The formula for f , the specific antiderivative of f is F(u) = 4㏑(u) + u²/2 + 11/2 .
In the question ,
it is given that ,
the function f(u) is f(u) = 4/u + u and f(1) = 6 ,
to find the antiderivative of f , we integrate it with respect to u ,
∫f(u) = 4∫(1/u)du + ∫u.du
On integrating ,
we get ,
F(u) = 4㏑(u) + u²/2 + c ......equation(1)
Substituting the value of u = 1 in equation(1) ,
we get ,
F(1) = 4㏑(1) + 1/2 + c
6 = 0 + 1/2 + c
c = 6 - 1/2
c = 11/2 .
Now , substituting the value of c = 11/2 in equation(1) , we get
F(u) = 4㏑(u) + u²/2 + 11/2
Therefore , the formula for f is F(u) = 4㏑(u) + u²/2 + 11/2 .
The given question is incomplete , the complete question is
Write a formula for f, the specific antiderivative of f.
f(u) = 4/u + u ; F(1) = 6 .
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For what value of x is line m parallel to n?
Answer: X is equal to 21
Step-by-step explanation:
Answer:
25 degrees
Step-by-step explanation:
5x - 10 = 115
5x = 115 + 10
5x = 125
5/5 x = 125/5
x = 25
a scatterplot shows: a. the average value of groups of data. b. scores on one variable plotted against scores on a second variable. c. the frequency with which values appear in the data d. the proportion of data falling into different categories.
Scores on one variable plotted against scores on a second variable.
The correct answer is (b)
Now, According to the question:
Let's know:
A scatterplot shows:
A scatterplot shows the relationship between two quantitative variables measured for the same individuals. The values of one variable appear on the horizontal axis, and the values of the other variable appear on the vertical axis. Each individual in the data appears as a point on the graph.
Hence, The correct answer is (b) i.e.,
Scores on one variable plotted against scores on a second variable.
Given,
In the question:
A scatterplot shows:
a. the average value of groups of data.
b. scores on one variable plotted against scores on a second variable.
c. the frequency with which values appear in the data
d. the proportion of data falling into different categories.
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Here is an incomplete calculation of 534 divided by 6
The missing number for A is
The missing number for B is
The missing number for C is
Answer:
Step-by-step explanation:
a 23
b 43
c 56
Mitch can make 7 bracelet every 30 minute. At thi rate, how many bracelet can he make in 3. 5 hour?
Answer:
49 bracelets
Step-by-step explanation:
Let the number of bracelets that can be made be x.
First, let us convert 3.5 hours into minutes.
3.5 * 60 = 210 minutes
Accordingly,
Time (min) Number of bracelets
30 ⇒ 7
210 ⇒ x
Now, we can make an expression like this using cross multiplication.
30x = 7 × 210
30x = 1470
Divide both sides by 30.
x = 49
A researcher is attempting to determine which ethnic group is more likely to go to the movies at a movie theatre. The dependent variable is metric. Which of the following tests is most appropriate?
analysis of variance
Since , a researcher is attempting to determine which ethnic group is more likely to go to the movies at a movie theatre. The dependent variable is metric. Therefore, the Multiple Regression method will be more appropriate analysis of variance.
Multiple regression analysis is a statistical technique that analyzes the relationship between two or more variables and uses that information to estimate the value of the dependent variable. The goal of multiple regression is to develop a model that describes the dependent variable y with multiple independent variables. Linear regression has only one independent and dependent variable. But for multiple regression, there are many independent variables that help explain or predict the dependent variable y better.
The multiple regression equation is given by
y = a + b 1×1+ b2×2+……+ bk xk
where x1, x2, ….xk are the k independent variables and y is the dependent variable
Advantages of multiple stepwise regression:
Only independent variables with non-zero regression coefficients are included in the regression equation. Several standard estimation errors and R-squared trends are displayed. Stepwise multiple regression is efficient for finding regression equations with only significant regression coefficients. The steps to create the regression equation are straightforward.Learn more about Multiple regression:
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the number 120 is increased by 50%, and the result is then decreased by 30% to give the number x. what is the value of x?
