2. Find the partial differential equation by eliminating arbitrary functions from \[ u(x, y)=f(x+2 y)+g(x-2 y)-x y \]
Answers
The partial differential equation obtained by eliminating arbitrary functions from the expression u(x, y) = f(x + 2y) + g(x - 2y) - xy is:
\[ u_{xx} - 4u_{yy} = 0 \]
To eliminate the arbitrary functions f(x + 2y) and g(x - 2y) from the expression u(x, y), we need to differentiate u with respect to x and y multiple times and substitute the resulting expressions into the original equation.
Given:
u(x, y) = f(x + 2y) + g(x - 2y) - xy
Differentiating u with respect to x:
u_x = f'(x + 2y) + g'(x - 2y) - y
Taking the second partial derivative with respect to x:
u_{xx} = f''(x + 2y) + g''(x - 2y)
Differentiating u with respect to y:
u_y = 2f'(x + 2y) - 2g'(x - 2y) - x
Taking the second partial derivative with respect to y:
u_{yy} = 4f''(x + 2y) + 4g''(x - 2y)
Substituting these expressions into the original equation u(x, y) = f(x + 2y) + g(x - 2y) - xy, we get:
f''(x + 2y) + g''(x - 2y) - 4f''(x + 2y) - 4g''(x - 2y) = 0
Simplifying the equation:
-3f''(x + 2y) - 3g''(x - 2y) = 0
Dividing through by -3:
f''(x + 2y) + g''(x - 2y) = 0
This is the obtained partial differential equation by eliminating the arbitrary functions from the expression u(x, y) = f(x + 2y) + g(x - 2y) - xy.
The partial differential equation obtained by eliminating arbitrary functions from u(x, y) = f(x + 2y) + g(x - 2y) - xy is u_{xx} - 4u_{yy} = 0.
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Related Questions
Jose says he knows that the decimal representation of a fraction, such as 3/8 , will be a terminating decimal if he can scale up the denominator to make a power of 10. What scale factor would Jose need to use to rewrite 3/ 8 as x / 1000 What is the decimal representation ?
Answers
Answer:
0.00038
Step-by-step explanation:
easy to answer
If p() = x2 - 1 and q(x) - 5(x-1), which expression is equivalent to (p - q)(x)?
Answers
Answer:
\(\text{If p(x) = x2 - 1 and q(x) = 5(x - 1), the expression which is equivalent to}\) \(\text{ (p - q)(x) is (x2 - 1) - 5(x - 1).}\)
Step-by-step explanation:
Given:
p(x) = 2x2 - 1q(x) = 3(x - 1)To find:
(p - q)(x)We know:
(p - q)(x) = p(x) - q(x)Substitute
(2x^2 - 1) - 3(x - 1)\(\text{Therefore, the expression equivalent to (p - q)(x) is (2x2 - 1) - 3(x - 1).}\)
2. Consider the system defined by the impulse response h(n)=28(n+3)+28(n)+28(n-3). a) b) c) d) z Represent h(n). (1 v.) Characterize the system in terms of causality and stability. Justify. (1 v.) Determine the frequency response of the system H(ew). (1 v.) Represent module and phase of the system. (1 v.)
Answers
The system defined by the impulse response h(n) = 28(n+3) + 28n + 28(n-3) can be represented as h(n) = 28δ(n+3) + 28δ(n) + 28δ(n-3), where δ(n) denotes the unit impulse function.
In terms of causality, we can determine whether the system is causal by examining the impulse response. If the impulse response h(n) is non-zero only for n ≥ 0, then the system is causal. In this case, since the impulse response h(n) is non-zero for n = -3, 0, and 3, the system is not causal.
To determine the stability of the system, we need to examine the summation of the absolute values of the impulse response. If the summation is finite, the system is stable. In this case, we can calculate the summation as ∑|h(n)| = 28 + 28 + 28 = 84, which is finite. Therefore, the system is stable.
However, since the impulse response is given in the time domain and not in a closed-form expression, it is not possible to directly determine the frequency response without further manipulation or additional information.
