If z = xy⁷ − x²y, x = t² + 1, y = t² − 1, then using chain rule the value of dz/dt = 2t(y⁷ + xy⁶(dy/dx) - 2xy - x²(dy/dx)) + 2t(xy⁷ + 7xy⁶ - x²)
To find dz/dt using the chain rule, we need to differentiate z with respect to t while considering the relationship between z, x, y, and t.
Given:
z = xy⁷ − x²y
x = t² + 1
y = t² − 1
We can start by finding dz/dx and dz/dy separately and then use the chain rule to combine them to find dz/dt.
First, let's find dz/dx:
Differentiating z with respect to x, keeping y constant:
dz/dx = (d/dx)(xy⁷) - (d/dx)(x²y)
Using the product rule for differentiation:
dz/dx = y⁷ + xy⁶(dy/dx) - 2xy - x²(dy/dx)
Next, let's find dz/dy:
Differentiating z with respect to y, keeping x constant:
dz/dy = (d/dy)(xy⁷) - (d/dy)(x²y)
Using the product rule again:
dz/dy = x(y⁷ + 7y⁶(dy/dy)) - x²
Since dy/dy = 1, we can simplify dz/dy as:
dz/dy = xy⁷ + 7xy⁶ - x²
Now, let's use the chain rule to find dz/dt:
dz/dt = (dz/dx)(dx/dt) + (dz/dy)(dy/dt)
Substituting the expressions we found earlier for dz/dx and dz/dy, and using dx/dt = 2t and dy/dt = 2t:
dz/dt = (y⁷ + xy⁶(dy/dx) - 2xy - x²(dy/dx))(2t) + (xy⁷ + 7xy⁶ - x²)(2t)
Simplifying this expression gives us dz/dt in terms of t, x, and y:
dz/dt = 2t(y⁷ + xy⁶(dy/dx) - 2xy - x²(dy/dx)) + 2t(xy⁷ + 7xy⁶ - x²)
This is the complete calculation for finding dz/dt using the chain rule.
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Complete question is:
Use the chain rule to find dz/dt. z = xy⁷ − x²y, x = t² + 1, y = t² − 1
The characteristics of the Liberty Company bond is listed below. How much is the annual interest payment? Coupon rate 10.20% Yield to maturity 10.55% Face value $1,000 Market price $850 $101.75 O $102.00 $105.50 O $120.00
The Liberty Company bond has the following characteristics:
Coupon rate: 10.20%
Yield to maturity: 10.55%
Face value: $1,000
Market price: $850, $101.75, $102.00, $105.50, or $120.00
The question asks for the annual interest payment.
To calculate the annual interest payment, we need to multiply the coupon rate by the face value of the bond. The coupon rate represents the annual interest rate as a percentage. In this case, the annual interest payment can be calculated as 10.20% of the face value, which is $1,000.
Therefore, the annual interest payment for the BCompany bond is $1,000 * 10.20% = $102.00.
Note: The market price of the bond is provided, but it does not affect the calculation of the annual interest payment. The market price represents the current market value of the bond and may vary depending on various factors such as supply and demand in the market.
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What is the area of the base?
6) Examples (a) j5 points Give an example of an infinite field such that 4-a -o for alle € F. (b) [5 points) Give an example of an infinite, non-commutative ring R such that for all a we have that 2a=0.
(a) An example of an infinite field such that 4-a -o for all e F is F_2.
Here, the only elements of the field are 0 and 1, and we have 1 + 1 = 0,
which is equivalent to 4 - 1 - 1 = 2 - 1 - 1 = 0. Therefore, for all a e F_2, 4 - a - a = 0, so F_2 satisfies the given condition.
(b) An example of an infinite, non-commutative ring R such that for all a we have that 2a = 0 is the ring of 2x2 matrices over the field F_2 (as defined in part (a)). If we identify the matrix \begin{pmatrix}a&b\\c&d\end{pmatrix} with the element ad + bc of F_2, then R becomes a ring.
Note that R is not commutative since the product of two matrices is not necessarily equal to the product of their entries, and that 2a = 0 for all matrices \begin{pmatrix}a&b\\c&d\end{pmatrix} in R since \begin{pmatrix}a&b\\c&d\end{pmatrix}\begin{pmatrix}0&1\\0&0\end{pmatrix} = \begin{pmatrix}0&a\\0&c\end{pmatrix} and \begin{pmatrix}a&b\\c&d\end{pmatrix}\begin{pmatrix}0&0\\1&0\end{pmatrix} = \begin{pmatrix}b&0\\d&0\end{pmatrix} have entries that are equal to 0 in F_2. Therefore, R satisfies the given condition.
