draw a contour map of the function f(x y)=ln(x^2+4y^2)
Answers
A level curve of the function f(x, y) is a curve that satisfies the equation f(x, y) = c, where c is a constant.
The diagram is attached at the end of the solution.
What is a contour map?A contour map, which is also called a topographic map, is a representation of a three-dimensional feature using contour lines on a plane surface.
The map shows a bird's-eye view and allows people to visualize the hills, valleys, and slopes that are being mapped.
People can see the hills, valleys, and slopes that are being mapped thanks to the map's bird's-eye perspective.
The title, scale, contour interval, legend, and whether latitude and longitude or Universal Transverse Mercator (UTM) coordinates are used are typically included.
Numerous activities, such as camping, urban planning, meteorology, and geologic investigations, can benefit from using this kind of map.
Consider the surface [tex]$f(x, y)=\ln \left(x^2+4 y^2\right)$[/tex].
The level curves for the surface are given by the equation, [tex]$k=\ln \left(x^2+4 y^2\right)$[/tex], where [tex]$k \in \mathbb{R}$[/tex]
Take k = . . . , -3, -2, -1, 0, 1, 2, 3, . . .
Then, draw the different level curves of the surface.
The diagram is attached at the end of the solution.
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Related Questions
Matei has 4 times as many stamps as arnav. If matei gives arnav 8 stamps, matei will have twice as many stamps as arnav. How many stamps does each boy have?.
Answers
Answer:
Step-by-step explanation:
big oily men like u
Answer:
M:48
A:12
Step-by-step explanation:
M=4A
M-8=(A+8)2
M=2A+24
4A=2A+24
2A=24
A=12
M=48
Find the volume of the largest right circular cone that can fit in a cube whose
edge (height) is 14cm.
Answers
The largest right circular cone that can fit within a cube has a volume of 718.67 cm3.
Explain about the circular cone?When a cone's axis is the line from the vertex to the circular base's midpoint, the cone is said to be right circular. In other words, a right angle is formed when the center of the circular base joins the cone's peak.
A three-dimensional form called an inverted frustum that resembles a conical cylinder. When the vertex of a cone is inverted after being sliced by a plane parallel to the shape's base, it is said to have this shape.
The formula r2+rl, where r is the radius of the circular base, h is the height of the cone, l is the slant height, and is an approximation, is used to determine the surface area of a cone as 3.14
Side of cube: 14 cm
Cube's radius is 14/2 cm, or 7 cm.
h=14cm for height
Volume'=1/3piR x 2hM =1/3 x 22 x 7 x 7 x7
= 718.67 cm3.
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show the work to prove that the series is convergent using one of the convergence series tests. b. what does the divergence test say and why does the divergence test fail for this series?
Answers
the work to prove that the series is convergent using one of the convergence series tests.the series a is convergent and series b is divergent.
a. The alternating series test can be used to prove that the series is convergent. The alternating series test states that if a series is of the form [tex]$a_1-a_2+a_3-a_4+\cdots$[/tex] and satisfies the conditions:
1. [tex]$a_n \geq 0$[/tex] for all n
2. [tex]$a_{n+1} \leq a_n$[/tex] for all n
3. [tex]$\lim_{n\to \infty} a_n = 0$[/tex]
Then the series is convergent.
In this case, the series is of the form [tex]$2-\frac{2}{2}+\frac{2}{3}-\frac{2}{4}+\cdots$[/tex] which satisfies all the conditions of the alternating series test.
Therefore, the series is convergent.
b. The divergence test states that if the limit of the sequence of partial sums is not finite, then the series is divergent. However, in this case, the limit of the sequence of partial sums is finite and thus the divergence test fails to prove that the series is divergent.
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Which inequality is represented by this graph?
Answers
The linear equality for the given graph is x > 0.
Option (B) is correct.
What is linear equality?
In mathematics, a linear inequality is an inequality that involves a linear function. A linear inequality contains one of the symbols of inequality. It shows the data which is not equal in graph form.
