Calculus: 9-12-3². (a) Find and sketch the largest possible domain of (b) Sketch 3 typical level curves for f(x, y) = y - 2². 2. Calculus: Find the following limits if they exist, if they do not exist explain why. x² - y² (a) lim (z.y)-(0.2) I (b) lim (2.9) (0,0)
Answers
The domain of f(x,y) = y-2² is all real numbers except for x=2. The level curves of f(x,y) = y-2² are all lines of the form y = c, where c is a real number.
The limit of (x²-y²)/(x²+y²) as (x,y) approaches (0,2) does not exist because the numerator approaches 0 while the denominator approaches 4. The limit of (x²-y²)/(x²+y²) as (x,y) approaches (0,0) does not exist because the function is not defined at (0,0).
The domain of f(x,y) = y-2² is all real numbers except for x=2 because the function is not defined at x=2. The level curves of f(x,y) = y-2² are all lines of the form y = c, where c is a real number, because the function is constant along these lines.
The limit of (x²-y²)/(x²+y²) as (x,y) approaches (0,2) does not exist because the numerator approaches 0 while the denominator approaches 4, which means that the function is not continuous at (0,2). The limit of (x²-y²)/(x²+y²) as (x,y) approaches (0,0) does not exist because the function is not defined at (0,0).
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Related Questions
pip rolls a fair dice 150 times. how many times would pip expect to roll an odd number?
Answers
Answer:
25
Step-by-step explanation:
Since each of the six possible outcomes is equally likely, you can expect to get each of the outcomes 150/6 = 25 times.
if this is wrong, let me know so I can fix it
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A contractor bought 7.6 to the power of 2 ft of sheet metal. she has used 2.3 to the power of 2 ft so far and has $159 worth of sheet metal remaining. The equation 7.6x-2.3x=159 represents how much sheet metal is remaining and the cost of the remaining amount. How much does sheet metal cost per square foot?
what does the sheet metal cost per foot?
Answers
Answer:
Step-by-step explanation:
he bought 7.6 ft2 of sheet metal He used 2.3 ft2 7.6x−2.3x= $95.40 simplify 5.3x = $95.40 divide by 5.3 to get x by itself x = 18 so each sheet of metal costs $18.00 per square foot.
If the median house price in your area is $350,000, and the 30 -year mortgage rate is %5, how expensive of a house can you afford if you have a downpayment of $15,000. Assume you make $90,000 a year.
Answers
With a down payment of $15,000, an annual income of $90,000, and a 30-year mortgage rate of 5%, you should be able to afford a house with a median price of $350,000 in your area.
To determine how expensive of a house you can afford, we need to consider several factors, including your income, down payment, mortgage rate, and the median house price.
First, let's calculate the loan amount. Subtracting your down payment of $15,000 from the median house price of $350,000 gives us a loan amount of $335,000.
Next, we need to calculate your monthly mortgage payment. To do this, we will use the 30-year mortgage rate of 5%. Converting this annual rate to a monthly rate, we get 0.05/12 = 0.0042.
Using an online mortgage calculator, we can determine that the monthly mortgage payment for a $335,000 loan at a 5% interest rate is approximately $1,794.
To determine how much you can afford, we need to consider your income. Assuming an annual income of $90,000, we can estimate your monthly income by dividing it by 12, which gives us $7,500.
As a general rule, lenders typically recommend that your monthly mortgage payment should not exceed 28% of your monthly income. In your case, 28% of $7,500 is $2,100.
Since your estimated monthly mortgage payment of $1,794 is below $2,100, you should be able to afford a house with a median price of $350,000, given your income, down payment, and mortgage rate.
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Is this function linear or nonlinear? Why?
X^4+x^2=y
Is this function linear or nonlinear? Why?
2x+3y-x-y=4
Is this function linear or nonlinear? Why?
X=y=45
Is this function linear or nonlinear? Why?
Y=5x-10
Is this function linear or nonlinear? Why?
