taking her medications as prescribed, including on the day of the test. It is crucial for her to bring her medications to the test appointment.
3. Avoid certain foods and drinks: Anita should be informed to avoid consuming certain substances before the spirometry test, such as caffeine, alcohol, and heavy meals. These can potentially affect the accuracy of the test results.
4. Arrive early for the test: Anita should be advised to arrive early for the test to allow herself sufficient time to relax and calm down before the procedure. This can help ensure more accurate results.
The rationale behind providing these instructions and information is that spirometry is a lung function test that measures the amount and speed of air being breathed in and out. By following the instructions and guidelines, Anita can achieve optimal results, aiding in the diagnosis and assessment of lung conditions.
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What's 704 divided by 24? Make sure to give an explanation for Brainliest!
Answers
Answer:29.3 repeating
Step-by-step explanation:Just use
calculator
A security car is parked 25 ft from a movie theater. Find at what speed the reflection of the security strobe lights is moving along the wall of the movie theater when the reflection is 30 ft from the car. The strobe lights are rotating with the speed 2 revolutions per second.
Answers
Answer:
v=20π ft/s
Step-by-step explanation:
Given:
Distance from the security car to the movie theater, D=25 ft
Distance of the reflection from the car, d=30 ft
Speed of rotation of the strobe lights, 2 rev/s
To find the speed at which the reflection of the security strobe lights is moving along the wall of the movie theater, we need to calculate the linear velocity of the reflection when it is 30 ft from the car.
We can start by finding the angular velocity in radians per second. Since the strobe lights rotate at 2 revolutions per second, we can convert this to radians per second.
ω=2πf
=> ω=2π(2)
=> ω=4π rad/s
The distance between the security car and the reflection on the wall of the theater is...
r=30-25= 5 ft
The speed of reflection is given as (this is the linear velocity)...
v=ωr
Plug our know values into the equation.
v=ωr
=> v=(4π)(5)
∴ v=20π ft/s
Thus, the problem is solved.
The speed of the reflection of the security strobe lights along the wall of the movie theater is 2π ft/s.
To solve this problem, we can use the concept of related rates. Let's consider the following variables:
x: Distance between the security car and the movie theater wall
y: Distance between the reflection of the security strobe lights and the security car
θ: Angle between the line connecting the security car and the movie theater wall and the line connecting the security car and the reflection of the strobe lights
We are given:
x = 25 ft (constant)
y = 30 ft (changing)
θ = 2 revolutions per second (constant)
We need to find the speed at which the reflection of the security strobe lights is moving along the wall (dy/dt) when the reflection is 30 ft from the car.
Since we have a right triangle formed by the security car, the movie theater wall, and the reflection of the strobe lights, we can use the Pythagorean theorem:
x^2 + y^2 = z^2
Differentiating both sides of the equation with respect to time (t), we get:
2x(dx/dt) + 2y(dy/dt) = 2z(dz/dt)
Since x is constant, dx/dt = 0. Also, dz/dt is the rate at which the angle θ is changing, which is given as 2 revolutions per second.
Plugging in the known values, we have:
2(25)(0) + 2(30)(dy/dt) = 2(30)(2π)
Simplifying the equation, we find:
60(dy/dt) = 120π
Dividing both sides by 60, we get:
dy/dt = 2π ft/s
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Solve for c law of sines
Answers
Answer:
c/sin(60°) = 14/sin(25°)
c = 14sin(60°)/sin(25°) = 28.7
consider slotted aloha with nodes retrying with probability p a. recall that when there are n active nodes, the probability that any node has successful transmission is np(1 − p)n−1. find the value of p that maximizes this expression. show your work. b. using the value of p found in (a), find the efficiency of slotted aloha by letting n approach infinity.
Answers
The efficiency of slotted aloha by letting n approach infinity is 1/e and the maximum value of probability is 1/n.
Given that:
No. of nodes = (n)
The efficiency of slotted aloha by letting n approach infinity is E (p)= np(1-p)^(n-1).
By derivation,
E' (p) = n(1-p)^(n-1) - np(n-1)(1-p)^(n-2)
E' (p) = n(1-p)^(n-2) x [(1- p) - p(n-1)]
E' (p) = n(1-p)^(n-2) x [1-np]
Let E'(p) =0
i.e. Either, n(1-p)^(n-2) = 0
=> p = 1 (minima)
Or [1-np] = 0
=> p = 1/n (maxima)
So, for the value of p* = 1/n, we can maximize this expression.