The hollow circle in the linear equality shows that the point should be excluded and the line is going towards the positive x-axis.
So we can prepare the linear equality as
x > 0
Hence, the linear equality for the given graph is x > 0.
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Find the value of this variable
A. 146 degree
B. 73 degree
C. 84 degree
D. 62 degree
Help!!!
Answers
Answer: B. 73 degree
Step-by-step explanation:
We know that a triangle has 180 degree
62 + 84 = 146 degree
180 - 146 = 34 degree
34 degrees is the angle inside the triangle. The inside angle must add with the outside angle = 180 degree
So the outside angle is
2x = 146
x = 73
Paul drives his delivery van 675 miles in 3 days. at this rate, how far will he drive in 15 days?
a. 45 miles
b. 225 miles
c. 2,025 miles
d. 3,375 miles
Answers
Therefore, the correct answer is 3,375 miles, or option (d) is the correct option.
To find out how far Paul will drive in 15 days, we need to determine his average distance per day and then multiply that number by 15. To find Paul's average distance per day, we can divide the total distance he drove in 3 days by the number of days:
675 miles / 3 days = 225 miles/day.
So Paul drives an average of 225 miles per day. If he continues to drive this same distance every day, he will drive 225 miles/day * 15 days = <<225*15=3375>>3,375 miles in 15 days.
Why does it have the name "average speed"?The total distance something has traveled is divided by the total amount of time it took to traverse that distance to arrive at its average speed. Speed is the current rate of movement of something. Average speed is the speed that a vehicle travels at on average over the course of a trip.
What does the term "average speed" mean?A moving object's average speed is calculated by dividing its total distance traveled by its entire travel time. Distance traveled divided by average speed Overall Time. Meter per second is the S.I. unit of speed. KPH, or kilometers per hour, is another unit of speed.
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Pls help with this I put in a photo
Answers
Step-by-step explanation:
to be a triangle the sum of any 2 sides must be larger than the third side.
so,
x + 10 > 18
x + 18 > 10
18 + 10 > x
the first inequality gives us
x > 8
the third inequality gives us
28 > x
the second inequality would give us
x > -8
but with the first inequality x > 8 we have already a stronger criteria than x > -8 (if x > 8 is true, then so is automatically x > -8, but not the other way around).
therefore x > 8 is the narrower criteria and answer.
so, we have in combination
8 < x < 28
Evaluating Expressions with Exponents
What is the value of the expression 3^3+6 x 3 ?
Answers
Answer:
here is the answer:
Step-by-step explanation:
the answer is 45
Answer:
45
Step-by-step explanation:
3^3+6x3First we multiply the 2 numbers3^3+18Second we multiply 3 into 3 times3x3x3+18
=45
Please help me respond this question
Answers
bc if you add 212+218 then you get 430 and divide that by 2
This data records the ages of people on a bus to the seaside.
2 4 25 31 3 23 24 26 37 42
60 76 33 24 25 18 20 77 5 13
18 13 15 49 70 48 27 25 24 29
Find the median age, making your method clear.
Answers
Answer:
The median is 25
Step-by-step explanation:
I counted the numbers and it was 30 I divided it to 2
Choose the equation of a line parallel to the given equation and passing through a point P. -3x - y= -4 ; P = (1,4)
A.) Y = 1/3x + 7
B.) Y = -3x + 7
C.) Y = -3x +5
D.) Y = 1/3x -3
Answers
The equation of a line parallel to -3x - y= -4 and passing through a point (1,4) is y = -3x + 7.
How to find the equation of a line?The equation of a line can be represented in slope intercept form as follows:
y = mx + b
where
m = slopeb = y-interceptTherefore, the line is parallel to -3x - y = -4 and it passes through (1, 4).
Parallel lines have the same slope.
Hence,
-3x - y = -4
y = -3x + 4
The slope of the line is -3.
Let's find y-intercept using (1, 4)
y = -3x + b
4 = -3(1) + b
4 + 3 = b
b = 7
Therefore, the equation of the line is y = -3x + 7.
