Using the following equation, find the center and radius of the circle x^2-2x+y^2-6y=26
please show work
Answers
The center of the circle is (1, 3) and the radius is 6.
To find the center and radius of the circle given by the equation x^2-2x+y^2-6y=26, we need to rewrite the equation in a standard form for a circle, which is (x-h)^2 + (y-k)^2 = r^2, where (h, k) represents the center of the circle and r represents the radius.
To rewrite the equation, we complete the square for both the x and y terms.
Starting with the x terms:
x^2 - 2x = x^2 - 2x + 1 - 1 = (x - 1)^2 - 1
Now, let's complete the square for the y terms:
y^2 - 6y = y^2 - 6y + 9 - 9 = (y - 3)^2 - 9
Substituting these completed square terms back into the original equation, we have:
(x - 1)^2 - 1 + (y - 3)^2 - 9 = 26
Simplifying the equation:
(x - 1)^2 + (y - 3)^2 = 36
Comparing this with the standard form of a circle equation, we can see that the center of the circle is (1, 3) and the radius is √36 = 6.
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Related Questions
meridians of identify degrees east and west of the . these lines are / are not (circle) scientifically based. why/why not?
Answers
The meridians of longitude identify the degrees east and west of the Prime Meridian. These lines are scientifically based because they are determined by the Earth's rotation and provide a consistent and accurate system for navigation, mapping, and timekeeping.
1. The meridians of longitude are imaginary lines that run vertically from the North Pole to the South Pole on the Earth's surface.
2. The Prime Meridian, located at 0 degrees longitude, serves as the starting point for measuring degrees east and west.
3. The degrees of longitude are divided into 360 equal parts, with each degree representing one hour of the Earth's rotation.
4. The meridians of longitude allow us to determine specific locations on the Earth's surface and measure the angular distance from the Prime Meridian.
5. The scientific basis of meridians of longitude enables global coordination and facilitates activities such as international travel, communication, and scientific research.
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Please help, I have a time limit on each question and its almost done
Answers
Answer:
B
Step-by-step explanation:
Solve the exponent first and thats the only remotely close answer
It takes 3 minutes to make one full rotation on each of the wheels.
Find the linear speed if you are riding on the green wheel
Answers
Answer:
Step-by-step explanation:
For the overdamped oscillations, the displacement x(t) is expressed by the following x(t) = e^-βt [A e^ωt + Be^-ωt]. The displacement can be expressed in terms of hyperbolic functions as the following: Hint: Use the following relations eʸ = cosh y + sinh y e⁻ʸ = coshy - sinhy A. x(t) = (cosh βt - sin βt) [(A + B) cosh ωt - (A - B) sinh ωt] B. x(t) = (cosh βt + sin βt) [(A + B) cosh ωt + (A - B) sinh ωt] C. x(t) = (cosh βt - sin βt) [(A - B) cosh ωt + (A - B) sinh ωt] D. x(t) = (cosh βt - sin βt) [(A + B) cosh ωt + (A - B) sinh ωt]
Answers
The displacement x(t) for overdamped oscillations is given by x(t) = (cosh βt + sin βt) [(A + B) cosh ωt + (A - B) sinh ωt].
The correct expression for the displacement x(t) in terms of hyperbolic functions is:
B. x(t) = (cosh βt + sin βt) [(A + B) cosh ωt + (A - B) sinh ωt]
To show this, let's start with the given expression x(t) = e^(-βt) [A e^(ωt) + B e^(-ωt)] and rewrite it in terms of hyperbolic functions.
Using the relationships e^y = cosh(y) + sinh(y) and e^(-y) = cosh(y) - sinh(y), we can rewrite the expression as:
x(t) = [cosh(βt) - sinh(βt)][A e^(ωt) + B e^(-ωt)]
= [cosh(βt) - sinh(βt)][(A e^(ωt) + B e^(-ωt)) / (cosh(ωt) + sinh(ωt))] * (cosh(ωt) + sinh(ωt))
Simplifying further:
x(t) = [cosh(βt) - sinh(βt)][A cosh(ωt) + B sinh(ωt) + A sinh(ωt) + B cosh(ωt)]
= (cosh(βt) - sinh(βt))[(A + B) cosh(ωt) + (A - B) sinh(ωt)]
Comparing this with the given options, we can see that the correct expression is:
B. x(t) = (cosh βt + sin βt) [(A + B) cosh ωt + (A - B) sinh ωt]
Therefore, option B is the correct answer.
