Answer:
Step-by-step explanation:
To write the standard equation of a circle with its center in the fourth quadrant tangent to x=7, y=-4 and x=17, we can first find the center of the circle.
Since the center is in the fourth quadrant and tangent to x=7, y=-4 and x=17, the center must lie on the line x=12 (the midpoint between 7 and 17) and y=-4 (the point of tangency).
So the center of the circle is (12, -4).
Next, we need to find the radius of the circle. Since the circle is tangent to x=7 and x=17, the radius is the distance from the center to either x=7 or x=17.
The radius is thus 12 (the difference between 12 and 7) or 5 (the difference between 12 and 17).
So the standard equation of the circle is:
(x - 12)^2 + (y + 4)^2 = 25
Select all equations that have infinitely many solutions
Answer:
2 and 4
Step-by-step explanation:
1)
14x+6=2(5x+3)
14x+6=10x+6
No Solutions
2)
3(x-5)+6=x-(9-2x)
3x-9=3x-9
Infinitely Many
3)
2+5x-9=3x+2(x-7)
5x-7=5x-14
No Solutions
4)
3(4x-6)+2=-4(4-3x)
12x-16=12x-16
Infinitely Many
у
3
Solve for y.
27
31>
=
y
30
y
y = [? ] v
Enter answer
y^2 = 90
y = √90 = 3√10
that's it
The function h(t) = 4 + 64t – 16t2 models the height h, in feet, of a ball thrown in the air, after t seconds.
Part A
What is the vertex of the graph of the function, (t, h(t))?
(
,
)
Part B
What does the t-coordinate of the vertex represent?
A. the ball's maximum height
B. the time it takes for the ball to reach its maximum height
C. the time it takes for the ball to hit the ground
D. the height the ball was thrown from
Part C
What does the h(t)-coordinate of the vertex represent?
A. the ball's maximum height
B. the time it takes for the ball to reach its maximum height
C. the time it takes for the ball to hit the ground
D. the height the ball was thrown from
Part A) The vertex of the graph of the function, (t, h(t)) is (2, 68).
Part B) The t-coordinate of the vertex represent is the time it takes for the ball to reach its maximum height (option b)
Part C) The h(t)-coordinate of the vertex represent is the ball's maximum height (option a).
Part A asks for the vertex of the graph of the function, which is the point where the function reaches its maximum or minimum value. To find the vertex of a quadratic function like
=> h(t) = 4 + 64t – 16t²,
we can use the formula
=> t = -b/2a,
where a, b, and c are the coefficients of the quadratic equation ax² + bx + c and t is the input variable (in this case, the time).
The t-coordinate of the vertex is simply the value we get when we plug this formula into our equation.
So, for
=> h(t) = 4 + 64t – 16t²,
we have a = -16, b = 64, and c = 4.
Plugging these values into the formula
=> t = -b/2a,
we get
=> t = -64/(2*(-16)) = 2.
The t-coordinate of the vertex is therefore 2.
To find the h(t)-coordinate of the vertex, we can simply plug t = 2 into the function h(t) = 4 + 64t – 16t² and evaluate it.
This gives us
=> h(2) = 4 + 64(2) – 16(2²) = 68.
Therefore, the vertex of the graph of h(t) is (2, 68).
Part B asks what the t-coordinate of the vertex represents. We know that the t-coordinate is the time at which the ball reaches its maximum height.
Therefore, the correct answer is B: the time it takes for the ball to reach its maximum height.
Part C asks what the h(t)-coordinate of the vertex represents. We just found that the h(t)-coordinate of the vertex is the maximum height of the ball.
Therefore, the correct answer is A: the ball's maximum height.
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What kind of geometric transformation is shown in the line of music?
•
reflection
translation
glide reflection
Answer:
translation
hope this helps:) !!
Which scenario can be represented using the inequalities below?
1.25 < x < 1.5
A container of milk costs at least $1.25 but less than $1.50.
A student spends at least 1 hour 15 minutes, but no more than 1 hour 30 minutes on homework.
A tip added to a restaurant bill is less than or equal to 25% or less than or equal to 50%.