Answer: x = 126
Step-by-step explanation:
We know that 50% of 120 is 60. So, to increase 120 by 50%, we add 60. This gets us 180. Next, we find 30% of 180. This is 54. So, we subtract 54 from 180. So, x = 126
assume a simple model with only two countries: the united states and germany, and two goods: beer and motorcycles. suppose that the opportunity cost for the united states to produce 1 beer is 3 motorcycles and the opportunity cost for germany to produce 1 beer is 1/2 motorcycles. which of the following statements is true
The statement opportunity cost for Germany to produce 1 beer is 1/2 motorcycles is true.
The German economy would be better off if it produced beer and traded motorcycles with the US.
Germans would benefit from specializing in producing beer and engaging in trade with the United States since their opportunity cost is lower (1/2 is less than 3).
A country is said to be having a comparative advantage in producing a good if it can produce it at a lower opportunity cost. Germany has a lower opportunity cost in producing beer so it has a comparative advantage in making beer.
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What is the simplified version of the expression
(x^1/2 y^1/9 )^3
The simplified version of the expression (x¹/² y¹/⁹)³ is (x³/² y¹/³)
How to determine the simplified expression?From the question, we have the following parameters that can be used in our computation:
(x^1/2 y^1/9 )^3
Rewrite the expression properly
So, we have
(x¹/² y¹/⁹)³
Open the brackets
This gives
(x¹/² y¹/⁹)³ = (x¹/²)³ * (y¹/⁹)³
Evaluate the expression in brackets
(x¹/² y¹/⁹)³ =(x³/² y¹/³)
Hence, the solution is (x³/² y¹/³)
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pls help me i really need help
Answer:
4 mph
1.5 mph
5 mph
Fastest: Kaliel, slowest: steve
Step-by-step explanation:
The unit for Melissia can be found by finding the slope of the line. The slope is shown to be 4 miles per hour. That is the unit rate, 4 miles per hour.
The unit rate for steve is also shown in the equation y = 1.5x. This equation is the filled in form of y = mx + b where m is equivalent to the slope. Therefore 1.5 is the slope meaning the unit rate is 1.5 miles per hour.
The unit rate for Kaliel is found using the information that he walks 10 miles in two hours. To find how much he goes in 1 hour divide by two getting you 5 miles per hour.
The fastest unit rate is Kalie with 5 miles per hour, and the slowest steve with 1.5 miles per hour.
last qustion i need so i need a right answer
The exponential equation of the logarithmic equation ㏑ (x² - 5 · x + 17) = 3 · x + 2 is x² - 5 · x + 17 = e³ˣ ⁺ ².
What is the exponential form of a logarithmic equation?
In this question we find that a logarithmic equation, in which we must eliminate the log operator must be eliminated by relationship between logarithmic and exponential equations, whose relationship is shown below:
Logarithm of an exponential equation
㏒ aˣ = x
Exponential up to an logarithmic equation
[tex]a^{\log x}[/tex] = x
Now, we proceed to eliminate the log operator by algebra properties and relationship between logarithmic and exponential equations:
㏑ (x² - 5 · x + 17) = 3 · x + 2
By using an "exp" operators, we get the following expression:
x² - 5 · x + 17 = e³ˣ ⁺ ²
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What is the difference between survey and experiment?
The main difference between experiment and survey is that experiment is laboratory research and survey is field research. Experiments are used to prove theories or hypotheses. Surveys are used to understand the notions of a group of people.
A single toss of a fair coin results in either 0 or 1 head, each with probability 1/2. Define H= number of
heads obtained on a single toss. The mean of His My = 0.5 and the standard deviation of His oH = 0.5.
Suppose you toss a fair coin four times. Define T= total number of heads obtained. Find the mean and standard deviation of T.
Answer:
µT = 2 (The mean of T is 2)
σT = 1 (The standard deviation of T is 1)
Step-by-step explanation:
This involves the transformation and combination of random variables. We know that the coin flips are independent as the knowledge of one coin flip will not affect the next or another coin flip.
The question has a transformation of H by essentially multiplying it by 4 that, then turns it into T. Knowing that we can multiply the mean of 0.5 by 4 with rules of a linear transformation when multiplying each observation by a positive constant. With that, we get the mean of T to equal 2.