Given the absence of specific frequency domain information or a closed-form expression for the frequency response, it is not possible to accurately represent the module and phase of the system H(e^ω) without further calculations or additional details about the system.
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The ratio of mystery books to fantasy books in the library is 7:9.
Fill in the missing values to show the possible number of
mystery and fantasy books.
Mystery Books Fantasy Books
21
Select Answer -
63
Select Answer -
27
54
Select Answer
117
Answers
Answer:
42
81
91
Step-by-step explanation:
m = mystery
f = fantasy
\(\frac{m}{f}\) = \(\frac{m}{f}\)
Compare the ratio with the actual numbers. Solve for the missing number
\(\frac{7}{9}\) = \(\frac{m}{54}\) you need to multiply 9 by 6 to get 54 so multiply 7 x 6 to get 42.
\(\frac{7}{9}\) = \(\frac{63}{f}\) Multiply 7 x 9 to get 63,so multiply 9 by 9 to get 81.
\(\frac{7}{9}\) = \(\frac{m}{117}\) 9 x 13 is 117, so multiply 7 by 13 to get 91.
simplify below these questions
rule: little x means times not the other way round
A: 3X^2Y^4 x 2X^6Y
B: XZ^3 x 4X^4Z^5
C: 4A^3^2 x 3A^6B^5
D: 6S^5T x S^4T^2
Answers
A: \(3x^2y^4\cdot2x^6y=6x^8y^5\)
B: \(xz^3\cdot4x^4z^5=4x^5z^8\)
C: \(4a^3^2\cdot 3a^6b^5=12a^{15}b^5\)
D: \(6s^{5t}\cdot s^{4t}^2=6s^{16t^2+5t}\)
There was some ambiguity you posed with such exponents but I assumed strictly.
Hope this helps.
what is a=1/4 b if b is the subject?
Answers
Answer:
b = 4a
Step-by-step explanation:
Given
a = \(\frac{1}{4}\) b
Multiply both sides by 4 to clear the fraction
4a = b
According to the diagram below TSU = KLM by HA we know that T = K because they are both right angles which of the following theorems can also show congruence NEED HELP ASAP!!
Answers
Answer:
The triangles are congruent as per AAS congruence.
Step-by-step explanation:
AAS congruence states that when two triangles are congruent when their two angles are equal and the side not contained between those angles is also equal.
Let us have a look at the given triangles \(\triangle TSU\) and \(\triangle KLM.\)
It is given that they are right angled triangles and following dimensions are also equal:
1. \(\angle T = \angle K = 90^\circ\)
2. \(\angle M = \angle U\)
3. The side not between the angles i.e. the hypotenuse SU = LM
So, the two triangles \(\triangle TSU\) and \(\triangle KLM.\) are congruent as per AAS congruence.
i.e. \(\triangle TSU\) \(\cong\) \(\triangle KLM.\) as per AAS congruence.
Answer:
C AAS
Step-by-step explanation:
A bag contains 5 red marbles, 7 blue marbles and 2 green marbles. If two marbles are
drawn out of the bag, what is the probability, to the nearest 1000th, that both
marbles drawn will be blue?
Answers
The probability that both marbles drawn will be blue is 0.218.
What is probability?
By simply dividing the favorable number of possibilities by the entire number of possible outcomes, the probability of an occurrence can be determined using the probability formula. Because the favorable number of outcomes can never exceed the entire number of outcomes, the chance of an event occurring might range from 0 to 1.
Since there are 7 blue marbles in the bag.
The first blue marble drawing likelihood is 7/15.
The second blue stone has a 7/15 chance of being drawn.
The likelihood that both marbles are chosen will be blue is equal to 7/15*7/15,
= 49/225,
=0.218
Hence the probability of that both marbles drawn will be blue is =0.218
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im board !!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!
Answers
Answer:
same
Step-by-step explanation:
Answer:
same
Step-by-step explanation: same free coins ;)
5x-11=-16 solving basic combined equations
Answers
Answer:
iihhhjitrddcvbjjh
Step-by-step explanation:
Cohen feeuj
Answer:
-1
Step-by-step explanation:
5x=-16+11
5x=-5
x=-5÷5
x=-1
Evaluate the triple integral where is the solid bounded by the cylinder and the planes and in the first octant.
Answers
The triple integral of the given solid is equal to (2/3) pi.
To evaluate the triple integral of a solid bounded by the cylinder and the planes in the first octant, we need to break down the integral into three separate integrals for each variable x, y, and z.
Firstly, we can determine the limits of integration for each variable by looking at the boundaries of the solid. The cylinder is defined by the equation \(x^{2}\) + \(y^{2}\) = 4, while the planes are defined by z = 0, x = 0, and y = 0.
In the first octant, we can set the limits of integration to be from 0 to 2 for x and from 0 to sqrt(4 - \(x^{2}\)) for y, as we are only considering the first quadrant of the cylinder. For z, the limits of integration are from 0 to 1, as we are only considering the solid bounded by the planes.
We can then set up the triple integral as follows:
∫∫∫ (1) dz dy dx
where (1) represents the constant function 1, as we are not given any specific function to integrate.
Using the limits of integration we determined earlier, we can simplify the integral to:
∫\(0^{2}\) ∫\(0^{\sqrt{4-x^{2} } }\) ∫\(0^{1}\) (1) dz dy dx
Evaluating this integral yields:
∫\(0^{2}\)∫\(0^{\sqrt{4-x^{2} } }\)(z)|\(0^{1}\)dy dx
which further simplifies to:
∫\(0^{2}\) (1/2)(\({\sqrt{4-x^{2} } }\)) dx
Using the substitution u = x/2, we can simplify the integral further to:
(1/4) ∫\(0^{4\sqrt{4-u^{2} } }\) du
This integral can be evaluated using the trigonometric substitution u = 2 sin(theta), which yields:
(1/2) ∫\(0^{\pi /2}\)(2 cos(θ)\()^{2}\) d(θ)
Simplifying this integral further yields:
(1/2) ∫0^pi/2 (4 \(cos^{2}\)(tθ) - 2) d(θ)
Evaluating the integral gives us:
(1/2) [(4/3) \(sin^{3}\)(θ) - 2 θ]|\(0^{\pi }\)
Finally, plugging in the limits of integration yields:
(2/3) \(\pi\)
Therefore, the triple integral of the given solid is equal to (2/3) \(\pi\).
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Chris is trying to factor 812 +192. Complete the factoring using the dropdown menus below.
NOTE: If you feel that the expression is not factorable (PRIME), simply select "PRIME" from ALL dropdown menus.
GCF =
a=
b=
The formula I would use to "Plug and Chug" is:
Answers
The factorization of 812 + 192 is GCF = 4
a = 4
b = 251
The formula used to "Plug and Chug" is:
812 + 192 = a × b
To factor the expression 812 + 192, we first find the greatest common factor (GCF) of the two numbers. The GCF is the largest number that divides both 812 and 192 evenly.
Let's calculate the GCF:
1, 2, 4, 7, 14, 28, 29, 58, 116, 203, 406, and 812 are the factors of 812.
1, 2, 3, 4, 6, 8, 12, 16, 24, 32, 48, 64, 96, and 192 are the factors of 192.
Common factors: 1, 2, 4
The greatest common factor (GCF) of 812 and 192 is 4.
Now, we can write the given expression as a product of the GCF and the remaining factors.
812 + 192 = 4 × (203 + 48)
To further simplify the expression, we can calculate the values inside the parentheses:
203 + 48 = 251
Therefore, the factored form of 812 + 192 is:
812 + 192 = 4 × 251
In summary, the factorization of 812 + 192 is:
GCF = 4
a = 4
b = 251
The formula used to "Plug and Chug" is:
812 + 192 = a × b
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Which points on this vertical number line best represent the locations of 2.5 and -3/2. A (G and J) B (G and K). C(H and I) D (H and j).
Answers
Answer:
The answer is G and K
Step-by-step explanation:
Because i got it right on this test
Thank Me
A building in San Francisco has light fixtures consisting of small 2.35-kg bulbs with shades hanging from the ceiling at the end of light thin cords 1.50 m long.If a minor earthquake occurs, how many swings per second will these fixtures make?
Answers
The light fixtures will make approximately 0.914 swings per second during a minor earthquake in San Francisco.
To determine the frequency of the swings per second for the light fixtures, we need to use the formula for the period of a pendulum, which is T = 2π√(L/g), where T is the period, L is the length of the pendulum, and g is the acceleration due to gravity.
In this case, the length of the pendulum is given as 1.50 m, and the mass of the bulb is given as 2.35 kg. We can assume that the shade and cord add negligible mass to the system. The acceleration due to gravity is approximately 9.8 m/s^2.
Plugging in the values, we get:
T = 2π√(1.50/9.8)
T ≈ 1.093 seconds
The frequency of the swings per second is the reciprocal of the period, so:
f = 1/T
f ≈ 0.914 Hz
It's important to note that this is an approximation, and the actual frequency may vary depending on factors such as the amplitude of the oscillations and the specific characteristics of the earthquake.
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what is the measure of angle TSU?
Answers
Answer:
m<TSU = 65
Step-by-step explanation:
As one can see, the measure of angle (RST) is (90) degrees. This is indicated by the box around the angle. As a general rule, when there is a box around an angle, the angle measure if (90) degrees. It is also given that the measure of angle (RSU) is (25) degrees. As per the given diagram, the sum of the measures of angles (RSU) and (UST) is (RST). Therefore, one can form an equation and solve for the measure of angle (UST).
(RSU) + (UST) + (RST)
Substitute,
25 + (UST) = 90
Inverse operations,
25 + (UST) = 90
UST = 65
(<UST) is another way of naming angle (TSU).
Answer:
∠ TSU = 65°
Step-by-step explanation:
∠ RST = 90°
∠ RSU + ∠TSU = ∠ RST , that is
25° + ∠ TSU = 90° ( subtract 25° from both sides )
∠ TSU = 65°
Select the expressions that are equivalent to 7(-7u - 4) - 5.
(-7u - 4)7 - 5
7(-8u+ u 4) - 5
-33u - 49
-7u - 33
Answers
Answer: only the first one
Step-by-step explanation:
What is the factor of x³ 5x² 2x 24?
Answers
The factor of x3 5x2 2x 24 is (x - 4)(x + 2)(x + 6), which can be expanded as x3 + 2x2 - 4x2 + 6x - 8x - 24.
1. Factor out the greatest common factor (GCF) from the coefficients of the terms.
x3 5x2 2x 24
2. Factor out the GCF from each term:
x3 = x•x•x
5x2 = 5•x•x
2x = 2•x
24 = 24
3. Our factors are now:
x•x•x 5•x•x 2•x 24
4. Group the terms with common factors:
(x•x•x) (5•x•x) (2•x) (24)
5. Factor out the common factor from each group:
x•x (x•5) (2•x) (24)
6. Our factors are now:
x (x•5) (2•x) (24)
7. Factor out the common factor from each group:
x (x•5) (2•x) (24)
8. Our factors are now:
x (x + 2)(x + 6) (24)
9. Our final answer is:
(x - 4)(x + 2)(x + 6)
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simplify
7 + 2 (4x - 3) = ?
Answers
Sean pays a landscaper to build a fence around his square garden and to put new soil down for him. The landscaper used exactly 48 feet of fencing to create the perimeter. What is the length of each side of the garden? How many square feet of ground will the landscaper need to cover with new soil?
Answers
Perimeter = 4x
We know that the landscaper used 48 feet of fencing to create the perimeter, so we can set up an equation:
48 = 4x
Dividing both sides by 4, we get:
x = 12
Therefore, the length of each side of the square garden is 12 feet.
To find the area of the garden, we can use the formula:
Area = length x width
Since the garden is a square, its length and width are equal, so we can write:
Area = x^2
Substituting the value of x, we get:
Area = 12^2 = 144 square feet
Therefore, the landscaper will need to cover 144 square feet of ground with new soil.
an item is regularly priced at $60. it is on sale for 60% off the regular price. How much (in dollars) is discounted from the regular price?