Y=56
Is this function linear or nonlinear? Why?
X^2+y=45
Is this function linear or nonlinear? Why?
Y=3x^5+4x^3
Is this function linear or nonlinear? Why?
Y=3x^5+4x^3
Is this function linear or nonlinear? Why?
Y=\|~11x+3
Answers
Answer:
1: No, x is raised to a power
2: Yes, can be solved in the form of y = mx + b
3: If this is supposed to be x + y = 45, then yes because it can be solved in the form of y = mx + b
4: Yes, it is in the form of y = mx + b
5: Yes, it is in the form of y = mx +b, it has a slope of zero and will be a horizontal line, which will pass the vertical line test
6: No, x is raised to a power.
7: No, x is raised to a power.
8: No, x is raised to a power
9: Is that supposed to be pi? If so, yes, it is in the form of y = mx + b
Step-by-step explanation:
acplete the pairs.Match each rational expression to its simplest form.2m2 - 4m21m - 2)m2 - 2m + 1m - 1m2 - 3m + 2m2 - mm2 - m - 2m2 - 1m-n>m-1>m->22m>
Answers
To rationalize the expression, we have to find common terms between numerators and denominators and then simplify:
\(\frac{2m^2-4m}{2\cdot\left(m-2\right)}=\frac{2m\cdot(m-2)}{2\cdot(m-2)}\)\(=\frac{2}{2}\cdot m\cdot\frac{(m-2)}{(m-2)}=\frac{1}{1}\cdot m\cdot\frac{1}{1}=m\)To simplify the numerator of the second expression we have to remember that:
\(x^2-2ax+a^2=(x-a)^2\)Then, the expression would be simplified as:
\(\frac{m^2-2m+1}{m-1}=\frac{(m-1)^2}{m-1}\)\(=\frac{(m-1)^2}{m-1}=(m-1)\cdot\frac{m-1}{m-1}=(m-1)\cdot1=m-1\)For the third expression, when factorizing we have to find two numbers that when added equals -3 and when multiplied equals +2, meaning:
\(x^2+(a+b)x+a\cdot b=(x+a)\cdot(x+b)\)Then, the factorization of the numerator of the third expression is:
\(\frac{m^2-3m+2}{m^2-m}=\frac{(m-1)(m-2)}{m(m-1)}\)\(=\frac{(m-1)}{(m-1)}\cdot\frac{(m-2)}{m}=1\cdot\frac{(m-2)}{m}=\frac{m-2}{m}\)Finally, to simplify the numerator of the last expression we will use the same factorization as in the third one. And for the denominator we have to use the following:
\((x^2-a^2)=(x-1)(x+1)\)\(\frac{m^2-m-2}{m^2-1}=\frac{(m+1)(m-2)}{(m_{}+1)(m-1)}\)\(=\frac{(m+1)}{(m_{}+1)}\cdot\frac{(m-2)}{(m-1)}=1\cdot\frac{(m-2)}{(m-1)}=\frac{m-2}{m-1}\)Answer:
\(\frac{m-2}{m}=\frac{m^2-3m+2}{m^2-m}\)\(m-1=\frac{m^2-2m+1}{m-1}\)\(\frac{m-2}{m-1}=\frac{m^2-m-2}{m^2-1}\)\(m=\frac{2m^2-4m}{2\cdot(m-2)}\)Use the data set below to determine measurements of central tendency.
(45, 65, 30, 50, 20, 30)
mean = 50, median = 40, no mode
mean = 45, median = 50, mode = 30
mean = 40, median = 37.5, mode = 30
Answers
PLS ANSWER QUICKLY What is the best approximation of the solution to the system to the nearest integer values? (7, 0) (0, 6) (7, 1) (1, 7)
Answers
Answer:
0 = 0 = 0 = 0 = 0 < 1 < 6 < 7
0 is equal to 0 is equal to 0 is equal to 0 is equal to 0 is less than 1 is less than 6 is less than 7
0/
1
= 0/
1
= 0/
1
= 0/
1
= 0/
1
< 1/
1
< 6/
1
< 7/
1
Step-by-step explanation:
Answer:
the correct answer is (1, 7)
Step-by-step explanation:
Please help.