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The average American gets a haircut every 43 days. Is the average smaller for college students? The data below shows the results of a survey of 13 college students asking them how many days elapse between haircuts. Assume that the distribution of the population is normal. 36, 42, 40, 45, 33, 31, 47, 47, 39, 41, 33, 48, 32 What can be concluded at the the α = 0.05 level of significance level of significance? For this study, we should use Select an answer The null and alternative hypotheses would be: H 0 : ? Select an answer H 1 : ? Select an answer The test statistic ? = (please show your answer to 3 decimal places.) The p-value = (Please show your answer to 3 decimal places.) The p-value is ? α Based on this, we should Select an answer the null hypothesis. Thus, the f conclusion is that ... The data suggest the population mean number of days between haircuts for college students is not significantly lower than 43 at α = 0.05, so there is insufficient evidence to conclude that the population mean number of days between haircuts for college students is lower than 43. The data suggest the population mean is not significantly lower than 43 at α = 0.05, so there is sufficient evidence to conclude that the population mean number of days between haircuts for college students is equal to 43. The data suggest the populaton mean is significantly lower than 43 at α = 0.05, so there is sufficient evidence to conclude that the population mean number of days between haircuts for college students is lower than 43.
The data suggest that the population mean is not significantly different from 43 at α = 0.05.
To determine whether the average number of days between haircuts for college students is smaller than the average for the average American (43 days), we can conduct a one-sample t-test. Here are the steps and results:
Step 1: Formulate the null and alternative hypotheses:
Null hypothesis (H0): The population mean number of days between haircuts for college students is equal to 43.
Alternative hypothesis (H1): The population mean number of days between haircuts for college students is smaller than 43.
Step 2: Calculate the test statistic:
We can calculate the test statistic using the formula:
t = (x- μ) / (s / √n)
where x is the sample mean, μ is the hypothesised population mean (43), s is the sample standard deviation, and n is the sample size.
Using the given data, the sample mean x is calculated to be 39.923, the sample standard deviation s is 6.106, and the sample size n is 13.
Substituting these values into the formula, we get:
t = (39.923 - 43) / (6.106 / √13) = -0.808
Step 3: Calculate the p-value:
The p-value represents the probability of obtaining a test statistic as extreme as the observed value (or more extreme) if the null hypothesis is true. We can use the t-distribution to calculate the p-value.
Using a t-table or a statistical software, we find that the p-value for t = -0.808 with 12 degrees of freedom is approximately 0.438.
Step 4: Make a decision:
Comparing the p-value (0.438) to the significance level α (0.05), we find that the p-value is greater than α.
Therefore, we fail to reject the null hypothesis.
Based on the results, we conclude that there is insufficient evidence to conclude that the population mean number of days between haircuts for college students is lower than 43. The data suggest that the population mean is not significantly different from 43 at α = 0.05.
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question number 7 and 8 only.
Please Answer!! Will give brainly!!
Answer:
480 - 12.25d = 50
To find the area, multiply the area of the entire circle by __?
What number goes in the box.
Answer:
3.142 × 6 = 18.852, thats : 19cm, then multiply 19 by 6 , so 19 would go in the square.
because area of a circle is p × r sq. u multiply one of the 6 by 3.142, you get 19, then multiply that 19 by the other 6. the answer is approximately 113.112.
Determine at which points f(z) = Reſiz) is differentiable by using the limit definition of the derivative
Main answer: f(z) = Reſiz is differentiable at every point of the complex plane where partial derivative with respect to x exists and the Cauchy-Riemann equations are satisfied.