The point value of a test item is more than 1.25 points and less than 1.5 points.
The scenario that can be represented by the inequalities 1.25 < x < 1.5 is: A. A container of milk costs at least $1.25 but less than $1.50
How to Represent a Scenario Using Inequalities?The inequality 1.25 < x < 1.5 represents a range of values between 1.25 and 1.5, where x falls within that range.
Option A, which states that a container of milk costs at least $1.25 but less than $1.50, fits this range.
Option B, which states that a student spends at least 1 hour 15 minutes, but no more than 1 hour 30 minutes on homework, does not fit this range, as it represents a range of time values and not a range of numerical values.
Option C, which states that a tip added to a restaurant bill is less than or equal to 25% or less than or equal to 50%, does not fit this range either, as it represents two separate ranges of values.
Option D, which states that the point value of a test item is more than 1.25 points and less than 1.5 points, fits this range as well.
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Find the area of the regular polygons and degree of central angle when given either the apothem or side length.
The length of the apothem is 10. 99cm
How to determine the valuesTo determine the apothem of a polygon, we have to use the formula;
a = s/2 tan (180/n)
Such that the parameters are;
a is the length of the apothem.s is the side length of the polygonn is the number of sides of the polygonNow, substitute the values, we have;
a = 8/2tan(180/9)
divide the values
a = 8/2tan 20
Find the values
a = 8/0. 7279
Divide the values
a = 10. 99cm
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Madison tossed a paper cup and records wether it lands on its side. In 20 trails the cup lands on its side 19 times. In 90 trials the cup lands on its side 81 times
Answer:90% probability
Step-by-step explanation:
To calculate the experimental probability of the cup landing on its side, we can use the formula:
experimental probability = number of times the cup landed on its side / total number of trials
For the first set of trials, the experimental probability is:
experimental probability = 19/20 = 0.95
For the second set of trials, the experimental probability is:
experimental probability = 81/90 = 0.9
So the experimental probability of the cup landing on its side for the first set of trials is higher than for the second set of trials. However, since the number of trials is relatively small, it is possible that this difference is due to chance and does not reflect a real difference in the probability of the cup landing on its side. To determine this with more confidence, we would need to conduct more trials and perform statistical tests to determine whether the difference is statistically significant.
PLEASE HURRY
Let u = - 4i + 2j , v = 3i - j and w = - 6j
Find the specified scalar or vector
5u(3v - 4w)
The specified scalar or vector 5u(3v - 4w) is equal to -420i + 250j.
We can begin by distributing the scalar 5 to the vector 3v - 4w:
5u(3v - 4w) = 5u(3v) - 5u(4w)
Next, we can find the scalar multiples:
5u(3v) = 5(-4i + 2j)(3(3i - j)) = 5(-36i + 10j)
5u(4w) = 5(-4i + 2j)(4(-6j)) = 5(48i - 40j)
Now we can substitute these values back into the original expression:
5u(3v - 4w) = 5(-36i + 10j) - 5(48i - 40j)
Simplifying:
5u(3v - 4w) = -420i + 250j
Therefore, 5u(3v - 4w) = -420i + 250j.
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Harrold is a dog walker. He walks 13 different dogs for the same distance around Greenpoint Park everyday. The park is a perfect square in shape. Harrold takes each dog for 1 full lap around the park. In one day Harrold will walk 6, 396ft all together. What is the length of 1 side of the park in yards.
Answer:
123 feet/41 yards
Step-by-step explanation:
When solving problems like this, we need to understand and note down what we already know to make our lives easier.
- He walks 13 different dogs
- the park is a perfect square
- he takes each dog for one full lap
- That day, he walked 6396ft
- He takes each dog the same distance
Now, let's find the unit value (how much ft does he walk if he takes JUST ONE dog around Greenpoint Park?)
Just divide: 6396 / 13 = 492 ft
Meaning, that when Harrold takes JUST ONE dog around the park, which is a perfect square, he walks 492 feet.
One full lap around the square shaped park is just 4 sides of the square.
So, he walks 492 ft every 4 sides.
However, the question specifically asked for one side.