Simplicity
Answers
Answer: -10x+38
Step-by-step explanation:
Take your given equation
-2(3x-5)+4(7-x)
Distribute the -2 and 4 into the parenthesis'
-6x+10+28-4x
Combine like terms
-10x+38
Use the distributive property of multiplication to find 7×32.
Hint: 32=2+30 please show your work :)
Answers
Answer:
224
Step-by-step explanation:
7 × 32 = 7 × (30 + 2) = 7 × 30 + 7 × 2 = 210 + 14 = 224
need help asap!! right answers please i can’t fail
Answers
Answer:
The answer is d
Step-by-step explanation:
Start with the y intercept and them go up two places over 1
a line with the slope of 3/4 contains the point (1.2). which plot also lies on the line?
A. (4,6)
B. (4,7)
C. (5,5)
D. (5.6)
Answers
Answer:
c or d
Step-by-step explanation:
2 = 3/4 + b, b = 1.25
Y = 3/4x + 1.25
Plug in the points and see
6 = 3 + 1.25, false
7 = 3 + 1.25, false
5 = 3.75 + 1.25, true
Solution: C. (5,5) is the answer
Brandie lives on the twelfth floor of her apartment building. She walks down 2 flights to visit a friend, then up 3 flights to
deliver a message to a neighbor. Which integer best represents the number of flights Brandie must walk to get back to
her starting point?
0-12
O-1
05
7
Mark this and return
Save and Exit
Next
Submit
Answers
D/4 = answer?
D=8
Pls help
Answers
Answer:
2
8/4=2
I think this is pretty easy:
D/4=(answer)
8/4=2/1
2/1=2
Answer:
2
Step-by-step explanation:
So if D=8, 8/4
8 divided by 4 is 2
If cos x = -2/5, what is the value of cos 2x?
Answers
The value of cos 2x = -21/25.
Given:
cos x = -2/5
we know that,
cos 2x = \(2cos^{2}x -1\)
= 1(\((-2/5)^{2}\) - 1
= 1\((2/5)^{2}\) - 1
= 1*4/25 - 1
= 4/25 - 1
= 4 - 25 / 25
= -21/25.
Therefore the value of cos 2x = -21/25.
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A student investigating study habits asks a simple random sample of 16 student at her school how many minutes they spent on their English homework the previous night. Suppose the actual parameter values for this variable are mu = 45 minutes and sigma = 15 minutes. Which of the following best describes what we know about the sampling distribution of means for the student's sample? O mu x = 45; sigma x unknown; shape of distribution unknown O mu x = 45; sigma x = 15; distribution approximately Normal O mu x = 45; sigma x = 15; shape of distribution unknown O mu x = 45; sigma x = 3.75; distribution approximately Normal O mu x = 45; sigma x = 3.75; shape of distribution unknown
Answers
The best description about the sampling distribution of means for the student's sample is mu x = 45, sigma x = 3.75, shape of distribution unknown.
What is Sampling Distribution?Sampling distribution is defined as the probability distribution of a statistical measure which is got by the repeated sampling of a specific population.
Given that,
μ = 45 minutes and σ = 15 minutes
Sampling distribution of means for the student's sample is :
μₓ = μ = 45
σₓ = σ / √n, where n is the sample size.
σₓ = 15 / √(16) = 15 / 4 = 3.75
Now since the sample size 16 which is less than 30, shape of the distribution is unknown.
Hence the sampling distribution is, μₓ = 45, σₓ = 3.75, and the shape of distribution is unknown.
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Solve for z.