Since we know it is independent, we can solve for standard deviation. To do so, we have to add 0.5 squared 4 times and square root it. That will look like this: Squareroot(0.5^2+0.5^2+0.5^2+0.5^2). That will give you 1 as the standard deviation for T.
I need HELPPP!!!!! Pls
ASAP PLEASE! A rectangular swimming pool is 8 ft deep. One side of the pool is 2.5 times longer than the other. The amount of water needed to fill the swimming pool is 2000 cubic feet. Find the dimensions of the pool.
The smaller dimension of the pool is {} ft and the larger dimension of the pool is {} ft.
The dimensions of the rectangular swimming pool are 25ft long 10ft wide and 8 feet deep.
What is a cuboid?A cuboid is a three-dimensional solid shape that has 6 faces, 8 vertices, and 12 edges. It is one of the most commonly seen shapes around us which has three dimensions: length, width, and height. Sometimes the cuboid shape is confused with a cube since it shares some properties of a cube, however, they are different from each other.
Volume of a cuboid = Length(L) x Width(W) x Depth(d)
but L = 2.5w
2.5w x w x 8 = 2000
20W^2 = 2000
W^2 = 2000/20
W^2 = 100
W = [tex]\sqrt{100}[/tex]
W = 10fft
L = 2.5W, but W = 10ft
L = 2.5 x 10
L = 25ft
In conclusion the length, width and depth are 25ft, 10ft, and 8ft respectively.
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an urban economist wishes to estimate the proportion of americans who own their homes. what size sample should be obtained if he wishes the estimate to be within 0.02 with 90% confidence if (a) he uses a 2010 estimate of 0.669 obtained from the u.s. census bureau
The sample size for the given problem is 1499.
What is sample size?
The process of deciding how many observations or replicates to include in a statistical sample is known as sample size determination. Any empirical study with the aim of drawing conclusions about a population from a sample must take into account the sample size as a crucial component.
Given:
An urban economist wishes to estimate the proportion of Americans who own their homes.
p cap = 0.669
1 - p cap = 0.331
margin of error = E = 0.02
[tex]Z_a_l_p_h_a_/_2[/tex]= 1.645
Sample size = n
[tex]n = (Z_a_l_p_h_a_/_2/E)^2*Pcap*(1 - Pcap)\\= (\frac{1.645}{0.02})^2*0.669*0.331\\ = 1499[/tex]
Hence, the sample size for the given problem is 1499.
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A bank vice president feels that each savings account customer has, on average, three credit cards. He collected data over a period of time and found the probability distribution given in the following table. The random variable X, represents the number of credit cards people own. If necessary, use a leading zero and round to 2 decimal places, e.g, 0.25. (a) Find the probability that a savings account customer selected at random will have more than two credit cards. (b) Find the expected value of the number of credit cards a randomly selected customer owns. (c) Find the standard deviation of the number of credit cards a randomly selected customer owns.
a)The probability that a customer selected will have more than two credit cards is 0.11 ,b)expected value is 1.34 and c)standard deviation is 0.96.
Given, probability distribution table
X p(X)
0 0.18
1 0.44
2 0.27
3 0.08
4 0.03
where,X= number of credit cards people own
probability that a savings account customer selected at random will have more than two credit cards, p(X>2)=p(3)+P(4)=0.08+0.03=0.11Expected value of the number of credit cards a randomly selected customer owns Expected value or mean,[tex]\mu=\sum\limits^4_{n=0} X*P(X)=0*P(0)+1*P(1)+2*P(2)+3*P(3)+4*P(4)\\\\\mu=0+1(0.44)+2(0.27)+3(0.08)+4(0.03)\\\\\mu=0+0.44+0.54+0.24+0.12\\\\\mu=1.34[/tex]Standard deviation of number of credit cards. Standard deviation,[tex]\sigma=\sqrt{\sum(X-\mu)^2P(X)}\\\\=\sqrt{(-1.34)^2(0.18)+(0.34)^2(0.44)+(0.66)^2(0.27)+(1.66)^2(0.08)+(2.66)^2(0.03)}\\\\=\sqrt{(1.7956)(0.18)+(0.1156)(0.44)+(0.4356)(0.27)+(2.7556)(0.08)+(7.0756)(0.03)}\\\\=\sqrt{0.323208+0.050864+0.117612+0.220448+0.212268}\\\\=\sqrt{0.9244}\\\\=0.96[/tex]Thus, the probability that a customer selected will have more than two credit cards is 0.11 ,expected value is 1.34 and standard deviation is 0.96.