Just divide again to get your answer:
492 / 4 = 123 ft
Therfore, the length of one side of the park is 123 feet, which is 41 yards.
Saloni computed in a two-way table the relative frequencies of boys and girls participation in school sports at her school which statement best describes the relationship between the two variables
The statement that best describes the relationship between the two variables is "There is an association because the relative frequencies by column are different, and the relative frequencies by row are also different." (option a).
To understand the relationship between these two variables, we need to analyze the frequencies by row and by column. The rows represent one variable (in this case, gender), and the columns represent the other variable (participation in school sports).
If we look at the relative frequencies by row, we see that the percentage of girls participating in school sports is higher in the fall (63%) than in the spring (43%), while for boys, the opposite is true. This indicates an association between gender and participation in school sports, as the relative frequencies vary by row.
Alternatively, if we look at the relative frequencies by column, we see that the percentage of boys participating in school sports is higher in the spring (57%) than in the fall (37%), while for girls, the opposite is true. This also indicates an association between gender and participation in school sports, as the relative frequencies vary by column.
Therefore, we can conclude that the best statement to describe the relationship between the two variables is option A: "There is an association because the relative frequencies by column are different, and the relative frequencies by row are also different."
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Complete Question:
Siloni computed in a two-way table the relative frequencies of boys’ and girls’ participation in school sports at her school.
School Sports Participation by Gender Fall Spring
Boys 37% 57%
Girls 63% 43%
Which statement best describes the relationship between the two variables?
a) There is an association because the relative frequencies by column are different.
b) There is an association because the relative frequencies by row are different.
c) There is no association because the relative frequencies by column are different.
d) There is no association because the relative frequencies by row are different.
Which equation represents a line that passes through the point (−12, 6) and is perpendicular to the graph of the equation y = 34
x + 7?
A. y = 43
x + 18
B. y = 34
x + 15
C. y = −43
x − 10
D. y = −34
x − 3
Answer:
C
Step-by-step explanation:
If it is perpendicular to the line y = ¾x+7 then the gradient if the line must be the negative reciprocal of 3/4. The gradient must be - 4/3. So A, B and D are rejected. Left is C
Let's replace now.
For C,
Let's take y=-4/3x-10 into consideration at the point (-12,6)
Y should be equal to 6 when we replace x by -12
Let's try
Y = -4/3(-12) - 10 = 16 - 10 = 6
Yup. C is your answer.
La distancia entre Bay Town y Oak Glen es de 175 millas. Si la ecuación y = -x +175 representa la distancia que queda por recorrer hasta Oak Glen, ¿qué representa el dominio? ¿Qué es el dominio?
The correct answer is: D) distance traveled since leaving Bay Town; x ≥ 0
How to solveThe equation y = -x + 175 represents the distance left to travel to Oak Glen.
In this equation, x is the distance traveled since leaving Bay Town, and y is the distance left to reach Oak Glen.
The domain represents the possible values of x, which is the distance traveled since leaving Bay Town.
Since distance traveled cannot be negative, the domain is x ≥ 0. Therefore, the correct answer is:
D) distance traveled since leaving Bay Town; x ≥ 0
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The question in English is:
The distance between Bay Town and Oak Glen is 175 miles. If the equation y = -x +175 represents the distance to go to Oak Glen, what does the domain represent? What is the domain?
Simplify. Simplify. Express your answer as a single term, without a denominator.
pls helpppppp
Simplifying further, you can move any negative exponents to the denominator by changing their sign:
t⁻² u⁻⁶ v⁴ = v⁴ / (t² u⁶)
what is denominator ?
In a fraction, the denominator is the bottom number that represents the total number of equal parts into which the whole is divided. For example, in the fraction 3/4, the denominator is 4, which indicates that the whole has been divided into four equal parts.