-z/5 - 37 = -18
Answers
Answer:
z = -95
explanation:
Monica sells lemonade over the summer and uses Conical paper cups to serve the lemonade. Each cup is 8 cm in diameter and 11 cm tall. She starts with a 10 gallon container (1 gallon is equivalent to 3085 cm)
Part A: Determine how many paper cups or needed to empty the entire 10 gallon cooler.
Part B: If the conical cups are solid and packages of 50. How many packages are needed to be bought?
Answers
Answer:
a) 167 cups
b) 4 packages
Step-by-step explanation:
Given:
Diameter, d = 8cm
Height, h = 11 cm
10 gallon container
Since 1 gallon = 3085cm, 10 gallons will be:
= 10 * 3085 = 30850 cm
a) Consider that the shape of the cup is a cone. To determine how many paper cups are needed to empty the entire 10 gallon cooler, let's first find the volume of the cone.
Formula for volume of a cone:
\( V = \frac{1}{3} \pi r^2 h\)
We know radius, r = d/2 = 8/2 = 4cm
Substituting figures in the formula, we have:
\( V = \frac{1}{3} \pi 4^2*11\)
V = 184.31 cm³
The number of paper cups are needed to empty the entire 10 gallon cooler would be:
\( = \frac{30850}{184.31} = 167.38 cups \)
Approximately 167 cups
b) if the cups are sold in packages of 50, the number of packages to be bought will be:
\( = \frac{167}{50} = 3.34 \)
Which is approximately 4 packages
I NEED HELP QUESTION IN PICTURE!!!!!!HAVE A NICE DAY
Answers
GIVE BRAINLY please tell if wrong
Number 8 please I don’t know anything
Answers
Answer:
A. Domain: 1,2 Range: 0,1,4
B. Domain: 0,2,4, Range: 1,2,3,
Step-by-step explanation:
Domain is the x axis
Range is the y axis
The angle by which AB turns clockwise about point B to coincide with BC is _ degrees. If from point B, a point E is drawn directly opposite point C so that B, E, and C are on the same straight line, the angle by which AB turns counterclockwise to coincide with BE is _ degrees.
Answers
The requried, to find the angle by which AB turns clockwise about point B to coincide with BC, we need to first identify points A, B, and C on a diagram.
What is the transformation of geometry over the coordinate plane?Transform the shapes on a coordinate plane by rotating, reflecting, or translating them. Felix Klein introduced transformational geometry, a fresh viewpoint on geometry, in the 19th century.
Here,
To find the angle by which AB turns clockwise about point B to coincide with BC, we need to first identify points A, B, and C on a diagram. Once we have done that, we can draw a line from B to C, and then compare the direction of AB to the direction of BC. The angle between these two lines will be the angle by which AB turns clockwise to coincide with BC.
Similarly, to find the angle by which AB turns counterclockwise to coincide with BE, we need to identify points A, B, C, and E on a diagram. Once we have done that, we can draw a line from B to E, and then compare the direction of AB to the direction of BE. The angle between these two lines will be the angle by which AB turns counterclockwise to coincide with BE.
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what is the radius of a right circular cylinder with a volume of 12 in3 if it has a minimum surface area?
Answers
The value of radius of a right circular cylinder is 1,248 in for which the minimum surface area is obtained.
Define right circular cylinder?A cylinder with two circular bases and a line connecting their centers that is perpendicular to both bases.Volume of the right circular cylinder be;
v(c) = 12 in³ = π*r²*h
In which, h is the height of the cylinder,
Then , h = 12 / π*r²
Surface area of a right circular cylinder is:
S = area of base and top + lateral area
S(A) = 2*π*r² + 2*π*r*h ....eq 1
Put value of 'h' in equation (1)
S(r) = 2*π*r² + 2*π*r* ( 12 / π*r²)
S(r) = 2*π*r² + 24 /r
Differentiate both sides,
S´(r) = 4*π*r - 24 /r²
Put , S´(r) = 0 to get the critical points.