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approximate fy(1,3) using the contour diagram of f(x,y) shown below.
Answers
The approximation of [tex]& f_y(x, y)[/tex] using the contour diagram of f(x, y) is 0.7.
As per the given data we have determine the value of approximation of [tex]& f_y(x, y)[/tex] using the contour diagram of f(x, y).
A contour or a contour line may be defined as the line of intersection of a level surface with the surface of ground.
This means every point on a contour line has the same altitude as that of the assumed intersecting surface.
The set of the curves f(x, y)=c
By definition,
[tex]& f_y(x, y)=\lim _{h \rightarrow 0} \frac{f(x, y+h)-f(x, y)}{h} \\[/tex]
At (x, y) = (1,3),
[tex]& f_y(1,3)=\lim _{h \rightarrow 0} \frac{f(1,3+h)-f(1,3)}{h}[/tex]
From the graph, observe that the value of f at (1, 5.7) is 16 and at (1, 3) is 14. Where approximate is considered as h = 2.7,
[tex]f_y(1,3) & =\frac{f(1,3+2.7)-f(1,3)}{2.7} \\[/tex]
[tex]& =\frac{f(1,5.7)-f(1,3)}{2.7} \\[/tex]
[tex]& =\frac{16-14}{2.7} \\[/tex]
[tex]& =\frac{2}{2.7} \\[/tex]
[tex]& \approx[/tex] 0.7
Therefore the answer is 0.7.
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Approximate [tex]& f_y(x, y)[/tex] using the contour diagram of f(x, y) shown below.
Diagram attached at the end of solution
Two friends visited a taffy shop. Winston bought 2 kilograms of strawberry taffy and 1 kilogram of banana taffy for $20. Next, Audrey bought 4 kilograms of strawberry taffy and 4 kilograms of banana taffy for $52. How much does the candy cost?
Answers
The costs for the given candy are $7 for strawberry taffy and $6 for banana taffy. By writing equations and simplifying them, we get the requiredd values.
How to solve two equations?To solve two equations,
Rewrite one of the equations for one of its variables.Substitute it in the other equation.On simplifying, we get a value for one variable.Then, substitute in one of the equations, and we get another variable.This method of solving is called the substitution method.Calculation:It is given that, two friends visited a taffy shop.
Winton bought - 2 kg of strawberry taffy and 1 kg of banana taffy for $20.
Audrey bought - 4 kg of strawberry taffy and 4 kg of banana taffy for $52.
Then, we can write the above information into equations as
2S + B = 20 ...(1)
4S + 4B = 52 ...(2)
Where S represents strawberry taffy and B represents banana taffy.
From (1), we can write
B = 20 - 2S
Then, on substituting in (2), we get
4S + 4(20 - 2S) = 52
⇒ 4S + 80 - 8S = 52
⇒ -4S = 52 - 80 = -28
⇒ 4S = 28
∴ S = 7
Thus, the cost of strawberry taffy is $7.
On substituting S = 7 in (1), we get
2(7) + B = 20
⇒ 14 + B = 20
⇒ B = 20 - 14
∴ B = 6
Thus, the cost of banana taffy is $6.
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How many times smaller is 1.2 × 106 than 1.35 × 107?
11.25
2.55
1.47
0.15
Answers
Answer:
11.25
Step-by-step explanation:
(1.35 × 10^7) / (1.2 × 10^6) =
= 135/12
= 11.25
Answer: 11.25 is the answer
5
X
+
X+5
3x 1
#5 is the one I need solved please.
Answers
Answer:
x = 11midline = 16baseline = 32Step-by-step explanation:
You have a triangle with its midline length given as x+5 and its parallel base line length given as 3x-1. We presume you want to know the value of x and the lengths of the segments.
MidlineThe midline is half the length of the parallel base line, so you have ...
x +5 = 1/2(3x -1)
Solution2x +10 = 3x -1 . . . . . . . multiply by 2
11 = x . . . . . . . . . . . . . add 1-2x
The midline length is x+5 = 11+5 = 16.