In the given question,
When multiplying two terms with the same base, you can add their exponents, so:
t⁻¹ u v⁴* t⁻¹ u⁻⁷ v⁰ = t⁻² u⁻⁶ v⁴
Simplifying further, you can move any negative exponents to the denominator by changing their sign:
t⁻² u⁻⁶ v⁴ = v⁴ / (t² u⁶)
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You are asked to advise Alpha Tire Co. on the feasibility of offering a 35,000-mile warranty on their tires. At this time Alpha Tire believes the mean time to failure is 40,000 miles
µ
with standard deviation of miles to failure at 3700 or
. If a free replacement warranty is offered, promising that the tires will last for at least 35,000 miles, what proportion of tires would qualify for the free replacement because they are expected to fail while they were still covered by the warranty? In light of your finding, what advice would you give to Alpha Tires about a warranty for a free tire replacement if the tires fail before 35,000.
Where the above conditions exist, the probability is that about 41.19% of tires woudl be eligible for free replacement.
Why is this so ?Using a standard normal distribution table or calculator, we can find the z scores corresponding to 35,000 miles and 40,000 miles...
z 1 = ( 35,000 - 40,000) / 3,700 = -1.35
z 2 = (40,000 - 40,000) / 3,700 = 0
Then, we can find the area between these z scores, which represents the proportion of tires that would fail before 40,000 miles and qualify for a free replacement:
P( -1.35 < Z < 0) = 0.4119 or 41.19%
What it means is that , about 41.19% of the tires would qualify for a free replacement.
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Identify an equation in standard form for ellipse with its center at the origin, a vertex at (3, 0), and a focus at (1, 0). HELP ASAP! This is due in 15 minutes!!
Answer:
Step-by-step explanation:
The standard form equation for an ellipse with center at the origin is:
x^2/a^2 + y^2/b^2 = 1
where 'a' is the distance from the center to the vertices along the x-axis and 'b' is the distance from the center to the vertices along the y-axis.
In this case, the center is at the origin, and a vertex is at (3, 0). So, we know that 'a' = 3.
We also know that the distance from the center to the focus is 'c', and that:
c^2 = a^2 - b^2
Since the center is at the origin, 'c' is the distance from the focus (1, 0) to the origin, which is 1. So, we can solve for 'b' as:
c^2 = a^2 - b^2
1^2 = 3^2 - b^2
b^2 = 3^2 - 1^2
b^2 = 8
b = sqrt(8) = 2sqrt(2)
Substituting these values into the standard form equation, we get:
x^2/3^2 + y^2/(2sqrt(2))^2 = 1
Simplifying:
x^2/9 + y^2/8 = 1
So, the equation in standard form for the given ellipse is:
9x^2 + 8y^2 = 72
need answer for this +explanation
______________________________
A = L × B × H = 2 × 2 × 5= 20in²______________________________
an expression that is equivelent to 12x-3x
Answer:
it would be 9x
Step-by-step explanation:
because subtract 3 from 12 and leave the x
50 Points! Multiple choice algebra question. Which function represents exponential growth? Photo attached. Thank you!
The exponential growth model is represented by the function y = 10 · 3ˣ. (Correct choice: D)
What function is an exponential growth function?
In this problem we must determine what function does represent an exponential growth model. With this purpose, we must define and understand the following functions:
Exponential growth model
y = a · rˣ, for r > 1.
Exponential decay model
y = a · rˣ, for 0 < r < 1.
Polynomic model
y = ∑ cₙ · xⁿ
The function y = 10 · 3ˣ represents an exponential growth model.
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Question 7(Multiple Choice Worth 1 points)
(07.04 HC)
Right triangle ABC is located at A (-1, -2), B (-1, 1), and C (-5, 1) on a coordinate plan
O (x + 1)2 + (y + 2)² = 9
O (x + 5)² + (1)² = 16
O(x + 1)2 + (y + 2)² = 25
O(x + 5)² + (y-1)² = 25
Answer:
O (x + 1)2 + (y + 2)² = 9
Step-by-step explanation:
This is because the distance between points A and B is 3 units, and the distance between points B and C is 4 units, making the triangle a 3-4-5 right triangle. Point B is located at (-1, 1), which is 3 units away from point A (-1, -2) and 4 units away from point C (-5, 1). Therefore, the circle with center (-1, -2) and radius 3 would pass through point B, and its equation would be:
(x + 1)2 + (y + 2)² = 3²
(x + 1)2 + (y + 2)² = 9
26 less than twice a number is 4. Find each number
Answer:
15
Step-by-step explanation:
Let's call the number we try to find "[tex]x[/tex]"
In the problem, we know that "26 is less than twice a number" is the same as "4". So we can write this as an equation:
[tex]2x - 26 = 4[/tex]
Now we can solve for x by isolating it on one side of the equation.