4*π*r - 24 /r² = 0
π*r - 6/r² = 0
π*r³ - 6 = 0
r³ = 1,91
r = 1,248 in
Check for the minimum surface area for r = 1,248 in.
Find the second derivative,
S´´(r) = 4*π + 48/r³
S´´(r) will always be positive.
Thus, the minimum surface area S is for r = 1,248 in.
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Mrs. Smith asked her students to write a situation that could describe the relationship between all of the values of x and y in the table.
X 0 1 2 3
Y 8 9 10 11
Which situation best describes the relationship between all the values of x and y in the table?
A. Danee had eight dance classes per week.
B. Yolanda had eight books and bought one new book each week.
C. Lincoln started with zero stamps in his collection for the first 8 months and then started to collect one stamp per month.
D. Gavin caught one fish in the first minute of fishing and eight fish each minute after.
Answers
The solution is Option B.
The equation of line is y = x + 8 , where the slope is m = 1
Yolanda had eight books and bought one new book each week
What is an Equation of a line?The equation of a line is expressed as y = mx + b where m is the slope and b is the y-intercept
And y - y₁ = m ( x - x₁ )
y = y-coordinate of second point
y₁ = y-coordinate of point one
m = slope
x = x-coordinate of second point
x₁ = x-coordinate of point one
The slope m = ( y₂ - y₁ ) / ( x₂ - x₁ )
Given data ,
Let the equation of line be represented as A
Now , the value of A is
Let the first point be P (
Let the second point be Q (
Now , the slope of the line is m = ( y₂ - y₁ ) / ( x₂ - x₁ )
Substituting the values in the equation , we getWhat is an Equation of a line?
The equation of a line is expressed as y = mx + b where m is the slope and b is the y-intercept
And y - y₁ = m ( x - x₁ )
y = y-coordinate of second point
y₁ = y-coordinate of point one
m = slope
x = x-coordinate of second point
x₁ = x-coordinate of point one
The slope m = ( y₂ - y₁ ) / ( x₂ - x₁ )
Given data ,
Let the equation of line be represented as A
Now , the value of A is
Let the first point be P ( 0 , 8 )
Let the second point be Q ( 1 , 9 )
Now , the slope of the line is m = ( y₂ - y₁ ) / ( x₂ - x₁ )
Substituting the values in the equation , we get
Slope m = ( 9 - 8 ) / ( 1 - 0 )
Slope m = 1
Now , the equation of line is y - y₁ = m ( x - x₁ )
Substituting the values in the equation , we get
y - 8 = 1 ( x - 0 )
On simplifying the equation , we get
y - 8 = x
Adding 8 on both sides of the equation , we get
y = x + 8
Hence , the equation of line is y = x + 8
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Answer: B
Step-by-step explanation:
I really need help on this
Answers
Answer:
Part A: \(\frac{3}{5}\)
Part B: \(\frac{1}{2}\)
Step-by-step explanation:
Pre-SolvingWe know that Alinn flipped a coin 20 times, and that 12 of those times resulted in heads. The other 8 times resulted in tails.
Part A wants us to find the experimental probability of the coin landing on heads. Experimental probability is the probability determined based on the experiments performed.
Part B wants us to find the theoretical probability of the coin landing on heads. Theoretical probability is determined based on the number of favorable outcomes over the number of possible outcomes.
Part A
Experimental probability is determined as # of times something occurred experimentally / total number of times.
Since 12 of the 20 times that Alinn flipped the coin resulted in heads, this means that the experimental probability of Alinn flipping heads is \(\frac{12}{20}\), which simplifies down to \(\frac{3}{5}\).
Part BTheoretical probability, as stated above, is the number of favorable outcomes / possible outcomes.
Our favorable outcome is flipping heads, and on a coin, there are two sides that a coin can land on: heads and tails. This means that there are two possible outcomes, and only one of them is favorable.
This means that our theoretical probability is \(\frac{1}{2}\).