Supporting answer: Given f(z) = ReſizLet z = x + iy∴ f(z) = Re(x + iy)z = x - iyi.e. x = ½ (z + z¯)and y = -½i(z - z¯)Hence f(z) = ½ (z + z¯ ) Differentiating f(z) partially with respect to x, we get,fx = ∂(x + y)/∂x = 1And differentiating f(z) partially with respect to y, we get,fy = ∂(x + y)/∂y = 1Now, for f(z) to be differentiable, it is necessary thatfx = uxx + ivxxandfy = uyx + ivyxwhere u = Re (f(z)) and v = Im(f(z))i.e. uxx = vyyanduyx = -vxy These equations are known as the Cauchy-Riemann equations. On substituting, we get uxx = vyy∴ 1 = 0which is not true. Hence f(z) is not differentiable when partial derivative with respect to y exists. So f(z) is differentiable at every point of the complex plane where partial derivative with respect to x exists and the Cauchy-Riemann equations are satisfied.
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In 2019, selected automobiles had an average cost of $14,000.
The average cost of those same automobiles is now $17,360. What was
the rate of increase for these automobiles between the two time
period
The rate of increase for the selected automobiles between 2019 and the present time is 24%. The average cost of the selected automobiles increased from $14,000 in 2019 to $17,360 at present.
To calculate the rate of increase, we can use the formula: rate of increase = (new value - old value) / old value * 100%. Substituting the values into the formula, we get (17,360 - 14,000) / 14,000 * 100% = 3,360 / 14,000 * 100% = 0.24 * 100% = 24%. Therefore, the rate of increase for these automobiles over the given time period is 24%.
In summary, the selected automobiles experienced a rate of increase of 24% between 2019 and the present time. This means that, on average, the cost of these automobiles increased by 24% over the specified period.
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Which equation represents a circle with a center at -3, -5) and a radius of 6 units?
O (x - 3)2 + (-5)2 = 6
0 (x - 3)2 + (-5)2 = 36
O (x + 3)2 + (y + 5)2 = 6
(x + 3)2 + (y + 5)2 = 36
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Answer:
(x+3)²+(y+5)² = 36
Step-by-step explanation:
The general equation of a circle is expressed as;
(x-a)²+(y-b)² = r² where;
(a, b) is the centre of the circle
r is the radius of the circle
Given
Centre (-3, -5)
a = -3 and b = -5
radius r = 6units
Substitute
(x-a)²+(y-b)² = r²
(x-(-3))²+(y-(-5))² = 6²
(x+3)²+(y+5)² = 36
hence the required equation is (x+3)²+(y+5)² = 36
The equation of a circle that represents a circle with a center at (-3, -5) and a radius of 6 unit is (x + 3)² + (y + 5)² = 36
Equation of a circleThe general equation of a circle is expressed as follows:
(x-a)²+(y-b)² = r²
where
r = radius of the circlea and b are the centre of the circleTherefore,
a = -3
b = -5
r = 6
Hence,
(x - (-3))² + (y - (-5))² = 6²
(x + 3)² + (y + 5)² = 36
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waht is the answer for this? −35−85+5−25
PEMDAS
-140
-35-85=-120
-120+5-25
-120+5=-115
=-115-25
-115-25=-140
-140
question 9 of 10 explain how you can determine the sign of the sum of two integers if one integer is positive and the other integer is negative.
To determine the sign of the sum of two integers when one integer is positive and the other is negative, we can follow a simple rule based on their magnitudes.
If the magnitude of the positive integer is greater than the magnitude of the negative integer, the sum will be positive. This is because the positive integer outweighs the negative integer, resulting in a positive value.
On the other hand, if the magnitude of the negative integer is greater than the magnitude of the positive integer, the sum will be negative. In this case, the negative integer dominates and determines the sign of the sum.
In both scenarios, the sign of the larger magnitude integer takes precedence and determines the sign of the sum. It is important to note that the sum will always have the sign of the integer with the larger magnitude, regardless of the specific values of the integers involved.
By considering the magnitudes of the integers, we can easily determine the sign of their sum when one integer is positive and the other is negative.
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A total of 397 tickets were sold for the school play. They were either adult tickets or student tickets. There were 53 fewer student tickets sold than adult tickets. How many adult tickets were sold?
A population of 60 foxes in a wildfire preserve doubles in size every 12 years. The function y = 60*2^x, where x is the number of 12-year periods, models the population growth. How many foxes will there be after 24 years?