First, we isolate "2x" by flipping "-26" to the other side, which will now be "26".
[tex]2x = 4 + 26[/tex]
Then we add
[tex]2x = 30[/tex]
finally, we isolate the x by dividing each side with 2
2x ÷ 2 = 30 ÷ 2
x = 15
The figure on the right is a scaled copy of the figure on the left
Which side in the figure on the right corresponds to segment UV?
What is the scale factor
The side that corresponds to uv is LK
The scale factor is 3 : 1
How to solve for the scale factorTo solve for the scale factor between two geometric figures, follow these steps:
Identify corresponding sides or corresponding lengths between the two figures.
Choose one pair of corresponding sides and write a proportion using the lengths of those sides.
Solve for the scale factor by simplifying the proportion.
The shape in UV occupies the space of 6 boxes
The space in LK is made of 2 boxes
Hence we have 6 : 2
= 3 : 1
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A group of 7 friends is planning a hike. Each friend will need of a gallon of water to drink during the hike. How many gallons of water will the group need for the hike?
Sketch the graph of the following function. Describe how
the graph can be obtained from the graph of the basic
exponential function ex.
f(x) = 2 (4-ex)
Use the graphing tool to graph the equation.
someone help pls, im not sure what to put in the little box for the vertical shift and vertical shrink
The vertical shift and vertical shrink of the exponential function are 2 and 1/2 respectively and the graph of the function is attached below
What is the graph of exponential function?A curve displaying an exponential function is known as an exponential graph. A curve with a horizontal asymptote and a rising or decreasing slope characterizes the graph of an exponential function. i.e., it begins as a horizontal line, grows or drops gradually, and then the growth or decay accelerates.
The vertical shift and vertical shrink of the function f(x) = 1/2(4 - eˣ) are 2 and 1/2
The vertical shift = 2
vertical shrink = 1/2
Kindly find the attached graph below
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Can anyone help with this part of my geometry notes ?
From the interior angle theorem:
m∠1 = ¹/₂(m∠AD + m∠BC)m∠2 = 180 - m∠1m∠AED = 77°m∠AEB = 103°m∠LK = 50°What is the interior angle theorem?The Interior Angle Theorem states that if two secants or chords intersect inside a circle, then the measure of the angle formed is equal to half the sum of the measures of the intercepted arcs.
Considering the given circles:
m∠AED = ¹/₂(45 + 109)
m∠AED = 77°
m∠AEB = 180 - 77
m∠AEB = 103°
m∠LK = (2 * 62) - 74)
m∠LK = 50°
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An annual depreciation rate is the percent that the value of an item decreases each year. A company purchases technology for $5,000. The company uses the function $r=1-\sqrt[3]{\frac{S}{5000}}$
to relate the annual depreciation rate $r$ (in decimal form) and the value $S$ (in dollars) of the technology after 3 years. Find $S$ when $r=0.15$ .
Please help if I don't finish this today my parents gonna take my phone away
Find the slope to solve the problem.
Sue drives 200 miles by 1:00 pm. She drives 350 miles by 4:00 pm if she continues at the same rate, how far will she drive by 5:00 pm?
To find the slope in this problem, we can use the formula for calculating slope, which is change in distance divided by change in time. In this case, the change in distance is 350 miles - 200 miles = 150 miles, and the change in time is 4:00 pm - 1:00 pm = 3 hours.
So, the slope (rate of driving) is 150 miles / 3 hours = 50 miles per hour.
Now, to find how far Sue will drive by 5:00 pm, we can use the slope and the additional time of 1 hour (from 4:00 pm to 5:00 pm).Distance driven by 5:00 pm = Slope * Time = 50 miles per hour * 1 hour = 50 miles.Therefore, Sue will drive an additional 50 miles by 5:00 pm, making her total distance driven by 5:00 pm 200 miles + 150 miles + 50 miles = 400 miles. So, Sue will drive 400 miles by 5:00 pm if she continues at the same rate. Note that in this problem, we are assuming that Sue maintains a constant speed throughout her drive. If her speed changes, the solution may be different.
Please help fast. Thanks! (:
The value of variable y from the system of vertical angles is equal to 125.
How to find the values of a variable associated with system of vertical anglesIn this problem we need to determine by algebra properties the value of a variable y from a system of two pairs of vertical angles. The system is represented by the following expression:
x + 20 = 3 · x - 50
2 · x = 70
x = 35
Then, by definition of supplementary angles:
(x + 20) + y = 180
55 + y = 180
y = 125
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Help me pleaseeeee :(
I'm taking linear algebra right now so this one hits home :)
Elementary Row Operations (EROs) are very important and not too difficult, so let's dive into the problem!
You're given the matrix below and asked to perform a single ERO to produce a matrix with a 1 at the position (1,1):
[tex]\begin{bmatrix}3 & 10 & 5\\2 & -1 & 1\end{bmatrix}[/tex]
Think of the two rows as separate entities in the matrix. Ultimately we want to have the index (1,1) currently holding the number 3 to become the number 1. To do this, logically you just need to subtract 2. Now, looking at the rows we have, a simple row operation is quite apparent.
Simply subtract row 2 from row 1, shown below:
[tex]\begin{bmatrix}3-2 & 10-(-1) & 5-1\\2 & -1 & 1\end{bmatrix}[/tex]
Now, simplify and you will have the answer:
[tex]\begin{bmatrix}1 & 11 & 4\\2 & -1 & 1\end{bmatrix}[/tex]
Notice that our matrix now has the required number 1 in row 1 and column 1, therefore, the matrix above is our answer! Let me know if you have any questions!
[tex]y=2cos^{2}(x) , y=2e^{-x}+2x-2[/tex]
(a) Write an equation whose solutions are the points of intersection of the graphs.
(b) Use the intersect feature of the graphing utility to find the points of intersection (to four decimal places). (Enter the point of intersection whose x-coordinate is within the interval [0, 2). If there is no solution, enter NO SOLUTION.)
a. The equation whose solutions are the points of intersection of the graphs is y = -0.14x + 0.80.
b. The points of intersection are (-0.827, 0.918) and (0.951, 0.675).
The solution has been obtained using the slope - intercept form.
What is the slope - intercept form?
When you are aware of the slope of the line being investigated and the given point is also the y intercept, use the slope intercept formula, y = mx + b. (0, b). The y value of the y intercept point is represented by the symbol b in the equation.
a. From the graph, we have two points of intersection.
Using this, we get the slope as;
m = -0.14
Now, using the slope intercept form, we get the intercept as
b = 0.80
So, the equation comes out to be
y = -0.14x + 0.80
b. The graph of the equations have been attached below.
From the graph, we get the points of intersection as (-0.827, 0.918) and (0.951, 0.675). Both the points have their x-coordinate within the interval [0, 2).
Hence, the required solutions have been obtained.
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find the extreme values of [tex]f(x,y) =x^{2} +y^2\\[/tex]
The function f(x,y) = x² + y² has a minimum value of 0 at the point (0,0) and has no maximum value.
What is a function?
A function is a relation between a set of inputs and a set of possible outputs, with the property that each input is related to exactly one output.
The function f(x,y) = x² + y² represents the sum of the squares of the variables x and y. To find the extreme values of this function, we need to take the partial derivatives with respect to x and y and set them equal to zero.
∂f/∂x = 2x = 0
∂f/∂y = 2y = 0
From these equations, we can see that the critical point occurs at (x,y) = (0,0).
To determine whether this is the maximum or minimum, we can use the second partial derivative test. The second partial derivatives are:
∂²f/∂x² = 2
∂²f/∂y² = 2
∂²f/∂x∂y = 0
At (0,0), ∂²f/∂x² > 0 and ∂²f/∂y² > 0, so the critical point is a minimum.
Therefore, the function f(x,y) = x² + y² has a minimum value of 0 at the point (0,0) and has no maximum value.
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