The displacement x(t) for overdamped oscillations is given by x(t) = (cosh βt + sin βt) [(A + B) cosh ωt + (A - B) sinh ωt].
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City Middle School is raising money for new gym equipment by selling cookie dough.
• 25% of all money collected from the sale will go towards the equipment.
• The sixth grade sold $511.94 worth of cookie dough.
• The seventh grade sold $385.96 worth of cookie dough.
• The eighth grade sold $491.12 worth of cookie dough.
About how much money did the school raise for the new gym equipment?
Answers
Explanation:
Add up the dollar figures given
511.94+385.96+491.12 = 1389.02
The school raised a total of $1,389.02
Of that total, 25% will go toward the gym equipment.
25% of 1389.02 = 0.25*1389.02 = 347.255 which rounds to 347.26
Answer:
$347.255
Step-by-step explanation:
add all the sales of sixth to eight grade and multiply to .25
Use the coordinates of the labeled point to find the point-slope equation of
the line
Answers
Answer:
C.
Step-by-step explanation:
The y-intercept is (0,4) and the slope is -3
So check letter C 4 + 5 = -3(0-3) = 9, it is a true statement
1.83 find some values of z. the wechsler adult intelligence scale (wais) is the most common iq test. the scale of scores is set separately for each age group, and the scores are approximately normal, with mean 100 and standard deviation 15. people with wais scores below 70 are considered developmentally disabled when, for example, applying for social security disability benefits. what percent of adults are developmentally disabled by this criterion?
Answers
The percent of adults who are developmentally disabled by the criterion of an IQ score below 70 is approximately 2.28%
We can use the standard normal distribution in order to find the probability of an IQ score below 70.
We know the mean IQ score is 100 and the standard deviation is 15, so we can use the formula:
z = (70 - 100) / 15
z = -2
Using a normal probability table, we find that the probability of a score less than -2 is approximately 0.0228.
Therefore, we get that approximately 2.28% of adults are considered developmentally disabled by the criterion of an IQ score below 70.
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What is the Greatest Common Factor of 6 and 3/4
Answers
1/3 bigger than 5/9?
Answers
Answer:
No 1/3 is not greater than 5/9.
Step-by-step explanation:
if a1 =1 and an = -5an-1-4 then find the value of a3
Answers
Answer:
According to a Wyzant page, if a1 = 1 and an = -5an-1+2, then we can find the value of a3 as follows:
a1 = 1 a2 = -5a1 + 2 = -5 + 2 = -3 a3 = -5a2 + 2 = -5(-3) + 2 = 15 + 2 = 17
Therefore, the value of a3 is 17.
which statement is correct? int k = 15 / 4; byte b = 100 * 1000; float f = 3.5 * 4; int k = (double) 4 * (int) 4.5; none of them
Answers
None of the given statements is correct
1. int k = 15 / 4; - This statement performs integer division, resulting in a quotient of 3. Therefore, k would be assigned the value 3.
2. byte b = 100 * 1000; - This statement performs integer multiplication, resulting in the product of 100,000. However, the value 100,000 is outside the range of a byte (-128 to 127), so it cannot be assigned to a byte variable.
3. float f = 3.5 * 4; - This statement performs floating-point multiplication, resulting in the product of 14.0. This value can be assigned to a float variable, so the statement is valid.
4. int k = (double) 4 * (int) 4.5; - This statement attempts to cast 4 to a double and 4.5 to an int. However, the cast of 4.5 to an int truncates the decimal portion, resulting in a value of 4. Then, the multiplication is performed, resulting in a product of 16. However, the assignment to an int variable is not valid because it violates the syntax rules of declaring the same variable twice in the same scope.
None of the given statements is correct. Statement 2 attempts to assign a value outside the range of a byte, and statement 4 violates the syntax rules of variable declaration.
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count how many of the class guesses are inside the 90% confidence interval. compute the percentage of the class guesses that are inside the interval. is this close to 90%? should it be?
Answers
The percentage of the class guesses that are inside the interval will be close to 90% is not expected.
Out of the class guesses, 8 are inside the 90% confidence interval.
This is a percentage of 53.33%, which is not close to 90%.
This should not be expected to be close to 90%, as the 90% confidence interval is a measure of the probability that the true population parameter lies within the interval and not a measure of the accuracy of the individual guesses.
The 90% confidence interval is a measure of the probability that the true population parameter lies within the interval.
It is not a measure of the accuracy of the individual guesses, but rather of the likelihood that the true population parameter lies within the interval.
Thus,
It is not expected that the percentage of the class guesses that are inside the interval will be close to 90%.
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FILL in the blank:AB E M nxn (R) (i) det (A.B) = ____________ . (ii) A is invertible if and only if _____________ .
Answers
Answer:
For square matrices A and B of equal size, the determinant of a matrix product equals the product of their determinants: det (A.B) = det (A) det (B) 1. A is invertible if and only if its determinant is nonzero 1.
Step-by-step explanation:
he second of a triangle is 6 more than the first angle. The third angle is 12 less than the first angle. Find all three angles if the sum of their angles is equal to 180°
Answers
Answer:
Let first angle be x
x+x+6+x-12=180°
3x-6=180°
3x=186
x=63°
First angle=63°
Second Angle=69°
Third angle=51°
Hope it helps you
Algorithm A requires exactly C(n)=n3 basic operations, where n is the input size. Suppose that on your current laptop, the algorithm takes t seconds to run on an input size nS ('S' stands for "slow"). Then the same algorithm will take t seconds for an input size nF on a laptop that is 8x faster than your current one ('F' stands for "fast"). What is nF?
Answers
The input size nF for the fast laptop can be calculated by finding the ratio of the speeds between the slow and fast laptops and applying it to the input size nS. In this case, the input size nF is 2.
Let's assume the speed of the speeds laptop is x and the speed of the fast laptop is 8x (as it is mentioned that the fast laptop is 8 times faster than the slow laptop).
According to the given information, the algorithm A takes t seconds to run on the slow laptop for an input size of nS. This implies that C(nS) = n\(S^3\) basic operations.
Since the fast laptop is 8 times faster, the algorithm A also takes t seconds to run on it for an input size of nF. This implies that C(nF) = n\(F^3\) basic operations.
We can equate the time complexity of the algorithm on both laptops:
C(nS) = C(nF)
n\(S^3\) = n\(F^3\)
Since the speed of the fast laptop is 8 times that of the slow laptop, we can write:
nS / x = nF / (8x)
nS = nF / 8
Simplifying the equation, we find that nF = 2.
Therefore, the input size nF for the fast laptop is 2.
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70 pupils in a sports centre are surveyed. The pupils can only use the swimming pool and the gym. 28 pupils use the swimming pool and the gym. 48 pupils use the swimming pool. 39 pupils use the gym. Find the probability to select a pupil that uses neither the swimming pool nor the gym.
Answers
The probability that a pupil uses neither pool nor gym is 11/70
What is Probability?Probability is the likelihood that an event will happen. This can range from an event being impossible to some likelihood to being absolutely certain. In math terms, probability is on a scale from 0 to 1. Zero means the event is impossible, like rolling a seven on a die that only has digits from 1 to 6.
Number of pupil that can use pool and gym = 28
Number of people that can use pool = 48
Number of people that can use gym = 39
Number of people that can use pool only = 48 - 28 which is 20
Number of people that can use gym only = 39 - 28 = 11
Total number of persons that can use either pool, gym or both = 20 + 11 + 28 which is 59
Number of people that cannot use either or both of the facilities = 70 - 59 which is 11.
Probability = required outcome / possible outcome
Required outcome = 11
possible outcome = 70
Probability = 11/70
In conclusion, the probability that a pupil uses neither swimming pool nor gym is 11/70
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Gavin combines Thirty-two and two-fifths ounces of water and 7.15 ounces of lemon juice in a pitcher to make lemonade. Which is the most reasonable estimate for the amount of liquid in the pitcher? 39 ounces 42 ounces 45 ounces 47 ounces
Answers
Answer:
OPTION A is correct
39 ounces
Step-by-step explanation:
Given:
The amount of water in the pitcher= 32 ounces
The amount of lemon juice in the pitcher = 7.15 ounces
We were to calculate the most reasonable estimate for the amount of liquid in the pitcher
To do this we need to sum up the Amount of water and Amount of lemon juice in the pitcher because the water is a liquid as well as the lemon juice which is
32 ounces + 7.15 ounces
=39.15 ounces
Therefore, the Estimated amount of liquid in the pitcher is approximately 39 ounces
Today is march 28 in 6 weeks and 1 day the freshmen class of 2025 will be going on to a carnival staycation what is the date on their field trip
Answers
HI
I WANT AN ANSWER THAT
HOW WILL I MAKE r the subject of the formula
A= ½πr2,
Answers
Answer:
r = √(A/π)
Step-by-step explanation:
HI
I WANT AN ANSWER THAT
HOW WILL I MAKE r the subject of the formula
A= ½πr²,
inverse formula
r = √(A/π)
noah draws this box plot for data that has measure of variability 0. explain why the box plot is complete even though there do not appear to be any boxes.
Answers
The box plot is complete because it displays the five-number summary of a set of data. The five-number summary is the minimum, first quartile, median, third quartile, and maximum.
Due to the fact that it shows a five-number summary of a collection of data, the box plot is finished. Minimum, first quartile, median, third quartile, and maximum are the five numbers that make up the summary.
The boxplot visually displays the minimum, lower quartile, median, upper quartile, and maximum of five sample data. The plot's box is a rectangle with ends at each quartile, enclosing the middle half of the sample. The sample's interquartile range is therefore represented by the box's length. The box's second dimension does not specifically symbolize anything.
The sample median is used to draw a line through the box. From the box's two ends, whiskers grow until they reach the sample's maximum and minimum. The crossbar at each whisker's extreme end is optional, and its length has no significance. The next diagram compares a boxplot of the same data with a dot-plot of a sample of 20 observations (actual sample values used in the display).
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Can some help meeeeeeeee?
Answers
Answer:
$46.54
Step-by-step explanation:
A=P(1+r/n)^nt
P=220
r=.0325
n=1
t=6
A=266.54
A=P+I
266.54=220+I
I=46.54
Pls help I need the answer quick
Answers
49
..............
25 percent of 400 is what amount?
Answers
Answer:
Step-by-step explanation:
it is 100
Answer:
100
Step-by-step explanation:
25 400 10000
----- × ------ = --------- = 100
100 1 100
Hope this helped you- have a good day bro cya)
it is a standard practice to use lagrange interpolation to approximate the deriva- tive of a function using difference schemes. why do we not use hermite interpo- lation instead?
Answers
The reason why Lagrange interpolation is preferred over Hermite interpolation when approximating the derivative of a function using difference schemes is that Hermite interpolation involves calculating both the function value and its derivative at each data point.
Why do not we use hermite interpo- lation instead? Explain more?This can be computationally expensive and may not always be possible if the function's derivative is not known or difficult to calculate.
On the other hand, Lagrange interpolation only requires knowledge of the function's values at the data points, making it a simpler and more practical choice for many applications.
Additionally, Lagrange interpolation produces a polynomial function that is continuous and differentiable, which is ideal for approximating derivatives.
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wich of the following numbers are greater than -185/100 -1.08190/100-35/20
Answers
-185/100 = -1.85
a) -1.08 this number id greater than -1.85
b) 190/100 = 1.9 this number is greater than -1.85
c) -35/20 = -1.75 this number is greater than -1.85
All these numbers are greater than -185/100
Work out
1/8
of 760
please help
Answers
Answer: 95
Step-by-step explanation:
Think of 1/8 times 760 as 760/8 because it’s the same thing.
Ava bought a rectangular rug for her hallway. The rug is 23 yards wide and 234 yards long. What is the area of the rug?.
Answers
Answer:
5,382 yards
Step-by-step explanation:
To find the area, just multiply the width and length together. Don't forget the unit!!
Can y’all help me plz
Answers
Answer:
3.65, because 14.60 divided by 4 is 3.65
Step-by-step explanation:
Answer:
3.65....................
Choose the graph of this equation. y = 2.5x
Answers
Answer:
A.
have a good day or night
The engineer's model of a sugar factory has a floor area of 30 inches by 52 inches. The floor area of the model is __________ square feet.
Answers
The floor area of the engineer's model of the sugar factory is 10.825 square feet.
To determine the floor area of the engineer's model of a sugar factory in square feet, we need to convert the given measurements from inches to feet. Since there are 12 inches in a foot, we can divide both dimensions by 12 to convert them.
The length of the model in feet is 30 inches / 12 = 2.5 feet, and the width is 52 inches / 12 = 4.33 feet.
To find the floor area, we multiply the length by the width:
Area = Length × Width
= 2.5 feet × 4.33 feet
= 10.825 square feet
It's important to note that the given measurements are not a standard aspect ratio or scale for a sugar factory. The given dimensions may be scaled down for the model's convenience, so the calculated floor area is only applicable to the scale of the model.
In actuality, a sugar factory would have much larger dimensions.
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