When p = 1/n, the efficiency of slotted aloha is
E(p*) = n.1/n (1-1/n)^(n-1)
E(p*) = (1-1/n)^(n-1)
E(p*) = (1-1/n)^n/(1-1/n)
Since, \(\lim_{n \to \infty} (1-1/n) = 1\\\)
\(\lim_{n \to \infty} (1-1/n)^n = 1/e\)
So, when n approaches infinite,
Efficiency => \(\lim_{n \to \infty} E(p*) = 1/e\)
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Which relation is a function?
I’m confused on this. can anyone help me out?
Answers
Answer:
The one the u have marked is a function.
Step-by-step explanation:
If you draw a vertical line through each one, each line only goes through one point
The terminal point of 0 is (3/2, 1/2). What is sin 0 ?
Answers
The sin of θ is 1/2.
Determine the number of sinWhen given the terminal point of an angle in the form (x, y), the sin of that angle is equal to the y-coordinate. In this case, the terminal point is given as (sqrt3/2, 1/2), so the sin of θ is 1/2. However, it is important to note that the question is incorrectly formatted.
The terminal point should be written as (sqrt3/2, 1/2), not sqrt3/2/1/2. This may have been a typo or an error in the formatting of the question. To find the sin of an angle given its terminal point, follow these steps:
1. Identify the y-coordinate of the terminal point.
2. The sin of the angle is equal to the y-coordinate. In this case, the terminal point is (sqrt3/2, 1/2), so the y-coordinate is 1/2.
Therefore, the sin of θ is 1/2.
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we are about to test a hypothesis using data from a well-designed study. which is true? i. a large p-value would be strong evidence against the null hypothesis. ii. we can set a higher standard of proof by choosing
Answers
Answer: 2+2
Step-by-step explanation: easy math
Answer:
Neither of the statements are true.
i. A large p-value indicates weak evidence against the null hypothesis. A small p-value (typically less than 0.05) is strong evidence against the null hypothesis.
ii. We cannot set a higher standard of proof by choosing a lower significance level (alpha) because doing so would increase the likelihood of making a Type II error, which is failing to reject a false null hypothesis. The level of significance should be chosen based on the goals of the study and the consequences of making a Type I or Type II error.
Apple trees need to be planted in an orchard. The process takes two hours per tree. The orchard owner wants to find out how many apple trees can be planted in a given amount of time. Which graph correctly represents this relationship between time ( y ) and apples trees planted ( x )?
Graph D
Graph A
Graph C
Graph B
Answers
Answer:
Graph C. Hope this is correct!!!
Step-by-step explanation:
Answer: It should be "B". the vertical axis is the time and the horizontal axis is number of trees.
This is what my teacher sent me.
3a + 7 + 2(3 + a)
\(what \: is \: anwser\)
Answers
Answer:
5a + 13
Step-by-step explanation:
3a + 7 + 2(3 + a)
3a + 7 + 6 + 2a
5a + 13
HELP ME
A 6-foot tall man has a 9-foot shadow. At the same time, a tree he is standing next to has a 30-foot shadow.
A. 20 ft
B. 27 ft
C. 45 ft
D. 21 ft
E. 24 ft
Answers
Answer:
A.20 ft
Step-by-step explanation:
the shadow is double the height of the object.
A scale that allows us to rank individuals or objects, but not to say anything about the meaning of the differences between the ranks, is a(n)?
Answers
A scale that allows us to rank individuals or objects, but not say anything about the meaning of the differences between the ranks, is an ordinal scale.
What is an ordinal scale?An ordinal scale is one that allows us to rank individuals or objects without saying anything about the significance of the differences between the ranks. The ordinal scale is the second level of measurement that reports data ranking and ordering without determining the degree of variation between them. Cases in the same class are regarded as equivalent. Movie ratings, political affiliation, military rank, and other variables that use ordinal scales are examples."Movie ratings" is an example of an ordinal scale. Students in a class, for example, could rate a movie using the scale below.Therefore, a scale that allows us to rank individuals or objects, but not say anything about the meaning of the differences between the ranks, is an ordinal scale.
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Find the value of x.