At the Pineville County Fair popcorn stand, Vivian scoops popcorn from a large container to fill smaller bags to sell. As she fills the bags, the amount of popcorn in the container decreases. This situation can be modeled as a linear relationship.
Answers
The situation of popcorn scooping at Pineville County Fair can be modeled as a linear relationship.
A linear relationship is a type of relationship between two variables that can be represented by a straight line. In this case, the two variables are the amount of popcorn in the container and the number of bags filled. As Vivian scoops popcorn from the container, the amount of popcorn decreases, and the number of bags filled increases. This creates a linear relationship between the two variables.
To model this relationship, we can use the equation of a straight line, which is y = mx + b, where y represents the dependent variable (in this case, the number of bags filled), x represents the independent variable (the amount of popcorn in the container), m represents the slope of the line, and b represents the y-intercept.
In this situation, the slope represents the rate at which Vivian is filling bags with popcorn, and the y-intercept represents the initial number of bags filled when the container is full. By analyzing the data, we can estimate the slope and y-intercept and use the linear model to make predictions about the amount of popcorn remaining in the container and the number of bags that can still be filled.
Overall, the linear relationship provides a useful tool for understanding and managing the popcorn scooping process at the Pineville County Fair.
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Please answer this below Question # 15
Answers
Answer:
\(c. \: 5x - 2y = 10 \\ \: \: \: \: \: 10x - 4y = 20 \\ \)
Lisa is playing a video game in which she takes care of cats and dogs. She takes care of 4 cats for every 1 dog.
If Lisa takes care of 12 cats in the game, how many animals does she take care of altogether? these are ratios
Answers
Answer:
3 dogs per 12 cats
Step-by-step explanation:
4 cats :1 dog
4x3=12
1x3=3
3 dogs per 12 cats
Answer:
15 animals
Step-by-step explanation:
If for every 4 cats she has 1 dog then you would just do 12 divided by 4 which would give you 3 (that's how many dogs she took care of) you would then just have to add 12 and 3 to get 15.
Help lots of point + brainliest plz
write in slope intercept and standard form
Answers
Answer: 4
Step-by-step explanation:
What is the slope of the line represented by the equation -5x + 2y = 10?
0 - 12/201
O
O
O
25
52
Answers
The slope of the line represented by the equation -5x + 2y = 10 is slope = -5/2 and y intercept= -5
In order to answer the question, we must first simplify the given linear equation so that it may be expressed as a regular linear equation with slope and intercept. A linear equation's slope intercept form is y=mx+b , where "m" denotes the line's slope and "b" its y-intercept. The value of y = 0 must then be entered for the x-intercept, and the value of "x" must then be determined. We will obtain all necessary values in this manner.
By slope-intercept form equation of the line:
y=mx+b
The advantage of the equation in this form is that m and b can be derived 'easily'
Rearrange -5x-2y = 10 in this form.
-2y=5x+10
y=-5/2x+-10/2
y=-5/2x-5
slope = -5/2
y intercept= -5
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How is mathematical thinking established? How can we have mathematical thinking?
修改翻译结果
Answers
Translate How is mathematical thinking established? How can we have mathematical thinking? in to Chinese.
数学思维是如何建立的？ 怎样才能有数学思维？
00B0J0DD:
TIME REMAINING
57:39
The head of the math department compared the scores of students in two classes on the Chapter 2 test. He found that
the mean score of both classes was the same. He also found that there was greater variability in the scores of Ms.
Biren's students than in the scores of Mr. Hayes's students. Which quality of the data sets would lead the department*
head to that conclusion?
The median score i Ms. Biren's class is greater than the median score in Mr. Hayes's class.
The
median score in Ms. Biren's class is less than the median score in Mr. Hayes's class.
The range of scores in Ms. Biren's class is greater than the range of scores in Mr. Hayes's class.
The range of scores in Ms. Biren's class is
less than the range of scores in Mr. Hayes's class. The median score
Answers
Answer: B.
Explanation and reasoning: