No, f(x, y) = 3x - 3y^2 is not a harmonic function.
A harmonic function is a twice continuously differentiable function f(x, y) that satisfies the Laplace equation:
∂²f/∂x² + ∂²f/∂y² = 0.
Let's check if f(x, y) = 3x - 3y^2 satisfies the Laplace equation:
∂²f/∂x² = ∂/∂x(3) = 0
∂²f/∂y² = ∂/∂y(-6y) = -6
∂²f/∂x² + ∂²f/∂y² = 0 + (-6) = -6 ≠ 0
Since the Laplace equation is not satisfied, f(x, y) = 3x - 3y^2 is not a harmonic function.
As for finding a corresponding analytic function, an analytic function is a function that is locally given by a convergent power series. Since f(x, y) is not a harmonic function, there is no corresponding analytic function.
Read more about harmonic functions at:
https://brainly.com/question/30385079
#SPJ11
The length of a cell phone is 1.41.4 inches and the width is 2.82.8 inches. The company making the cell phone wants to make a new version whose length will be 1.611.61 inches. Assuming the side lengths in the new phone are proportional to the old phone, what will be the width of the new phone?
Answer:
Step-by-step explanation:
Since the side lengths are proportional, the ratio of the width to length in the old phone will be equal to the ratio of the width to length in the new phone. That is:
(width of old phone) / (length of old phone) = (width of new phone) / (length of new phone)
We know the length of the old phone is 1.41.4 inches, and the width is 2.82.8 inches, so we can use that information to solve for the width of the new phone:
(2.82.8 inches) / (1.41.4 inches) = (width of new phone) / (1.611.61 inches)
Cross multiplying, we get:
(width of new phone) = (2.82.8 inches) * (1.611.61 inches) / (1.41.4 inches)
Using a calculator, we can find that the width of the new phone is approximately 3.23.2 inches.
eighteen foot-pounds of work is required to stretch a spring 4 inches from its natural length. find the work required to stretch the spring an additional 3 inches.
The work required to stretch the spring an additional 3 inches is 10.125 foot-pounds.
We can use Hooke's law to find the force required to stretch the spring 4 inches from its natural length:
[tex]F = kx[/tex]
where F is the force in pounds, x is the displacement in inches, and k is the spring constant in pounds per inch (which we want to find).
Since 18 foot-pounds of work is required to stretch the spring 4 inches, we know that the work done is equal to the potential energy stored in the spring:
[tex]W = (1/2) k x^2[/tex]
Solving for k, we get:
[tex]k = (2W) / x^2[/tex]
Plugging in the values for W and x, we get:
[tex]k = (2 * 18) / (4^2) = 2.25[/tex]
So the spring constant is 2.25 pounds per inch.
Now we can use Hooke's law again to find the force required to stretch the spring an additional 3 inches:
[tex]F = kx[/tex]
= [tex]2.25 * 3[/tex]
= 6.75 pounds
Finally, we can find the work required to stretch the spring an additional 3 inches:
[tex]W = (1/2) k x^2[/tex]
= [tex](1/2) * 2.25 * 3^2[/tex]
= 10.125 foot-pounds
Therefore, the work required to stretch the spring an additional 3 inches is 10.125 foot-pounds.
Learn more about Hooke's law here:
https://brainly.com/question/4404276
#SPJ4
What is 2x times 2x in algebra
Answer: 4x2
Step-by-step explanation:
Answer:
[tex]4x^2[/tex]
Step-by-step explanation:
[tex](2x)(2x)=(2*2)(x*x)=4x^2[/tex]
Find the value of the following expression and round to the nearest integer:
Answer:
53
Σ900(1.04)"+1
n=1
Answer:
The expression is a summation, or the sum of a sequence of terms. Each term is equal to 900 * (1.04)^n+1, where n starts at 1 and goes up to infinity.
To calculate this sum, we would need to find the limit of the sequence as n approaches infinity. However, finding the exact value of this sum is not possible and would require the use of mathematical tools like mathematical analysis.
To estimate the value, we can use a calculator or spreadsheet to calculate the sum for a finite number of terms and then see how the sum changes as we increase the number of terms. For example, if we calculate the sum for n = 1 to 100, we would get an estimate of the value. If we then calculate the sum for n = 1 to 200, we would get a closer estimate.
In this case, we can round the expression to the nearest integer, which would be 53.
Step-by-step explanation:
Mackenzie has 8 markers. Ty has three times as many. If they combine their markers, how
many do they have?
Show your work
Answer:
32 markers
Step-by-step explanation:
Ty has 8 x 3 = 24 markers.
Together, they have 8 + 24 = 32 markers.
A large rectangular movie screen in an IMAX theater has an area of 11,224 square feet. Find the dimensions of the screen if it is 30 feet longer than it is wide
With an area of 11,224 square feet and the dimensions of the screen if it is 30 feet longer than it is wide, the width of the screen is 91.5 feet, and the length of the screen is 121.5 feet.
Let's call the width of the screen "w". Then, the length of the screen would be "w + 30". The area of the screen is 11,224 square feet, so we can set up an equation:
w * (w + 30) = 11,224
Expanding the right side of the equation, we get:
w^2 + 30w - 11,224 = 0
We can use the quadratic formula to solve for w:
w = (-b ± √(b^2 - 4ac)) / 2a
Where a = 1, b = 30, and c = -11,224.
Plugging in the values, we get:
w = (-30 ± √(30^2 - 4 * 1 * -11,224)) / 2 * 1
= (-30 ± √(900 + 44,896)) / 2
= (-30 ± √(45,796)) / 2
= (-30 ± 213) / 2
Taking the positive solution, we get:
w = (183 / 2) = 91.5 feet
So the width of the screen is 91.5 feet, and the length of the screen is 91.5 + 30 = 121.5 feet.
To learn more about area click on,
https://brainly.com/question/14726830
#SPJ4
There are 21 pieces of $2 notes and $10 notes in an envelope. If the total value of all the notes is less than
$110, find the minimum number of $2 notes in the envelope.
Answer:
Let the number of $2 notes be x, while that of $10 notes be y.
Set two equations
x + y = 21 y = 21 - x ------- 1
2x + 10y < 110 ------ 2
Sub 1 into 2
2x + 10(21-x) < 110
2x + 210 - 10x < 110
-8x < -100
x > 12.5
Minimum number of $2 notes in the envelope = 13
AB and BC form a right angle at point B. If A = (-3-1) and B = (4,4) what is the equation of Bc
Answer: The equation of a line in the form y = mx + b can be found using the slope-intercept form, where m is the slope of the line and b is the y-intercept. To find the equation of BC, we need to find the slope of the line and one point on the line.
The slope of the line can be found using the two points A and B. The slope of the line can be calculated using the formula:
m = (y2 - y1) / (x2 - x1)
where (x1, y1) and (x2, y2) are the coordinates of points A and B, respectively. Plugging in the values, we get:
m = (4 - (-1)) / (4 - (-3)) = 5 / 7
So the slope of the line BC is 5/7.
One point on the line BC is B = (4, 4), so we can use this point and the slope to find the y-intercept:
b = y - mx
where y and x are the y and x coordinates of point B, respectively. Plugging in the values, we get:
b = 4 - (5/7) * 4 = 4 - 20/7 = -16/7
So the equation of line BC in the slope-intercept form is:
y = (5/7)x - 16/7
Step-by-step explanation:
The temperature in Wintergreen Resort in Virginia fell from 15.8
degrees Celsius to - 2.7 degrees Celsius. What is the difference
between the two temperatures?
The term "difference" os the result of subtracting one number from another.
So in other terms you want to know what would be the result of subtracting -4.6 from 13.5 :
13.5 - -4.6 = Difference between the two temperatures
Two minus signs turn into a positive sign so :
13.5 - -4.6 =
13.5 + 4.6 =
18.1 = Difference between the two temperatures
Your answer is : The difference between the two temperatures is 18.1
Belle has a collection of trading cards. The table shows how many of each type of card she has. A card will be randomly drawn from her collection and replaced 60 times
Type: Number:
Baseball 13
Football. 8
Basketball. 5
Soccer. 9
What is a reasonable prediction for the number of times a basketball or soccer card will be drawn?
If P is the centroid, and GP=2.2, find the indicated
lengths.
A
PC =
GC =
ttt
B
++
H
type your answer...
type your answer...
C
The length of PC and GC is 4.4 and 6.6 respectively.
What is centroid of a triangle?
A centroid of a triangle is defined as a equidistant from all the point present on the triangle. It is always lies on the interior of the triangle. The centroid divided the median in the ratio 2:1
Given ABC is the triangle.
In which G, H, J are the midpoints on AB, BC, AC sides respectively.
Then, AH, CG, BJ are the medians and they are intersect at the point P.
P is the centroid of the triangle.
Given, GP =2.2 we have to find the PC and GC.
We know that the centroid divided the median in 2:1 ratios.
i.e., AP:PH = CP:PG = BP:PJ = 2:1
We know , GP = 2.2, then, [tex]\frac{CP}{PG} = \frac{2}{1}[/tex]
⇒CP= 2(2.2)= 4.4then, GC = GP+PC= 2.2 + 4.4= 6.6.
Hence, the length of PC and GC is 4.4 and 6.6 respectively.
Learn more about centroid of triangle here:
https://brainly.com/question/10708357
#SPJ1
3. The width of a rectangle is 8 inches less than the length, x, of the rectangle. The sum of the length
and width is more than 60 inches. Which of the following represent the possible values of the length
of the rectangle?
A x > 34
B
x <34
C
X> 24
D
x > 26
8-X < 60
The possible values of the length of the rectangle is x > 34, the correct option is A.
How to find the area and the perimeter of a rectangle?For a rectangle with length and width L and W units, we get:
Area of the rectangle = [tex]L \times W \: \rm unit^2[/tex]
Perimeter of the rectangle = [tex]2(L + W) \: \rm unit[/tex]
The area of the rectangle is the product of the length and width of a given rectangle.
The area of the rectangle = length × Width
Given that width is 8 inches less than the length x
Sum of length and width more than 60
Now, the length is x
Width is x-8
x-8+x>60
2x>60
x>30
Therefore, the length of rectangle will be x > 34
Learn more about rectangles here;
https://brainly.com/question/15019502
#SPJ9
what value of k makes -4 > k + 15 true
Answer:
-19 > k
Step-by-step explanation:
-4 > k + 15
Subtract 15 from each side.
-4-15 > k + 15-15
-19 > k
Any value less than -19 would make this statement true
Answer:
- 19 > k
Step-by-step explanation:
- 4 > k + 15
Subtract 15 from both sides.
- 4 - 15 > k
- 19 > k
Select all the measures of variability that can be used to compare two data sets.
A. Mean
B. Interquartile Range
C. Median
D. Mode
E. Range
Range, interquartile range, standard deviation, and variance are four measures of variability that can be used to compare two data sets.
Variability is most generally measured proving the following descriptive data:area:
Difference between highest and lowest values.
Range is the straightforward allowance to calculate variability. To asset the area, follow these steps:
Sort all the values in the dataset from lowest to highest.
Subtract the lowest value from the highest value. Interquartile range:
area of the middle half of the distribution
standard deviation:
mean distance from mean
Standard deviation is a useful measure of the variance of a normal distribution.
A normal distribution distributes data symmetrically without skew. Most of the values are clustered around the central region, with values tapering away from the center. Standard deviation indicates how far the data are, on average, from the center of the distribution.
deviation:
mean squared distance from mean
Learn more about Measure o variability at:
brainly.com/question/3806824
#SPJ
imagine math - item 92070
I'm sorry, but I'm not sure what you mean by "Imagine math - item 92070." Can you please provide more context or clarification so I can assist you better?
What is A ‘ C please help
Answer: 11.7 in.
Step-by-step explanation:
I don't really know this stuff myself since I'm in 8th grade, but I can say that AA is 12in. long. I measured the length of A'C, and it was a little shorter than AA. So therefore, I think the answer is 11.7 in. I just wanted to help you out.
Hexagonal prism B is the image of hexagonal prism A after dilation by a scale factor of 2. If the surface area of hexagonal prism B is 172 cm^2, find the surface area of hexagonal prism A, the preimage.
Hexagonal prism A has a surface area of 43 cm2.
What is the surface area equation?A three-dimensional shape's surface area is the total area on its surface. A cuboid's surface area is calculated by adding the areas of each of its six rectangular sides. The cuboid's length, width, and height may all be identified, and the formula SA=2lw+2lh+2hw can be used to determine its surface area (SA).
The surface area of a hexagonal prism is given by the formula:
SA = 2B + PH
where B is the base's surface area, P is its perimeter, and H is the prism's height.
Since prism B is a dilation of prism A with a scale factor of 2, its surface area is four times the surface area of prism A. So we can write:
SA_B = 4×SA_A
where SA_B is the surface area of prism B and SA_A is the surface area of prism A
We are given that SA_B = 172 cm², so we can substitute this value into the equation above to find SA_A:
172 = 4×SA_A
SA_A = 43 cm²
To know more about surface area visit:-
https://brainly.com/question/29298005
#SPJ1
the angle of depression from the top of a cliff to a nearby town is 23 degrees. if the top of the cliff is 360 feet above the town, how far is the town from the base of the cliff? do not round until you reach your answer, and then round your answer to the nearest tenth of a foot.
The length of town from the base of the cliff is 848.25 feet
Concept of height and distance
You can use trigonometry formulas to find height and distance from anything. If you know the distance from the Qutub Minar to your current location and the angle at which you can see the top of the Minar, you can find the altitude of the Qutub Minar. Use trigonometry to find the elevation. This is because the ground, minaret elevation, and contour lines all combine to form a 90 degree right triangle between the minaret and the ground.
The distance is usually the "base" of the right triangle formed by the minar's elevation and line of sight. The length of the horizontal plane also forms the base of a triangle parallel to the ground at a given height, so we know the distance. The line of sight forms the "hypotenuse" of a right triangle. Lines perpendicular to the ground form the "height" of the triangle.
To calculate elevation or depression you can use the following formulas:
sinθ = hypotenuse /height.
cosθ = hypotenuse /base,
tanθ = base /height
where θ is the elevation or depression angle.
and in this question the angle of depression is 23 degree and height is 360 feet and we have to calculate the base
tan 23 degree = 360/base
base = 360/tan 23
=360/0.4244
= 848.25 feet.
know more about height and distance click here;
https://brainly.com/question/25708841
#SPJ4
Find the slope of the line graphed below.
Answer:
the slope is -6/-5
the sun is shining and a spherical snowball of volume 260 ft3 is melting at a rate of 11 cubic feet per hour. as it melts, it remains spherical. at what rate is the radius changing after 6.5 hours?
If the spherical snowball is melting , then the rate at which the radius changing after 6.5 hours is 0.208 ft/h .
A spherical snowball has volume = 260 ft³ that is melting at a rate of 11 cubic feet per hour, while remaining spherical.
We have to find the rate at which the radius is changing after 6.5 hours.
So , let "V" = volume of snowball, "r" = radius of snowball, and "t" = time.
Volume Of Sphere is V = (4/3)πr³ and dV/dt = -11 ft³/h ;
So, dr/dt when t = 6.5 hours. is dV/dt = (dV/dr)×(dr/dt) ;
derivative of volume formula with respect to "r", we get:
⇒ dV/dr = 4πr² ;
Substituting the given values in chain rule equation, we get:
⇒ -11 = (4/3)πr² × dr/dt ;
⇒ dr/dt = -11/((4/3)πr²)
For rate of change of the radius when t = 6.5 hours, we find the radius at that time.
The initial volume of the snowball = 260 ft³.
After 6.5 hours of melting at a rate of 11 ft³/h, the remaining volume will be: V = 260 - (11 × 6.5) = 188.5 ft³ ;
So , V = (4/3)πr³
⇒ 188.5 = (4/3)πr³
⇒ r³ = (188.5 × 3 / (4π)) ;
≈ 3.55ft
Now we substitute r = 3.55 feet
⇒ dr/dt = -11/[(4/3)π(3.55)²] ;
⇒ dr/dt ≈ -0.208 ft/h ;
Therefore , the rate at which radius is changing after 6.5 hours is approximately 0.208 feet per hour and negative sign represents that radius is decreasing .
Learn more about Rate Of Change here
https://brainly.com/question/28891125
#SPJ4
Solve for x.
-x+8=259
X =
Answer:x=251
Step-by-step explanation:
Step 1: Subtract 8 from both sides of the equation.
Explanation: Subtracting 8 from both sides of the equation keeps the equality balanced.
Step 2: x = 251
Explanation: Subtracting 8 from both sides of the equation gives us
x = 259 - 8 = 251.
Answer:
Step-by-step explanation:
x = -251
Karen likes to make lemonade using the lemons from her grandmother's
trees. There is a proportional relationship between the number of pitchers of
lemonade Karen wants to make, x, and the number of lemons she needs, y.
4) The equation that models this relationship is y = 5x.
4) How many pitchers of lemonade can Karen make with 15 lemons?
Answer: If there is a proportional relationship between the number of pitchers of lemonade Karen wants to make, x, and the number of lemons she needs, y, and the equation modeling this relationship is y = 5x, then we can find the number of pitchers Karen can make with 15 lemons by solving for x:
15 = 5x
Dividing both sides by 5:
3 = x
So Karen can make 3 pitchers of lemonade with 15 lemons.
Step-by-step explanation:
Find the number that makes the ratio equivalent to 1:2.
The equivalent to the ratio 1:2 is 2 : 4
How to determine the equivalent ratioFrom the question, we have the following parameters that can be used in our computation:
Ratio = 1 : 2
To determine the equivalent expression, we multiply each proportion of the ratio by the same number (say 2)
Using the above as a guide, we have the following:
Ratio = 2 * 1 : 2 * 2
Evaluate
Ratio = 2 : 4
Hence, the ratio is 2 : 4
Read more about ratio at
https://brainly.com/question/12535721
#SPJ1
W X
Y
Z
List the sample space for the experiment.
Os = {X, Y, Z}
Os = {W, Z, Z}
Os = {W.Y.Y. Z}
Os = {W, X, Y, Z}
Answer:
Os = {W, X, Y, Z}
Step-by-step explanation:
The sample space for the experiment is the set of all possible outcomes, in this case, W, X, Y, and Z. It represents all the outcomes that can occur in a single trial of an experiment. The sample space is usually denoted as a set, and the elements in the set are the individual outcomes. In this case, the sample space is the set {W, X, Y, Z}.
Answer:
the answer is the last one
Step-by-step explanation:
os= {w, x, y, z}
suppose 4 math majors and 6 computer science majors randomly take seats in the front row of a classroom. a. what's the probability the math majors are seated together? b. what's the probability the math majors are seated together and the computer science majors are seated together?
The probability the math majors are seated together is 0.028 and all seated togeather with their group is 0.0047.
Probability is the probability that something will happen. Whenever the outcome of an event is uncertain, we can speak of the probability, or likelihood, of a particular outcome. Analyzing events according to their probabilities is called statistics.
Probability determines the likelihood of an event occurring.
P(A) = f / N. Odds and probabilities are related, but odds depend on probabilities. Before we can determine the probability that an event will occur, we first need the probability.
total number of teacher is 10
so number of ways total 10 teacher seat = 10!/(6!*4!)
= 210
and
the number of ways the math majors are seated together
= 6
probability = 6/210 = 0.028
the number of ways the math majors are seated together and the computer science majors are seated together
= 1
probability = 1/210
know more about probability click here;
https://brainly.com/question/30034780
#SPJ4
Equation 1: 2x - 5y = -8
Equation 2: 4x + 5y = 14
Emily solved the system of equation above using the Elimination Method. She
multiplied equation 1 by a number, then added the resulting equations
together to eliminate the variable . What number did Emily multiply equation
1 by so that she could eliminate the x terms?
To solve the given equations multiply equation 1 with - 2 and the solutions are x = 1 and y = 2.
Elimination Method:In mathematics, the Elimination method is about deleting one of the words containing any of the variables to make the calculations easier.
To solve the equations, multiply or divide a number by the equation(s) until all of the variable terms' coefficients are the same.
The term is then eliminated or removed from the result by adding or subtracting from both equations.
Here we have
Equation 1: 2x - 5y = -8
Equation 2: 4x + 5y = 14
We can multiply given equations as follows
To eliminate 'x' terms multiply the multiply equation 1 with -2
-2 × Equation 1 => - 4x + 10y = 16 ---- (Equation 3)
Now add Equation (2) and Equation (3)
=> 4x + 5y - 4x + 10y = 14 + 16
=> 15y = 30
=> y = 2
Now substitute y = 2 in equation (2)
=> 2x - 5(2) = -8
=> 2x - 10 = -8
=> 2x = 2
=> x = 1
Therefore,
To solve the given equations multiply equation 1 with - 2 and the solutions are x = 1 and y = 2.
Learn more about Elimination method at
https://brainly.com/question/30287548
#SPJ1
Label each figure correctly. Area is understood to be square feet and perimeter is understood to be feet. (PLEASE HELP)
The area and perimeters of the shapes are: (1) Area = 702 ft², perimeter = 96 ft (2): Area = 20 in² Perimeter = 21 in
How to find the area and perimeters?Perimeter is the distance round the object while the area is the floor space the object occupies
1) Area = (l*w) + (L*W)
Area = (6*9) + (24*27)
Area = 54 + 648
Area = 702 ft²
ii) perimeter = 24+27+30+9+6= 96 ft
2) Area = (l*w) + (L*W)
Area = (2*3) +( 7*2)
Area = 6+14 = 20 in²
ii) perimeter =2+7+2+2+3+2+3 = 21 in
Learn more about perimeter and area on https://brainly.com/question/11957651
#SPJ1
The perimeter of a rectangle is 30 inches. The width of the rectangle is two-thirds of its
length, as shown.
What are the length and the width of the rectangle? Check your solution.
Answer:
The length is [tex]9[/tex] inches and the width is [tex]30[/tex] inches.
Step-by-step explanation:
The perimeter of the rectangle is [tex]2x + \frac{4x}{3} = 30[/tex]. We multiply [tex]3[/tex] by both sides which will give us [tex]6x + 4x = 90[/tex]. Adding, we have [tex]10x = 90[/tex]. Dividing [tex]10[/tex] by both sides will give us [tex]x = 9[/tex]. The length of the rectangle is [tex]9[/tex], and the width is [tex]\frac23 \cdot 9 = 6.[/tex] Checking our answer, we have [tex]6 + 6 + 9 + 9 = 30.[/tex] Therefore, the length of the rectangle is [tex]\boxed{9 \text{ inches}}[/tex] and the width of the rectangle is [tex]\boxed{30 \text{ inches}}[/tex].
Hope that helps!
What is the common ratio of the geometric sequence shown? -2,4,-8,16,. . .
Answer:
-2,-4,-8,-16
common ratio of geometric sequence shown is -2
this sequence is in the decreasing form.
the next number in this sequence is -32
I hope that helps.
Which expression would NOT be equivalent to 4(10+5)?
Answer:
Not Possible
Step-by-step explanation:
No answer choices are shown however, we can solve for some that are equivalent so we know which ones are not.
Here are some that are equivalent:
20(2+1)
2(20+10)
40+20
60