-2x = 3x + 6
Answers
Answer:
x= -6/5
Step-by-step explanation:
-2x=3x +6
collect like terms
-6=3x+2x
-6=5x
x= -6/5
Answer: x= -6/5 make that a fraction
decimal form: x= -1.2
mixed number form: x= - 1 1/5, 1 is the whole number
Step-by-step explanation: Isolate the variable by dividing each side by factors that don't contain the variable.
A randomized experiment was performed to determine whether two fertilizers, A and B, give different yields of tomatoes. A total of 33 tomato plants were grown; 16 using fertilizer A, and 17 using fertilizer B. The distributions of the data did not show marked skewness and there were no outliers in either data set. The results of the experiment are shown below.[table]Which of the following statements best describes the conclusion that can be drawn from this experiment?A. There is no statistical evidence of difference in the yields between fertilizer A and fertilizer B (p > 0.15).B. There is a borderline statistically significant difference in the yields between fertilizer A and fertilizer B (0.10 < p < 0.15).C. There is evidence of a statistically significant difference in the yields between fertilizer A and fertilizer B (0.05 < p < 0.10).D. There is evidence of a statistically significant difference in the yields between fertilizer A and fertilizer B (0.01 < p < 0.05).E. There is evidence of a statistically significant difference in the yields between fertilizer A and fertilizer B (p < 0.01).
Answers
Answer:
There is evidence of a statistically significant difference in the yields between fertilizer A and fertilizer B (0.01 < p < 0.05).
Step-by-step explanation:
You and a friend are playing a board game. your final score $x$ is $12$ points less than your friend's final score. write and solve an equation to find your final score. round 9 round 10 final score your friend 22 12 195 you 9 25 ? equation: $=195$ your final score is points.
Answers
The equation formed using the given data is 195 = x + 12 and your final score is 183 points.
How to form an equation?
Determine the known quantities and designate the unknown quantity as a variable while trying to set up or construct a linear equation to fit a real-world application.
In other words, an equation is a set of variables that are constrained through a situation or case.
Let's say your final score is x
Given that,
Your final score x is 12 points less than your friend's final score.
So,
x = friend final score - 12
Now,
Friend final score = 195
So,
x = 195 - 12
x + 12 = 195
195 = x + 12
Now,
x = 195 - 12 = 183
Hence "The equation formed using the given data is 195 = x + 12 and your final score is 183 points".
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3 of the 4 points below lie in a straight line.
Which point does NOT?
O (-2,-3)
(2,1)
O(-4,-2) O (0,0)
Answers
Answer:
O(-4,-2) is the answer
Step-by-step explanation:
because it lies between a horizontal line
(10 Points) Question is In picture:
Answers
If we wanted to analyze the variables Birth Rate and Death Rate at the same time, what would be appropriate to use? Mark all that apply..
- two-way table
- scatterplot
- boxplots
- histogram
- split bar chart
- stacked bar chart
Answers
The appropriate methods for analyzing the variables Birth Rate and Death Rate at the same time would be scatterplot, two-way table, and stacked bar chart.
Scatterplot: A scatterplot can be used to visually display the relationship between two quantitative variables, such as Birth Rate and Death Rate. Each point on the scatterplot represents a pair of values for the two variables, making it easy to identify patterns or trends in the data.
Two-way table: A two-way table can be used to display the distribution of two categorical variables, such as Birth Rate and Death Rate, and how they relate to each other. It can help identify the joint frequency or relative frequency of different categories.
Stacked bar chart: A stacked bar chart can be used to show how two categorical variables, such as Birth Rate and Death Rate, are related to each other. Each bar represents the total frequency for each category, and the bars are divided into sections representing the subcategories of the other variable. This makes it easy to compare the distribution of the two variables across each category.
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Please help I’ll mark brainliest!
Answers
Answer:
Disciminant of f = 0
x-intecept = \((\frac{3}{2}, 0)\)
Step-by-step explanation:
Given the quadratic function, -4x² + 12x - 9
where a = -4, b = 12, and c = -9
The discriminant, b²- 4ac, is the expression inside the radical (numerator) of the quadratic formula:
\(x = \frac{-b +/- \sqrt{b^{2}-4ac} }{2a}\)
The first part of your given problem asks for the discriminant. Substitute the values for a, b, and c:
b²- 4ac = 12² - 4(-4)(-9) = 144 - 144 = 0 → This implies that the quadratic function has one real root.
Therefore, the disciminant of f is 0.