The base line length is 3x-1 = 33 -1 = 32, twice the length of the midline.
The solution to the triangle is ...
x = 11midline = 16base line = 32As a pharmacist, you are responsible for knowing about medication dosage, and how long a dose stays in the patient's system. Let's look at an example of a common medication, called ibuprofen. When a patient takes a 400 mg dose of ibuprofen, it releases into the bloodstream at a certain rate, and then decreases over time. The function that models this concentration of medicine over time is complex and looks like this:
P(t) = 0.5t + 3.45t³ - 96.65t² + 347.7t, when 0 ≤t≤6 . In this function above, P(t) is the amount of medication (in mg) in the
blood stream at time t (in hours).
When put into a graphing software, it looks like this:
1) Why do we only need to look at the interval 0 ≤ t ≤ 6
Answers
The effect of the medicine is only left for the interval of 0 ≤ t ≤ 6.
What is an expression?The mathematical expression combines numerical variables and operations denoted by addition, subtraction, multiplication, and division signs.
Mathematical symbols can be used to represent numbers (constants), variables, operations, functions, brackets, punctuation, and grouping. They can also denote the logical syntax's operation order and other properties.
Given that Let's look at an example of a common medication, called ibuprofen. When a patient takes a 400 mg dose of ibuprofen, it releases into the bloodstream at a certain rate and then decreases over time. The function that models this concentration of medicine over time is complex and looks like this:
P(t) = 0.5t + 3.45t³ - 96.65t² + 347.7t, when 0 ≤t≤6.
The graph is repeating after the value of t as 6.
Hence, the interval will be 0 ≤t≤6.
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The length, L, of a teel rod i 7. 36, correct to 2 decimal place. Complete the error interval for length L
Answers
The length, L, of a teel rod i 7. 36, correct to 2 decimal place then The error interval for L is [7.355,7.365)
we know that
In this problem
The least significant digit is in the hundredths place.
The error can be as much 0.005 m
Determine the lower bound
To find out the lower bound subtract the error from the value
so 7.355
Determine the upper bound
To find out the upper bound adds the error to the value
7.365
so
Since 7.365 is rounded up to 7.37, the maximum value of L must be less than that.
therefore
7.355 < L < 7.365
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Directions: Evaluate the following logarithmic functions.
1. log100.1
2. log5125
3. log864
4. log1/3 9
5. log1/21/2
6. log497
7. log9 3
8. log3 81
9. log4 8
10. log100 10,000
Answers
The result of the logarithmic functions by logarithm tables are listed below:
- 232- 211 / 21 / 243 / 22How to evaluate logarithmic functions
This question can be resolved by means of logarithm properties and logarithm tables or numerical methods. Now we proceed to evaluate each logarithmic functions:
Case 1:
㏒₁₀ 0.1
By using rational numbers:
㏒₁₀ (1 / 100)
By logarithm properties:
㏒₁₀ 1 - ㏒₁₀ 100
By logarithm tables:
0 - 2
- 2
Case 2:
㏒₅ 125
By logarithm tables:
3
Case 3:
㏒₈ 64
By logarithm tables:
2
Case 4:
[tex]\log_{\frac{1}{3} } 9[/tex]
By logarithm tables:
- 2
Case 5:
[tex]\log_{\frac{1}{2}} \frac{1}{2}[/tex]
By logarithm tables:
1
Case 6:
㏒₄₉ 7
By logarithm tables:
1 / 2
Case 7:
㏒₉ 3
By logarithm tables:
1 / 2
Case 8:
㏒₃ 81
By logarithm tables:
4
Case 9:
㏒₄ 8
By logarithm tables:
3 / 2
Case 10:
㏒₁₀₀ 10,000
By logarithm tables:
2
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suppose a test of significance desires to see if there is a difference in mean ssha scores between men and women. which is the appropriate alternative hypothesis?
Answers
The appropriate alternative hypothesis is the opposite of null hypothesis that there is a difference in mean SSHA scores between men and women.
The alternative hypothesis is the opposite of the null hypothesis, which is typically stated as there being no difference between the two groups. In this example, the null hypothesis is that there is no difference in mean SSHA scores between men and women. The alternative hypothesis is then that there is a difference in mean SSHA scores between men and women. This can be stated as "There is a difference in mean SSHA scores between men and women". This is the appropriate alternative hypothesis for this test of significance.
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Noah thinks the answers to these two questions will be the same.
Do you agree with him? Explain your reasoning.
◦ This year, a herd of bison had a 10% increase in population. If there were 550 bison in the herd last year, how many are in the herd this year?
◦ This year, another herd of bison had a 10% decrease in population. If there are 550 bison in the herd this year, how many bison were there last year?
Answers
Answer: No, it works out to a different number. The 1st will end up with 605 bison.
Step-by-step explanation:
1st Herd: (550 x 10%) = 55 Bison
550 + 55 = 605 Thus 550 with a 10% increase is 605 Bison.
2nd herd: if you take 10% of 605 bison that number of (60.5) will give you a greater loss when taken away from 605.
605 - 60.5 = 544.5 bison remaining if 605 has a 10% loss.
Herd 2 started with approximately 611 bison. Check your math by multiplying 611 by 10% = 61.1
then subtract (611 - 61.1) = 549.9
So Herd 1 Does Not Equal Herd 2.
Directions: Plot the positive rational numbers on the number line. 12 134.16 310 / 8 0 1 - 2.05 Warm-Up 2 + 3 4 5
Answers
Answer:
Step-by-step explanation:
To plot the positive rational numbers on the number line, you can use the following steps:Start by drawing a number line, with 0 at the left end and positive numbers increasing as you move to the right.Place the first number, 12, on the number line. You can place it to the right of 0, since it is a positive number.Place the next number, 134.16, to the right of 12. You can place it farther to the right, since it is a larger number.Place the next number, 310/8, to the right of 134.16. Since 310/8 is equal to 38.75, you can place it slightly to the right of 134.16, but still to the left of 39.Place the next number, 0, at the left end of the number line, since it is equal to 0.Place the next number, 1, to the right of 0, since it is a positive number.Place the next number, -2.05, to the left of 0, since it is a negative number.Place the final two numbers, 2 and 3, to the right of 1, since they are both positive numbers.The resulting number line should look something like this:-2.05 0 1 2 3 12 134.16 38.75 (310/8)
pls tell me the qanswer da
Answers
Answer: B
Step-by-step explanation:
Answer:
it's point B
Step-by-step explanation:
The difference between -4 and -2 is -2 . And there are 8 steps from -2 and to -4.This means each step represents -2/8 which equals to -1/4. Then divide that number by -1/4
[tex] -2 \frac{6}{8} \div \frac{1}{4} \\ = 11[/tex]
Then count 11 steps from 0
ok.
21 divided 34 HELP MEH
Answers
Answer: 0.617
Step-by-step explanation:
Find the volume of this prymaid in question 10.
PLEASE HELP ME.
Answers
Answer:
5.083
Step-by-step explanation:
[tex]V=\frac{1}{3}Bh=(1/3)(1/2)(1.7)(3.9)(4.6)=5.083[/tex]
if the coefficient of determination is a positive value, then the regression equation
Answers
Answer:
close to 1, good fit
Step-by-step explanation:
If the coefficient of determination is a positive value, it means that the regression equation is a good fit for the data. The coefficient of determination, denoted by r^2, is a measure of how well the regression equation explains the variation in the data. A value of r^2 close to 1 indicates that the regression equation explains a large portion of the variation in the data, while a value of r^2 close to 0 indicates that the regression equation does not explain much of the variation in the data.
Therefore, if the coefficient of determination is a positive value, it means that the regression equation is a good fit for the data and explains a significant portion of the variation in the data. This means that the regression equation is likely to be a reliable model for the data and can be used to make predictions about the values of the dependent variable based on the values of the independent variable.
please help me im not very smarts
Answers
Answer:
1,5,7 = 145 degrees
2,3,6,8 = 35 degrees
Step-by-step explanation:
1,5, and 7 are interior angles:
Interior angles are those that lie inside a polygon. For example, a triangle has 3 interior angles. The other way to define interior angles is "angles enclosed in the interior region of two parallel lines when intersected by a transversal are known as interior angles".
2,3,6, and 8 are exterior angles:
An Exterior Angle is the angle formed by one side of a polygon and the extension of the adjacent side. In all polygons, there are two sets of exterior angles, one that goes around clockwise and the other goes around counterclockwise.
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A power outage affected all homes and businesses within a 5 mi radius of the power station. If the power station is located 1 mi west and 3 mi north of the center of town, find an equation of the circle consisting of the furthest points from the station affected by the power outage.
Answers
Answer: x^2 - 2x + y^2 - 6y + 10 = 0.
Step-by-step explanation: The power station is located 1 mi west and 3 mi north of the center of town, which means that it is located at the point (1, 3) on the coordinate plane. The power outage affected all homes and businesses within a 5 mi radius of the power station, which means that the furthest points from the station affected by the power outage are located on a circle with a radius of 5 mi.
The equation of a circle with center (h, k) and radius r is given by:
(x - h)^2 + (y - k)^2 = r^2
Substituting the values for the center of the circle (h, k) = (1, 3) and the radius r = 5, the equation of the circle consisting of the furthest points from the power station affected by the power outage is:
(x - 1)^2 + (y - 3)^2 = 5^2
This simplifies to:
x^2 - 2x + 1 + y^2 - 6y + 9 = 25
Combining like terms, the equation becomes:
x^2 - 2x + y^2 - 6y + 10 = 0
This can be written in standard form as:
x^2 - 2x + y^2 - 6y + 10 = 0
Therefore, the equation of the circle consisting of the furthest points from the power station affected by the power outage is x^2 - 2x + y^2 - 6y + 10 = 0.
Luke is going to rent an apartment in Hillwood, where other monthly expenses will sum up to $2929. Luke makes $7504 each month. Write the inequality for the possible amounts of money Luke can spend renting his apartment in Hillwood in order for Luke to have some money left over each month. Use x to represent the cost of the rent in Hillwood and don't use the $ symbol in the inequality. Show your work here Hint: To add inequalities (<, >, ≤, ≥), type “less” or “greater” Enter your answer
Answers
Answer:
He can waste 4,575 a month
Step-by-step explanation:
What is the value of (−135) − 72 − (−16)?
−47
−79
−191
−223
Answers
Answer:
-191
Step-by-step explanation:
Answer:
[tex] \sf \: c) - 191[/tex]
Step-by-step explanation:
Given problem,
→ (-135) - 72 - (-16)
Let's solve the problem,
→ (-135) - 72 - (-16)
→ (-135) - 72 + 16
→ (-135 - 72) + 16
→ -(135 + 72) + 16
→ -207 + 16
→ -191
Hence, answer is -191.
when a person's test performance can be compared with that of a representative and pretested sample of people, the test is said to be
Answers
when a person's test performance can be compared with that of a representative and pretested sample of people, the test is said to be norm-referenced.
Norm-referenced tests are assessments that measure an individual's performance against a predetermined group, or norm. A norm-referenced test is designed to evaluate how a person performs in comparison to a representative and pretested sample of people. This type of testing is especially common with achievement tests, such as the SAT or IQ tests, where the scores are meant to represent how the individual compares to others of the same age or in the same educational setting. The results of norm-referenced tests can be used to rank individuals according to their performance on the test, allowing for an easy comparison between individuals. Norm-referenced tests are designed to provide a comprehensive view of an individual’s strengths and weaknesses in comparison to a predetermined group.
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