You measure 47 watermelons' weights, and find they have a mean weight of 33 ounces. Assume the population standard deviation is 7.7 ounces. Based on this, construct a 90% confidence interval for the true population mean watermelon weight. Give your answer as m (round to 2 decimal places) + ounces You measure 21 turtles' weights, and find they have a mean weight of 56 ounces. Assume the population standard deviation is 2.9 ounces. Based on this, construct a 99% confidence interval for the true population mean turtle weight. Enter your answer as #Im.Give your answers as decimals, to two places + ounces You measure 34 textbooks' weights, and find they have a mean weight of 62 ounces. Assume the population standard deviation is 9.4 ounces. Based on this, construct a 99% confidence interval for the true population mean textbook weight. Give your answers as decimals, to two places Out of 200 people sampled, 104 had kids. Based on this, construct a 99% confidence interval for the true population proportion of people with kids. Enter your answer as p m Give your answers as decimals, to three places. + Out of 300 people sampled, 189 had kids. Based on this, construct a 99% confidence interval for the true population proportion of people with kids. Give your answers as decimals, to three places
a. The 90% confidence interval for the true population mean watermelon weight is 30.41 to 35.59 ounces.
b. The 99% confidence interval for the true population mean turtle weight is 54.56 to 57.44 ounces.
c. The 99% confidence interval for the true population mean textbook weight is 56.884 to 67.116 ounces.
d. The 99% confidence interval for the true population proportion of people with kids is 0.464 to 0.576.
e. The 99% confidence interval for the true population proportion of people with kids is 0.585 to 0.675.
a. For the watermelon weights:
Sample mean (m) = 33 ounces
Population standard deviation (σ) = 7.7 ounces
Sample size (n) = 47
Confidence level = 90%
To construct the confidence interval, we can use the formula:
Confidence Interval = m ± Z * (σ/√n)
Where Z is the z-score corresponding to the desired confidence level. For a 90% confidence level, Z = 1.645 (obtained from the standard normal distribution table).
Confidence Interval = 33 ± 1.645 * (7.7/√47)
Confidence Interval ≈ 33 ± 2.586
Confidence Interval ≈ (30.41, 35.59) ounces
The 90% confidence interval for the true population mean watermelon weight is 30.41 to 35.59 ounces.
b. For the turtle weights:
Sample mean (m) = 56 ounces
Population standard deviation (σ) = 2.9 ounces
Sample size (n) = 21
Confidence level = 99%
Using the same formula as above and considering a 99% confidence level, the z-score is Z = 2.576.
Confidence Interval = 56 ± 2.576 * (2.9/√21)
Confidence Interval ≈ 56 ± 1.438
Confidence Interval ≈ (54.56, 57.44) ounces
The 99% confidence interval for the true population mean turtle weight is 54.56 to 57.44 ounces.
c. For the textbook weights:
Sample mean (m) = 62 ounces
Population standard deviation (σ) = 9.4 ounces
Sample size (n) = 34
Confidence level = 99%
Using the same formula as above and considering a 99% confidence level, the z-score is Z = 2.576.
Confidence Interval = 62 ± 2.576 * (9.4/√34)
Confidence Interval ≈ 62 ± 5.116
Confidence Interval ≈ (56.884, 67.116) ounces
The 99% confidence interval for the true population mean textbook weight is 56.884 to 67.116 ounces.
d. For the proportion of people with kids:
Number of people with kids (p) = 104
Sample size (n) = 200
Confidence level = 99%
To construct the confidence interval for a proportion, we can use the formula:
Confidence Interval = p ± Z * √[(p(1-p))/n]
Using the z-score corresponding to a 99% confidence level (Z = 2.576), we can calculate the confidence interval.
Confidence Interval = 104/200 ± 2.576 * √[(104/200)(1 - 104/200)/200]
Confidence Interval ≈ 0.52 ± 0.056
Confidence Interval ≈ (0.464, 0.576)
The 99% confidence interval for the true population proportion of people with kids is 0.464 to 0.576.
e. For the proportion of people with kids:
Number of people with kids (p) = 189
Sample size (n) = 300
Confidence level = 99%
Using the same formula as above and considering a 99% confidence level, the z-score is Z = 2.576.
Confidence Interval = 189/300 ± 2.576 * √[(189/300)(1 - 189/300)/300]
Confidence Interval ≈ 0.63 ± 0.045
Confidence Interval ≈ (0.585, 0.675)
The 99% confidence interval for the true population proportion of people with kids is 0.585 to 0.675.
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Function B has a greater rate of change and a smaller y-intercept than function A. Which equation could represent function B?
Answer:
function A : y = 50 + 0.5x ; y = 40 + 0.6x
Step-by-step explanation:
Function is a relationship between values in set x & set y.