Next, the given problem asks for the x-intercepts. The x-intercept is the point on the graph where it crosses the x-axis. As I mentioned earlier, the function has one real root. Therefore, it means that there is only 1 x-intercept. To find out what the x-intercept is, use the quadratic formula:
\(x = \frac{-b +/- \sqrt{b^{2}-4ac} }{2a}\)
\(x = \frac{-12 +/- \sqrt{12^{2}-4(-4)(-9)} }{2(-4)}\)
\(x = \frac{-12 +/- \sqrt{144 - 144} }{-8}\)
\(x = \frac{-12}{-8} = \frac{3}{2}\)
Therefore, the x-intercept is \((\frac{3}{2}, 0)\).
help, I'm braindead and don't know what I am doing
Answers
3x + y =11
5x - y = 21
Answers
5x - y = 21 (4th equation)
Add (3rd equation and 4th equation)
3x + 5x = 32 (+y and -y got canceled)
=> 8x = 32
=>x = 4
(Substitute x with equation 3)
3x + y = 11
=> 12 + y = 11
=> y = -1
\(\bold{Heya...}\)
3x + y = 11.
E x p l a n a t i o n : -Let's solve for x ~
3x + y = 11
Step 1: Add -y to both sides.
\(\mathtt{3x \: + \: y \: + \: -y \: = \: 11 \: + \: -y}\)
\(\mathtt{3x \: = \: -y \: + \: 11}\)
Step 2: Divide both sides by 3.
\(\mathtt{\frac{3x}{3} \: = \: \frac{-y \: + \: 11}{3}}\)
↓ \(\underline{A \: n \: s \: w \: e \: r :}\) ↓
\(\bold{x \: = \: \frac{-1}{3}y \: + \: \frac{11}{3}}\)
Let's solve for x ~
5x - y = 21.
Step 1: Add y to both sides.
\(\mathtt{5x \: - \: y \: + \: y \: = \: 21 \: + \: y}\)
\(\mathtt{5x \: = \: y \: + \: 21}\)
Step 2: Divide both sides of 5.
\(\mathtt{\frac{5x}{5} \: = \: \frac{y \: + \: 21}{5}}\)
↓ \(\underline{A \: n \: s \: w \: e \: r :}\) ↓
\(\bold{x \: = \: \frac{1}{5}y \: + \: \frac{21}{5}}\)
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\(\huge{\bold{\red{\star{\pink{ItzSehzadi}}}}\)
Match the written mathematical operation to the equivalent symbolic form.
The quotient of 2 and g
The sum of 2 and 9
The difference of 2 and 9
The square of 9
The product of 2 and 9
2(9)
2/9
2-9
2 + 9
9
Answers
The written mathematical operations to their equivalent symbolic forms:
The quotient of 2 and 9: 2/9
The sum of 2 and 9: 2 + 9
The difference of 2 and 9: 2 - 9
The square of 9: 9^2 or 9²
The product of 2 and 9: 2(9)
Mathematical operations can be represented symbolically to express various computations. Let's break down each operation:
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A consumer watchdog organization estimates the mean weight of 1-ounce "Fun-Size"
candy bars to see if customers are getting full value for their money. A random sample
of 25 bars is selected and weighted, and the organization reports that a 95% confidence
interval for the true mean weight of the candy bars is 0.982 to 0.988 ounces.
a) What is the point estimate (=sample mean) from this sample?
b) What is the margin of error?
(Hint: find the distance between the sample mean and the upper limit).
c) Interpret the confidence level of 90% in the context of the problem?
Answers
Point estimate from the sample is 0.985, margin error is 0.003.
What is Confidence Interval?Confidence interval is defined as the interval which is the estimate for the parameter of the sample or population to be contained.
(a) To calculate point estimate or sample mean :
Point estimate is the mid point of the confidence interval.
Given that true mean weight of candy bars is 0.982 ounces to 0.988 ounces.
Point estimate = (0.982 + 0.988) / 2 = 1.97 / 2 = 0.985
(b) Margin error is the one half of the total width of the interval.
Margin error = (0.988 - 0.982) / 2 = 0.003
(c) The confidence level of 90% in this problem can be interpreted as , if we do the interval construction for many times, about 90% of the total constructed intervals has the true population mean of weight of fun size candy bars.
Hence the point estimate and margin error are 0.985 and 0.003 respectively.
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What is 4,000x25000=
Answers
100,000,000
Hope this helps
Answer:
29,000
Step-by-step explanation:
this is the answer
The table below shows Aubree's earnings on the job.
Time (hours) Earnings (dollars)
4
$84.40
18.
$379.80
28
$590.80
How long does it take her to make $137.152
hours
Suomit Answers
Answer
Answers
Answer:
6.5 hours
Step-by-step explanation:
the pay per hour is $21.1
137.15÷21.1=6.5
tan (tt/2) =. i neeed help baddddd
Answers
Answer:
D: Undefined
Step-by-step explanation:
You can use the unit circle or your calc for this (don't forget to put it in radians!). I will use the unit circle to explain.
Tangent on the unit circle is on the xy lines themselves. tan (π/2) would be on the positive y axis. Remember that tan∅ is sin∅/cos∅ and that the unit circle's radius is always one. If that is the case, the coordinate for tan (π/2) would be (0, 1). If cos is always x and sin is always y, you plug it in for tan∅. The fraction 1/0 is undefined, since you can't divide anything by 0. Therefore, tan (π/2) is undefined.
which of the relations given by the following sets of ordered pairs is a function?
a. {(5,2),(4,2),(3,2),(2,2),(1,2)}{(5,2),(4,2),(3,2),(2,2),(1,2)}
b. {(−4,−2),(−1,−1),(3,2),(3,5),(7,10)}{(−4,−2),(−1,−1),(3,2),(3,5),(7,10)}
c. {(−8,−3),(−6,−5),(−4,−2),(−2,−7),(−1,−4)}{(−8,−3),(−6,−5),(−4,−2),(−2,−7),(−1,−4)}
d. {(−6,4),(−3,−1),(0,5),(1,−1),(2,3)}
Answers
{(5, 2), (4, 2), (3, 2), (2, 2), (1, 2)}, {(−8, −3), (−6, −5), (−4, −2), (−2, −7), (−1, −4)} and {(−6, 4), (−3, −1), (0, 5), (1, −1), (2, 3)} are the sets of ordered pairs considered as a function.
{(−4, −2), (−1, −1), (3, 2), (3, 5), (7, 10)} is not a function.
In mathematics, ordered pair is a pair of numbers that are written in a specific order. They are generally written in (x, y) form. For example (3, 5) is an ordered pair.
The function can also be represented by a set of ordered pairs. A function Is a set of ordered pairs in which no two different ordered pairs have the same value of x coordinate.
Option (a) : {(5, 2),(4, 2),(3, 2),(2, 2),(1, 2)}
No two ordered pairs have the same value of the x coordinate.
So it is a function.
Option (b) : {(-4, -2),(-1, -1),(3, 2),(3, 5),(7, 10)}
Two ordered pairs have the same value of x coordinate (3, 2) and (3, 5).
So, it can not be considered a function.
Option (c) : {(-8, -3),(-6, -5),(-4, -2),(-2, -7),(-1, -4)}
No two ordered pairs have the same value of the x coordinate.
So it is a function.
Option (d) : {(-6, 4),(-3, -1),(0, 5),(1, -1),(2, 3)}
No two ordered pairs have the same value of the x coordinate.
So it is a function.
Therefore, Options (a), (c), and (d) are the functions.
Option (b) is not a function.
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All polynomials of degree at most 3 with integer coefficients. Determine if the given set is a subspace of P, for an appropriate value of n. Justify your answer.
Answers
The zero polynomial is a polynomial of degree at most 3 with integer coefficients, and it belongs to the given set.
Thus, the given set is a subspace of P for n = 3.
The set P of all polynomials of degree at most 3 with integer coefficients.
The given set is a subspace of P for an appropriate value of n.
It can be justified by the following explanation:
A subspace is a subset of the vector space such that it has three properties, that are:
It is closed under addition, It is closed under scalar multiplication, and It contains the zero vector.
A polynomial is an expression consisting of variables and coefficients which involves only the operations of addition, subtraction, multiplication, and non-negative integer exponents of variables.
The given set is a subspace of P with n = 3 because it satisfies all the three properties of a subspace.
i) The sum of two polynomials is a polynomial of degree at most 3 with integer coefficients.
ii) Multiplication of a polynomial by a scalar is a polynomial of degree at most 3 with integer coefficients.
iii) The zero polynomial is a polynomial of degree at most 3 with integer coefficients, and it belongs to the given set.
Thus, the given set is a subspace of P for n = 3.
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