Both functions are the solution to the given Laplace solution.
Given Laplace's equation: [tex]u_{x x}+u_{y y}=0[/tex]
We must determine whether a given function is the solution to a given Laplace equation.If a function is a solution to a given Laplace's equation, it satisfies the solution.(1) [tex]u=e^{-x} \cos y-e^{-y} \cos x[/tex]
Differentiate with respect to x as follows:
[tex]u_x=-e^{-x} \cos y+e^{-y} \sin x\\u_{x x}=e^{-x} \cos y+e^{-y} \cos x[/tex]
Differentiate with respect to y as follows:
[tex]u_{x x}=e^{-x} \cos y+e^{-y} \cos x\\u_{y y}=-e^{-x} \cos y-e^{-y} \cos x[/tex]
Supplement the values in the given Laplace equation.
[tex]e^{-x} \cos y+e^{-y} \cos x-e^{-x} \cos y-e^{-y} \cos x=0[/tex]
The given function in this case is the solution to the given Laplace equation.
(2) [tex]u=\sin x \cosh y+\cos x \sinh y[/tex]
Differentiate with respect to x as follows:
[tex]u_x=\cos x \cosh y-\sin x \sinh y\\u_{x x}=-\sin x \cosh y-\cos x \sinh y[/tex]
Differentiate with respect to y as follows:
[tex]u_y=\sin x \sinh y+\cos x \cosh y\\u_{y y}=\sin x \cosh y+\cos x \sinh y[/tex]
Substitute the values to obtain:
[tex]-\sin x \cosh y-\cos x \sinh y+\sin x \cosh y+\cos x \sinh y=0[/tex]
The given function in this case is the solution to the given Laplace equation.
Therefore, both functions are the solution to the given Laplace solution.
Know more about Laplace's equation here:
https://brainly.com/question/14040033
#SPJ4
The correct question is given below:
Determine whether each of the following functions is a solution of Laplace's equation uxx + uyy = 0. (Select all that apply.) u = e^(−x) cos(y) − e^(−y) cos(x) u = sin(x) cosh(y) + cos(x) sinh(y)
–6.4 − 7.2 what is the an
Answer:
-13.6
Step-by-step explanation:
Use the keep change change method when subtracting negative number. So, it would look like this: -6.4 + -7.2 = -13.6.
After adding them, just add a negative sign in front of your answer since you're adding two negative numbers.
Let me know if you don't understand or need more explanation.
-5,5 postać ułamka zwykłego -4,8 postać ułamka zwykłego pomocy
Answer:
[tex]-5.5 = \frac{-11}{2}[/tex]
[tex]-4.8 = \frac{-24}{5}[/tex]
Step-by-step explanation:
Postać ułamka zwykłego oznacza postać [tex]\frac{licznik}{mianownik}[/tex].
Zaczynamy od zauważenia, że [tex]-5.5 = -55/10 = -\frac{55}{10} = -\frac{11}{2} = \frac{-11}{2}[/tex]
-4.8 robimy analogicznie, tylko skracamy przez 2 a nie przez 5.
Po kolejne pytania po polsku należy się udać na brainly.pl
Solve for xxx. Enter the solutions from least to greatest. Round to two decimal places. (x - 6)^2 - 5 = 0
[tex]\boldsymbol{\sf{(x-6)^{2}-5=0 }}[/tex]
Take the square root of both sides to eliminate the exponent on the left side.[tex]\boldsymbol{\sf{x-6=\pm\sqrt{5} }}[/tex]
The complete solution is the result of the positive or negative portions of the solution.First, use the positive value of ± to find the first solution.[tex]\boldsymbol{\sf{x-6=\sqrt{5} }}[/tex]
Add 6 to both sides of the equation.[tex]\boldsymbol{ \sf{x=\sqrt{5}+6 }}[/tex]
Then use the negative value of ± to find the second solution.[tex]\boldsymbol{\sf{x-6=-\sqrt{5} }}[/tex]
Add 6 to both sides of the equation.[tex]\boldsymbol{\sf{x=-\sqrt{5}+6 }}[/tex]
The complete solution is the result of the positive or negative portions of the solution.[tex]\boldsymbol{\sf{x=\sqrt{5}+6,-\sqrt{5}+6 }}[/tex]
[tex]\huge \red{\boxed{\boldsymbol{\sf{Answer \ \ \longmapsto \ \ \ x=\pm\sqrt{5}+6 }}}}[/tex]
Skandar4. The
sum of a number z and 16.2 is at most 30.
z + 16.2 ≤ 30
z ≤ 13.8
2.4z + 1.2z - 6.5 = 0.7
Answer: z = 2
Step-by-step explanation:
2.4z+1.2z-6.5=0.7
3.6z-6.5=0.7
3.6z=0.7+6.5
3.6z= 7.2
z=7.2/3.6
z=2
In the diagram, roads a and b are parallel.
Solve for x and find the measure of VTU.
Answer:
102
Step-by-step explanation:
<QRT and <VTU are alternate exterior angles, so they are congruent.
m<QRT = m<VTU
x + 40 = 2x -22
62 = x
m<QRT = x + 40 = 62 + 40 = 102
m<VTU = 2x - 22 = 62*2 - 22 = 124 - 22 = 102
A local hamburger shop sold a combined total of 380 hamburgers and cheeseburgers on Saturday. There were 70 fewer cheeseburgers sold than hamburgers.
How many hamburgers were sold on Saturday?
Answer:
310 hamburgers were sold on Saturday
Step-by-step explanation:
1x + 70 =380
-70 -70 Reverse
1x = 310
/1 /1 Divide
x =310
Show that
5x+2
3x
+1⁄/12
can be written in the form
ax+b
CX
where a, b and c are integers.
Answer:
Step-by-step explanation:
When completing the square, an expression like,
ax2 + bx + c is written in the form (Ax + B)2 + C.
We will begin with the simple example where a = 1. In this case we will write expressions in the form
x2 + bx + c as (x + B)2 + C
If we expand (x + B)2 + C we get x2 + 2Bx + B2 + C.
Comparing this with x2 + bx + c shows that
b = 2B and c = B2 + C
which gives B =
b
2
and C = c – B2
Rewrite literal equations.
Solve for m:
e=mc squared.
Answer:
m = e/c
Step-by-step explanation:
x^3=-115 pleasess i need the answer now
Answer:
x = -∛115
Step-by-step explanation:
x^3 - (-115) = 0
= x^3 + 115
Factoring
(a+b) • (a^2-ab+b^2) =
a^3-a^2b+ab^2+ba^2-b^2a+b^3 =
a^3+(a^2b-ba^2)+(ab^2-b^2a)+b^3=
a^3+0+0+b^3=
a^3+b^3
(115 isn't a cube.)
Polynomial roots
P: -1, -5, -23, -115, 1, 5, 23, 115
Q: 1
P/Q: -1, -5, -23, -115, 1, 5, 23, 115
Divisor(s): None
In these sets of data, there are no rational roots shown.
Step-by-step explanation(part 2):
x^3 + 115 = 0
x^3 = -115
x = ∛-115
Negative numbers will always have real cube roots.
∛ -115 = ∛ -1 × 115 = ∛ -1 × ∛ 115 = (-1) × ∛ 115
Therefore,
x = -∛115
Suppose that the height of the slide is 2 feet, when x = 20. what is t brainlyhe average rate of change over the entire slide?
The average rate of change over the entire slide is 0.01 per unit.
A slope is also known as the gradient of a line is a number that helps to know both the direction and the steepness of the line.
The slope of a line is defined as the change in y coordinate with respect to the change in x coordinate of that line. The net change in y coordinate is Δy, while the net change in the x coordinate is Δx. So the change in y coordinate with respect to the change in x coordinate can be written as,
Introduction to Slope of a Line | The slope of line is the measure of steepness or the direction of line the coordinate plane.
m = Δy/Δx
where, m is the slope
Note that tan θ = Δy/Δx
We also refer this tan θ to be the slope of the line
Given,
the height of the slide = 2 feet
the value of x is 20 units
The average rate of change is the slope of the line
Therefore, the rate of change over the entire slide will be,
Rate of change = 2/20 = 0.1 feet per unit
Hence, the rate of change is 0.1 feet per unit.
To know more about "Slope of the line"
Refer this link:
https://brainly.com/question/14511992
#SPJ4
PLEASE HELP (at least c)
A machinist is required to manufacture a circular metal disk with area 715cm squared
. Give your answers in exact form. Do not write them as decimal approximations.
a) What radius, x , produces such a disk?
b) If the machinist is allowed an error tolerance of ±5cm2 in the area of the disk, how close to the ideal radius in part (a) must the machinist control the radius?
c) Using the ε / δ definition of a limit, determine each of the following values in this context:
f(x)=
a=
L=
ε=
δ=
The 715 cm² area of the disc and the ±5 cm² error tolerance, gives;
a) x = √(715/π) cm
b) The range for the radius is; [√(710/π) cm, √(720/π) cm]
c)
f(x) = π•x²
L = 715 cm²
E = 5 cm
d = √(5/π) cm
How can the variables in the [tex] \epsilon / \delta [/tex] definition of limits be found?Area of the circular metal disk = 715 cm²
a) Required; The disk radius
Let A represent the area of the disk and let x represent the radius, we have;
A = π•x²
Therefore;
x = √(A/π)
Which gives;
x = √(715/π) cm
b) Allowed area error tolerance = ± 5 cm²
The allowed range of values for the area is therefore;
710 ≤ A ≤ 720Which gives;
√(710/π) ≤ x ≤ √(720/π)
c) From the [tex] \epsilon / \delta [/tex] definition of limits, we have;
[tex] \lim\limits_{x → √(715/π)} f(x) = 715 [/tex]
Which gives;
f(x) = A = π•x²
L = 715
|f(x) - L| < E = 5 cm
|x - √(715/π)| < d = √(5/π)
Learn more about the properties of limits here:
https://brainly.com/question/13233499
#SPJ1
jeremy has 25 marbles, he gives 5 to his teacher, then he give five to his best friends. once he gets home he gives 5 to his sister right the terms in order to determine how many marbles he has
Answer: 25 - 15 = 10
Step-by-step explanation:
In the figure below, m ZABD = 104°, BC bisects LABD, and BE bisects ZCBD. Find mZEBD.
Check
A
B
C
E
D
mZEBD
X
2022 McGraw
The measure of ∠EBD from the given figure is 26°.
Given that, m∠ABD=104°, BC bisects ∠ABD, and BE bisects ∠CBD.
What is an angle bisector?An angle bisector is defined as a ray, segment, or line that divides a given angle into two angles of equal measure. The word bisector or bisection means dividing one thing into two equal parts.
Since BC bisects ∠ABD, we get ∠ABC=∠CBD
So, ∠ABD=∠ABC+∠CBD
⇒2∠CBD=104°
⇒∠CBD=52°
Here, BE bisects ∠CBD, we get ∠CBE=∠EBD
So, ∠CBD=∠CBE+∠EBD
⇒2∠EBD=52°
⇒∠EBD=26°
Therefore, the measure of ∠EBD from the given figure is 26°.
To learn more about the angle bisector visit:
https://brainly.com/question/12896755.
#SPJ1
What is the slope of the line? Coordinate grid ranging from negative five to five on the x and y axes. A line passes through points (negative two, one) and (two, negative one). Responses −12 negative fraction 1 over 2 end fraction 2 2 12 1 half −2
The Slope of the line passing through the points (-2,1) and (2,-1) is -1/2 .
The Slope(m) of the line is defined as the change in y coordinate with respect to change in x coordinate ,
The Slope(m) of line passing through the points A(a,b) and B(c,d) is calculated using the formula
m = (d-b)/(c-a)
In the question
it is given that the line passes through the points (-2,1) and (2,-1) .
name the points as A(-2,1) and B(2,-1) .
the values are a=-2 , b=1 , c=2 , d=-1 .
Substituting the values in the formula of Slope we get
m = (-1-1)/(2-(-2))
= -2/(2 + 2)
= -2/4
= -1/2
Therefore , the slope of the line passing through the points (-2,1) and (2,-1) is -1/2 .
Learn more about Slope of Line here
https://brainly.com/question/18298097
#SPJ1
Answer:
Step-by-step explanation:
The Slope of the line passing through the points (-2,1) and (2,-1) is -1/2 .
The cost of bananas varies directly with the number of pounds bought. If 6 pounds
cost $5.22, find the cost of 3 pounds.
Answer:
$2.61
Step-by-step explanation:
So, We have $5.22 for 6 pounds of Bananas.
If we need to find the cost for 3 pounds, we would divide $5.22 by 2 because 6/2=3
In order to do this, we need to turn 5.22 into a whole number, so we multiply by 100
5.22*100=522
Now we divide
522/2 = 261
Now we divide 261 by 100, since we multiplied by 100 earlier.
261/100 =2.61
So our answer is $2.61 for 3 pounds of bananas .
Hope this helps! ^^
Answer:$2.61 for 3 pounds
Thank for the brainliest
Step-by-step explanation:first you divided $5.22/6 because the money always goes on the top and you get 0.87, you multiply 0.87 by 3 which is $2.61
Please help with algebra!
Answer:
[tex]x=29[/tex]
Step-by-step explanation:
These two angles add up to 180 degrees. We can make an equation saying that [tex](2x+6)+4x=180[/tex]. Simplifying, we get [tex]6x+6=180\\[/tex].
Now when we subtract 6 from both sides we get [tex]6x=174[/tex]. Then we divide both sides by 6 to get our final answer: [tex]x=29[/tex]
Hope this helps!
6/4 + 0.68
Jason solved this problem by changing 6/4 to 1.2. He then added 1.2 to 0.68 and got 1.88.
This answer is incorrect. What did he do wrong?
Multiple choices accepted
Group of answer choices
1.2 + 0.68 should have equaled 8.0
1.2 + 0.68 should have equaled 0.80
6/4 should have been changed to 1.5
6/4 should have been changed to 1.24
PLEASE ANSWER FASTTT IM TIMED
Answer
1.2 + 0.68 should have equaled 0.80
Step-by-step explanation:
jason solved this problem by changing 6/4 to 1.2. He then added 1.2 to 0.68 and got 1.88.
This answer is incorrect. What did he do wrong?
If Jason solved this problem by changing 6/4 to 1.2, The wrong thing he did is ; 6/4 should have been changed to 1.5. Option C is correct
How to solve the problemTo find the correct answer, let's first evaluate the expression step by step:
1. 6/4 is equal to 1.5, not 1.2.
2. 1.5 + 0.68 equals 2.18, this is not 1.88.
So, the correct answer is: Jason made a mistake in the first step. He changed 6/4 to 1.2, but it should have been 1.5.
Therefore, the correct calculation is 1.5 + 0.68 = 2.18.
Read more on fractions here https://brainly.com/question/30154928
#SPJ3
Consider any subset of the real numbers that consists only
of negative numbers. What can you conclude about whether the set is closed
under multiplication?
Explain.
Answer: Not closed under multiplication
====================================================
Explanation:
Pick any two negative numbers that you want.
I'll go for -3 and -5
They multiply to (-3)*(-5) = 15 which is a positive number. The two negatives cancel out to form a positive.
This is an example to show that multiplication is not closed for this subset of the real numbers. We consider it to be closed if the result of any two negative numbers multiplied would get us some other negative number.
In a sense, this is the complete opposite of closed since the result is never negative.
Here's an example of a set that is closed under multiplication: integers
Picking any two integers and multiplying them together gets us some other integer. Each item is found in the same set, i.e. the result never leaves or goes outside the set.
For the following relation, provide the domain and range.
Domain: [A, B] Range: [C, D]
A=
B=
C=
D=
Answer:
Domain: [-4,2]
Range: [-3,3]
Step-by-step explanation:
A = -4
B = 2
C = -3
D = 3
Find an equation of the sphere determined by the given information. passes through the point (8, 3, -3), center (5, 6, 5)
The equation of the sphere is
[tex]x^{2} +y^{2}+z^{2}+-10x-12y-10z+4=0[/tex]
The standard form of the equation of the sphere is :
[tex](x-a)^{2}+(y-b)^{2}+(z-c^{2} )=r^{2}[/tex]
Where A (a, b , c) is the center and r is the radius.
From the question we should first find the radius
r = [tex]\sqrt{(x-a)^{2}+(y-b)^{2}+(z-c)^{2}[/tex]
Point = (x , y , z) = (8 , 3 , -3)
Center = (a, b , c)= (5 , 6 ,5)
Substituting it in the formula
r = [tex]\sqrt{(8-5)^{2}+(3-6)^{2}+(-3-5)^{2} }[/tex]
By further calculation
r = [tex]\sqrt{9+9+64}[/tex]
So, we get
r =[tex]\sqrt{82}[/tex]
Substituting it in the standard form
[tex](x-5)^{2}+(y-6)^{2}+(z-5)^{2}=\sqrt{82}^{2}[/tex]
[tex](x-5)^{2} +(y-6)^{2} +(z-5)^{2}=82[/tex]
[tex]x^{2} +y^{2}+z^{2}+25+36+25-10x-12y-10z=82[/tex]
[tex]x^{2} +y^{2}+z^{2}+-10x-12y-10z+86-82=0[/tex]
[tex]x^{2} +y^{2}+z^{2}+-10x-12y-10z+4=0[/tex]
Therefore, the equation of the sphere is
[tex]x^{2} +y^{2}+z^{2}+-10x-12y-10z+4=0[/tex]
Learn more about Sphere of the equation at:
https://brainly.com/question/11141686
#SPJ4
A recent report stated that less than 35 percent of adult residents in a certain city will be able to pass a physical fitness test. Consequently, the city's Recreation Department is trying to convince the City Council to fund more physical fitness programs. The council is facing budget constraints and is skeptical of the report. The council will fund more physical fitness programs only if the Recreation Department can provide convincing evidence that the report is true. The Recreation Department plans to collect data from a sample of 185 adult residents in the city. A test of significance will be conducted at a significance level of a= 0.05 for the following hypotheses.
H0:p=0.35
Ha:p<0.35
where p is the proportion of adult residents in the city who are able to pass the physical fitness test.
The Recreation Department recruits 185 residents who volunteer to take the physical fitness test. The test is passed by 77 of the 185 volunteers, indicating that more than 35 percent of the city is in shape. Describe the primary flaw in the study described in part and explain why it is a concern.
The primary flaw is that the sample will slightly overestimate the physical fitness of the people of the town.
The given hypothesis are,
[tex]H_0:p=0.35\\H_1:p < 0.35[/tex]
Type II error is accepted in null hypothesis when it is not actually true.
In the given question null hypothesis p= 0.35
The conclusion is that in the given sample proportion is not equal to 0.35, though we know that proportion is not equal to 0.35 we accept the null hypothesis, that is wrong.
Now given n=185,x=77 P=0.53 then Q=1-0.35=0.65
[tex]H_0:P=0.35\\H_1:P < 0.35[/tex]
Now test statistic [tex]Z=\frac{p-P}{\sqrt{\frac{PQ}{n}}}[/tex]
Solving for Z using the given values we get :
Z=1.99
Now 1.99>-1.65
So we accept [tex]H_0[/tex]
The primary flaw in the system is that the sample is not randomly selected rather they are volunteers. So it is reasonable to think that the physical fitness of the town will be slightly over estimated by the experiment.
To learn more about sample of an experiment:
https://brainly.com/question/24466382
#SPJ9
Saeed plans to run 10 km. On the first day, he runs 2 km. What percent of the total distance does he run the first day?
Answer:
He runs 20% or 1/5 of the total distance the first day
Step-by-step explanation:
We know this due to the fact that 2km / 10km is equal to 1/5 and we then know that 1/5 equates to the percentage equivalence value of 20%
answer this question
Answer: 166
We’ll give it your best mate keep it up
Solve and represent X< -2 or X<5 in all ways
Answer:
x<−2 or x<5
Step-by-step explanation:
x<−2 or x<5
We know either x<−2 or x<5
x<−2(Possibility 1)
x<5(Possibility 2)
Solve the equation
3(4z-7)=-21+12z
Answer:
Step-by-step explanation:
Let's open the brackets,
12z - 21 = -21 + 12z (distributive property)
12z - 12z = -21 + 21
0z = 0
z = 0
A county has 225 acres of vacant land.
Residents voted to turn some of the vacant land
into parks. Now, there are 36% less acres of
vacant land. How many acres of vacant land
does the county have now?
The acres of vacant land that the county have now will be 144 acres.
How to calculate the value?Since 36% has been used, the remaining percentage will be:
= 1 - 36%
= 64%
Therefore, the acres of vacant land that the county has now will be:
= 64% × 225
= 64/100 × 225
= 0.64 × 225
= 144
Therefore, the acres of vacant land that the county have now will be 144 acres.
Learn more about percentages on:
brainly.com/question/24877689
#SPJ1
17k to 19.04k increase. What is the percent increase?
Need Answered ASAP
Answer:
4 %
Step-by-step explanation:
Point N is the midpoint of segment FG. If FN = 2z2 + 4z +3, write the expression below that represents FG.
The center of segment FG is located at point N. Write the formula that expresses FG if FN = 2z2 + 4z + 3.
Since O represents the midway, both FO and OG must be equal.
3x + 17 = 7x - 15
Add 3x to both sides and subtract:
17 = 4x -15
To both sides, add 15:
32 = 4x
Subtract 4 from both sides:
x = 32/4
X = 8
Now that you know the value of X, find the lengths:
FO = 3x +17 = 3(8) +17 = 24 +17 = 41
OG = 7x -15 = 7(8) -15 = 56-15 = 41
Total length would be 41 + 41 = 82
To learn more about midway visit : https://brainly.com/question/13357792
#SPJ9
If p(a | b) = 0.4, p(b) = 0.8, and p(a) = 0.5, are the events a and b independent?
The events A and B are not independent.
Given that,
P(A|B) = 0.4
P(A) = 0.5
P(B) = 0.8
Two events A and B are said to be independent, if P(A∩B) = P(A) P(B)
We have, P(A|B) = P(A∩B)/P(B)
Therefore, P(A∩B) = P(A|B) P(B) = 0.4 x 0.8 = 0.32
Now P(A) P(B) = 0.5 x 0.8 = 0.4
So P(A∩B) ≠ P(A)P(B)
Therefore, the events A and B are not independent.
Learn more about independent events at https://brainly.com/question/22881926
#SPJ4