In case functional relationship equation is y = c + sx . c is the y intercept ie constant value of y when x = 0, & s is slope rate of change ie = change in y / change in x.
If function A is y = 50 + 0.5x. Intercept (c) = 50 , change rate (slope) = 0.5
If function B is y = 40 + 0.6x. Intercept (c) = 40 ie lesser, change rate (slope) = 0.6 ie greater
ANOTHERRR >: D
THANKS FOR ALL THE PEOPLE HELPINGG < 3
Answer: it C trust me it right & can you please mark me Brainliest
Step-by-step explanation: Hope this help :D
☁️ Answer ☁️
C, x < 4.
2/x −3< − 1
Multiply both sides of the equation by 2.
x−6< −2 (negative 2)
Add 6 to both sides.
x < (negative 2) −2 + 6
Add −2 and 6 to get 4.
x < 4
Hope it helps.
Have a nice day noona/hyung.
what is this please? i'll give u brainliest
Answer:
i dont know i just want points
Step-by-step explanation:
>;)
You Got to Leon and mango house and you decide to eat them, You Eat Mango 328 Times And You eat Leon 338 Times. How many times did you eat my friends leon and mango today? Dana Says That 60 Times And I Say That 666 Times.... Say Your answer Down below
A. 60 Times
B. 11 Times
C. 100 Times
D. 666 Times
PLEASE HOW YOUR WORK!
Answer:
The answer for the question is 666
Step-by-step explanation:
328+338=666
Answer:
666
Step-by-step explanation:
328+338=666
i ate ur friends 666 times
convert 53 m = cm
help pls
Suppose x’s represent solutions and y’s represent problems. S(x, y) means "x is a solution for problem y". Explain, in English, what each of these statements is saying. They do not mean the same thing.
1. ∃x∀yS(x, y)
2. ∀y∃xS(x, y)
The first statement focuses on the existence of a single solution that works for all problems, while the second statement emphasizes that for each problem, there is at least one solution available, without specifying whether it is the same solution for all problems.
1) ∃x∀yS(x, y):
This statement means "There exists at least one solution that works for all problems." In other words, there is a specific value of x that can be applied to every problem y, resulting in a solution.
2) ∀y∃xS(x, y):
This statement means "For every problem, there exists at least one solution." In other words, for any given problem y, there is at least one value of x that can be applied to it to find a solution.
The main distinction between these two statements lies in the order of quantifiers (∃ and ∀). In the first statement, the existential quantifier (∃x) appears before the universal quantifier (∀y), indicating that there is a single solution that can be applied to all problems.
In the second statement, the universal quantifier (∀y) appears before the existential quantifier (∃x), indicating that for each problem, there is at least one solution that exists.
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What is the equation of the following line please help
Answer:
C
Step-by-step explanation:
Bob a builder has come to you to build a program for his construction business. He needs to determine the square footage of a room in order to buy materials and calculate costs. Bob charges $425 per square metre. The program is going to ask the user to enter the name of a room. It will then ask for the width and length of the room (in meters) to be built. The program will calculate the room area and use this information to generate an approximate cost. Your program will display the room, the total area and the approximate cost to the screen. Using Pseudocode, develop an algorithm for this problem.
Answer : The below pseudocode will calculate the cost by multiplying the area with 425. The output will be the room name, area of the room, and approximate cost to construct the room in dollars.
Explanation:
Given:Bob charges $425 per square metre.To develop an algorithm to calculate the area of the room and the approximate cost.
Pseudocode:
Step 1: Start Step 2: Declare variables : room Name of string type,Width of float type,Length of float type,Cost of float type
Step 3: Display "Enter the name of the room:" Step 4: Read the room Name Step 5: Display "Enter the width of the room (in meters):" Step 6: Read the Width Step 7: Display "Enter the length of the room (in meters):" Step 8: Read the Length Step 9: Calculate the area of the room as Area = Width * Length Step 10: Calculate the cost of the room as Cost = Area * 425 Step 11: Display "Room Name:", roomName Step 12: Display "Area of the Room (in square metres):", Area Step 13: Display "Approximate Cost of Construction:", Cost Step 14: Stop
The program will take the input as the name of the room, width, and length of the room, and then it will calculate the area of the room by multiplying width and length. Then it will calculate the cost by multiplying the area with 425. The output will be the room name, area of the room, and approximate cost to construct the room in dollars.