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Your question is incomplete, Here is the complete question.
A bank vice president feels that each savings account customer has, on average, three credit cards. He collected data over a period of time and found the probability distribution given in the following table. The random variable X, represents the number of credit cards people own.
X p(X)
0 0.18
1 0.44
2 0.27
3 0.08
4 0.03
If necessary, use a leading zero and round to 2 decimal places, e.g, 0.25.
(a) Find the probability that a savings account customer selected at random will have more than two credit cards ?
(b) Find the expected value of the number of credit cards a randomly selected customer owns ?
(c) Find the standard deviation of the number of credit cards a randomly selected customer owns ?
a repeated-measures anova with 5 subjects has df within-treatment equal to 12. what is the value for dferror for this analysis?
the value for dferror for this analysis is 8.
What is error?
Error is the difference between an actual value and an estimate, or approximate, representation of that value in applied mathematics. The discrepancy between the population's average and the average of a sample taken from that population is a frequent example in statistics. The discrepancy between an irrational number's true value and the values of rational expressions like 22/7, 355/113, 3.14, or 3.14159 serves as an example of round-off error in numerical analysis. A truncation error happens when an infinite series is ignored for all but a small number of terms. For instance, the sum of the infinite series can be used to express the exponential function ex.
df-error = (df-within treatment) - (df-subjects)
df-subjects = n - 1 = 5 - 1 = 4 {n is the no of subjects}
df-within treatment = 12
df-error = 12 - 4 = 8
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Put the steps in order that are used to solve the following systems of equations by substitution.
-7x - 2y
2y
= x= 2 (-4) +11 → x = 3
x
-
=
= - 13
11
= x - 2y = 11 → x = 2y + 11
=y=-4
= -7 (2y + 11) - 2y = -13
= (3,-4)
= -16y = 64
= -16y - 77 = -13
= -14y-77-2y = -13
Answer:
yes I will get suspicious and then
Step-by-step explanation:
he was in a meeting
The point A(6,-6) is rejected over the origin and it’s image is point B what is are coordinates of point B
The coordinates of point B is (-6, 6) if the point A(6,-6) is rejected over the origin and it’s image is point B
What is geometric transformation?It is defined as the change in coordinates and the shape of the geometrical body. It is also referred to as a two-dimensional transformation. In the geometric transformation, changes in the geometry can be possible by rotation, translation, reflection, and glide translation.
It is given that:
Point A(6,-6) is reflected over the origin and it’s image is point B
The rule for transformation:
(x, y) --> (-x, -y)
(6, -6) --> (-6, 6)
Thus, the coordinates of point B is (-6, 6) if the point A(6,-6) is rejected over the origin and it’s image is point B
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Water leaks from a crack in a vase at a rate of 0.5 cubic inches per minute. How long does it take for 20% of the water to leak from a full vase? I either got 10 minutes or 2.5...
The amount of time it would take for 20% of the water to leak from a full vase is equal to 24.128 minutes.
How to calculate the volume of a cone?Mathematically, the volume of a cone can be calculated by using this formula:
V = 1/3 × πr²h
Where:
V represents the volume of a cone.h represents the height.r represents the radius.From the diagram of the cone (see attachment), we have the following parameters:
Diameter of cone = 4.8 in.
Height of cone = 10 in.
Radius of cone = diameter/2 = 4.8/2 = 2.4 in.
Substituting the given parameters into the formula, we have;
Volume of cone, V = 1/3 × 3.142(2.4² × 10)
Volume of cone, V = 60.32 in³.
For the volume of water that has leaked, we have:
Volume of water leaked = 20/100 × 60.31
Volume of water leaked = 12.062 in³.
For the required amount of time, we have:
Time = Volume/Rate
Time = 12.064/0.5
Time = 24.128 minutes.
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3
Select all the correct answers.
Which expressions are equal to ¹.2*?
O 12³
0 2³.33
0 26.33
O 125
It seems that there is perhaps some missing info here. Could you double check your question to validate the information being asked? Tysm!
I need help on this it’s Unit 3: Parallel & Perpendicular Lines
Homework 7: Point-Slope Form
The equation for given Parallel & Perpendicular Lines points and slope and given below.
what is parallel and perpendicular lines?
In a plane, parallel lines are those whose distances between them are constant. Parallel lines do not cross. Lines that cross at a right angle of 90 degrees are said to be perpendicular.
The equation of a line in slope-intercept form y = mx + c
1. substitute x = 0, y = 3 and m = -2 in equation
3 = -2*0 + c
c = 3, substitute in equation
Then y = -2x + 3
2. substitute x = -3 , y = - 5 and m = -( 3/5 ) in equation
-5 = -( 3/5 )*(-3 ) + c
c = - 34/5 , substitute in equation
Then 5y = -3x - 34
3. substitute x = -8 , y = 6 and m = -(1/4) in equation
6 = -(1/4)*(-8 )+ c
c = 8, substitute in equation
Then y = -2x + 8
The equation of line passing through two points is m = ( y2 - y1) / ( x2 - x1)
4. The given points is ( 1, 3) and ( -3, -5) and substitute in above equation.
Then m = 2
substitute m = 2 and ( 1, 3) in equation y = mx + c
Then c = 1
substitute m = 2 and c = 1 in equation of y = mx + c
Then the equation is y = 2x + 1
5. The given points is ( 1, 4) and ( 6, -1 ) and substitute in above equation.
Then m = - (5/4)
substitute m = - (5/4) and ( 1, 4) in equation y = mx + c
Then c = 21/4
substitute m = - (5/4) and c = 21/4 in equation of y = mx + c
Then the equation is 4y = -5x + 21
6. The given points is ( -12,14) and ( 6, -1 ) and substitute in above equation.
Then m = - (5/6)
substitute m = - (5/6) and( -12,14) in equation y = mx + c
Then c = 4
substitute m = - (5/6) and c = 4 in equation of y = mx + c
Then the equation is y = - ( 5/6 ) + 4
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Let F be the radial force field F(x, y) = xi + yj. Find the work done by this force along the following two curves, both which go from (0, 0) to (4, 16). (Use the Fundamental Theorem for Line Integrals instead of computing the line integral from the definition, as you did in the previous set. This way shows why the answers to the two parts must be the same - independence of path!) A. If C_1 is the curve: x = t, y = t^2, 0 lessthanorequalto t lessthanorequalto 4, then integral_C_1 F middot dr = B. If C_2 is the curve: x = 4t^2, y = 16t^2, 0 lessthanorequalto t lessthanorequalto 1, then integral_C_2 F middot dr =
To know the answer check the given file.
If the probability that the Islanders will beat the Rangers in a game is 4/7, what is the probability that the Islanders will win exactly two out of four games in a series against the Rangers? Round your answer to the nearest thousandth.
The probability that the islanders will win exactly two games is 0.359.
How to find probability using binomial distribution?The binomial distribution is based on the binomial theorem which can be written as (a + b)ⁿ = ⁿC₀aⁿb⁰ + ⁿC₁aⁿ⁻¹b¹ + ⁿC₂aⁿ⁻²b²+ ....+ ⁿCₙa₀bⁿ.
In order to use in the probability, there should be events independent of each other and the sum of there probabilities is 1.
Given that,
The probability of winning is 4/7.
Then the probability to lose is 1 - 4/7 = 3/7.
If islanders win exactly two games out of four, it implies that they will lose 2 as well.
Now, the probability of winning exactly two games can be found using binomial distribution as given below,
⁴C₂(4/7)²(3/7)²
= 6 × 16/49 × 9/49
= 864/2401
= 0.359
Hence, the probability of winning exactly two games is 0.359.
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Select the correct answer. The average rate of change of f(x) is given by the formula . Over what interval does this formula give the average rate of change for f(x)? A. [4, 7] B. [-7, 3] C. [3, 7] D. [3, 4]
Answer:
34
Step-by-step explanation:
hope u new it have fun hsm s
if 40% of population is 4500 what is the total population?
Answer:
11250
Step-by-step explanation:
in the photo below please!!!!
Answer:
[tex]\cos(\theta) + \sin(\theta)[/tex]
Step-by-step explanation:
Use the sine angle sum identity.
[tex]\sin(a+b)=\sin(a)\cos(b)+\cos(a)\sin(b)[/tex]
[tex]\sin(45\textdegree + \theta)=\sin(45\textdegree)\cos(\theta)+\cos(45\textdegree)\sin(\theta)[/tex]
Now, simplify [tex]\sin(45\textdegree)[/tex] and [tex]\cos(45\textdegree)[/tex] to [tex]\dfrac{\sqrt2}{2}[/tex]:
[tex]\sin(45\textdegree + \theta)=\dfrac{\sqrt2}{2} \cdot \cos(\theta)+\dfrac{\sqrt2}{2} \cdot \sin(\theta)[/tex]
Then, factor out [tex]\dfrac{\sqrt2}{2}[/tex] from each term.
[tex]\sin(45\textdegree + \theta)=\dfrac{\sqrt2}{2} \cdot ( \cos(\theta)+\sin(\theta))[/tex]
Finally, identify what is in the parentheses corresponding to the blank space in the question.
[tex]\cos(\theta) + \sin(\theta)[/tex]
Line d pae through point (3, 5) and (10, 1). Line a pae through point (5, 8) and (2, 13). Are line d and line are parallel or perpendicular
lines a and d are neither parallel nor perpendicular.
What is the slope of line?
Given two line-side coordinates, use the slope formula to determine the slope of the line. The slope is defined as the ratio of the change in the y values to the change in the x values using the formula m=(y2-y1)/(x2-x1). x1 and y1 are represented by the first point's coordinates. The second points are located at x2, y2, and their locations. Whichever point you choose to classify as the first and which as the second doesn't matter.
The given points of line d is (3,5) and (10,1)
and line an of line a is (5, 8) and (2, 13).
The slope of line d is m 1 = [tex]\frac{1-5}{10-3}[/tex]
m1 = -4/ 7
The slope of line d is m2 = [tex]\frac{13-8}{2-5}[/tex]
m2 = -5/3
if the slope of two lines is equal that is m1 = m2 , then the lines are parallel and the relation m1*m2=−1, then the lines are perpendicular to each other.
Here both condition fails.
Hence, lines a and d are neither parallel nor perpendicular.
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obtain the three best subsets according to the c p criterion, whicbi:of these subset models appears to have the smallest bias?
I may utilize the Cp Criterion, AICp, and SBCp to aid in choosing the optimal model. All of them impose sanctions for introducing predictions.
What is subset regression model?
Best subsets regression is a model-building regression analysis that is exploratory. It compares every model that might be built using a specified set of predictors.
There are Cp Criterion, AICp and SBCp that I can use to help select the best model. They all place penalties for adding predictors.
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For each of the described curves, decide if the curve would be more easily given by a polar equation or a Cartesian equation. Then write an equation for the curve. (a) A circle with radius 2 and center (3, 2).
(b) A circle centered at the origin with radius 1.
The equation of circle for both the parts will be as,
(a) (x-3)² +(y-2)²= 4
(b) x²+y² = 1
What is circle?
A circle may be a form consisting of all purposes in a very plane that ar at a given distance from a given point, the centre. Equivalently, it's the curve copied out by a point that moves in a very plane so its distance from a given point is constant.
Main Body:
(a) When the circle is offset from the origin, the equation for the radius gets messy. In general, it will be the root of a quadratic equation in sine and cosine, not easily simplified. The Cartesian equation is easier to write.
Circle centered at (h, k) with radius r:
(x -h)² +(y -k)² = r²
The given circle is ...
(x -2)² +(y -2)² =2²
(x -2)² +(y -2)² = 4
__
(b) When the circle is centered at the origin, the radius is a constant. The desired circle is most easily written in polar coordinates:
x²+y² = 1
Hence the equation of circle is such.
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