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Lavonne estimated 38% of 63 by rounding 38% up to 40%, rounding 63 up to 70, and then multiplying 70 by 0.4 to get 28. Is her estimate reasonable?
a. Yes, her estimate is reasonable.
b. No, her estimate is too high.
c. No, her estimate is too low.
d. It is impossible to determine without more information.
No, her estimate is too high.
Given,
Lavonne estimated 38% of 63 by rounding 38% up to 40%, rounding 63 up to 70, and then multiplying 70 by 0.4 to get 28 .
Now
Firstly calculate the actual answer:
38% of 63
= 38/100 * 63
= 23.94
Now
The approximated portion :
40% of 70
= 0.4 *70
= 28
Hence the answer should be around 24 but after approximation it is coming 28 .
Thus the estimate made by Lavonne is high .
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the diagram shows a triangle.
2s
40°
2s
What is the value of s?
Answer:
s would be 20
Step-by-step explanation:
because 2 x 10 = 20 so you then would add the second 20 to the first 20 and get 40
what is the absolute value of -l8|
Answer:
-8 i think
Hope you get it right
Answer:
the absolute value of -l8| is 8
Step-by-step explanation:
Absolute value means the opposite
The scatter plot shows the relationship between annual salary and years of experience. What is the range of the cluster shown in the scatter plot?
A) 1 to 15 years of experience
B) 8 to 12 years of experience
C) $10,000 to $90,000 annual salary
D) $40,000 to $60,000 annual salary
Answer: 8 to 12 years
Step-by-step explanation: A cluster is formed when several data points lie in a small interval. The domain of the cluster is the set of x-coordinates.
The range of the cluster in the scatter plot is between $40,000 and $60,000 when the data points are heavily clustered between the years 8 to 12.
What is scatter plot?Scatter plots are used to observe and plot relationships between two numeric variables graphically with the help of dots. The dots in a scatter plot shows the values of individual data points.
Given that, on scatter plot
Years of experience is represented at x-axis
Annual Salary is represented at y-axis
From the scatter plot, it is clear that from the x-axis the data points are tightly clustered between the years 8 to 12. As major portion of the data points lie between 8 to 12 years.
Similarly, from the y-axis the data points are tightly clustered between between $40,000 and $60,000. As major portion of the data points lie between $40,000 and $60,000.
When the certain data points in a scatter plot make distinct groups, these groups are considered as clusters. Those data points normally appear to be converged around a particular value.
Therefore, the range of the cluster in the scatter plot is between $40,000 and $60,000 for the data points between the years 8 to 12.
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There are 20,502 seats in the stadium. If there are 19,624 people in attendance, what percent of the seats are filled?
Approximately 4.28% of the seats are filled in the stadium when there are 19,624 people in attendance. To determine the percentage of seats filled in the stadium, we need to calculate the ratio of the number of people in attendance to the total number of seats and then convert it to a percentage.
The number of seats filled can be found by subtracting the number of empty seats from the total number of seats. Using the given information:
Number of seats filled = Total number of seats - Number of empty seats
Number of seats filled = 20,502 - 19,624
Number of seats filled = 878
Now, we can calculate the percentage of seats filled by dividing the number of seats filled by the total number of seats and multiplying by 100:
Percentage of seats filled = (Number of seats filled / Total number of seats) * 100
Percentage of seats filled = (878 / 20,502) * 100
Percentage of seats filled ≈ 4.28%
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A circle has a radius of 15 cm. Find the diameter
Answer:
15 times 2 = 30
diameter = 30
Step-by-step explanation:
1. Find the coordinates of the center and the measure of the radius for a circle whose equation is
(x - 8) + (y + 4) = 12
Answer:
the center of this circle is (8, -4) and the radius is 2√3.
Step-by-step explanation:
Compare this equation
(x - 8) + (y + 4) = 12 Don't forget to type in the " ^ " symbol to indicate exponentiation.
(x - 8)^2 + (y + 4)^2 = 12
to the standard equation of a circle with center at (h, k) and radius r:
(x - h)^2 + (y - k)^2 = r^2
In this way we learn that h = 8, k = -4 and r^2 = 12 (or r = 2√3).
Then the center of this circle is (8, -4) and the radius is 2√3.