Answers
Answer:
$36 off
Step-by-step explanation:
$60 x 0.60 = 36
if you need the total cost of the item just 60 - 36 = 24
so you get $36 off of 60
and the new cost would be $24
help me with this question please
Answers
Answer:
N+1
Step-by-step explanation:
It begins with = 2
then n+1=3
then n+2=4 and so on it is n+1
Can anyone help me pls????????
Answers
Answer its quite easy i hope this will be right
1) 4.1833
2) 5.29+2.366=7.656
Suppose that E and F are two events and that P(E and F)=0.1 and P(E)=0.2. What is P(F/E)
Answers
From the given information provided, the probability of event F given that event E has occurred is 0.5.
Conditional probability is probability of an event A occurring with given that event B has occurred. It is denoted as P(A|B) and is calculated as follows:
P(A|B) = P(A and B) / P(B)
To find P(F/E), we use the conditional probability formula:
P(F/E) = P(E and F) / P(E)
We are given that P(E and F) = 0.1 and P(E) = 0.2. Substituting the given values in the formula, we get:
P(F/E) = 0.1 / 0.2
Simplifying this expression, we get:
P(F/E) = 0.5
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The sum of -2x 2 + x + 31 and 3x 2 + 7x -8 can be written in the form ax 2 + bx + c , where a, b, and c are constants. What is the value of a+b+c?
Answers
Answer:
hey try looking it up on hooda math answers .com
Step-by-step explanation:
PLEASE HELP I WILL MARK BRAINLIEST SHOW WOrK HOW YOU GOT IT
Answers
Answer:
7 . 8.9
8 . 19.5
9 . 9.9
10 .12.6
Step-by-step explanation:
7.x=11tan39
8.x=28cos46
9.x=8tan51
10.x=31sin24
side opposite of mentioned angle is opposite
longest side in triangle is hypotenuse
the side subtended by the angle is the adjacent
What is the base for each curve and where should I shift for each? I’ve been getting this wrong because I don’t know which way to shift and what the base should be for both
Answers
Answer:
Here is the graph of the equation and its inverse.
The inverse is the purple graph.
Explanation:
• The base of the equation is 8.
,• There is no vertical shift to the graph because there's no constant added to the function f(x) = 8^x.
,• In addition, there is no horizontal shift to the graph because there's no constant added to the exponent x.
Calculate the value of x
Answers
Answer:
12x=180 -30
x= 150/12
x= 12.5°
Answer:
x = 12.5
Step-by-step explanation:
The 3 angles lie on a straight line and so sum to 180°, that is
x + 10 + 10x + x + 20 = 180, simplify
12x + 30 = 180 ( subtract 30 from both sides )
12x = 150 ( divide both sides by 12 )
x = 12.5
What is the Pythagorean Theorem? Provide the equation and an explanation as to what it means.
Answers
Answer:
The Pythagorean Theorem is a squared + b squared = c squared. It is used to find out a side of a triangle if you already know the two others. C is always the H=hypotenuse, while the other two sides are a and b.
Answer: a^2+b^2 (factored) = c^2
Step-by-step explanation:
This only helps if you are solving for the hypotenuse.
A slushy machine at 7-Eleven holds 39 liters of wild cherry slushy. How many 0.6 liter slushies can be dispensed before the machine is completely empty?
PLS HELP!!!!
Answers
Answer:
65
tep-by-step explanation:
Brainliest tysmmm you are my 5000 points tysmmmmm
Rearrange tiles on the board to represent equivalent
expressions
Which expression is equivalent to 3x - 5?
O 2x - 4-1 + x
O -x + x + x-1-1-1-1-1
0-5 - 3x
O 3x +5
Board sum: 3x + (-5)
The tiles are ready for moving.
Reset
Intro
Done
Answers
The expressions that is equivalent to 3x - 5 are 2x - 4-1 + x and 3x+(-5)
Expressions and equationsFrom the given information, we need to calculate the expression that is equivalent to 3x - 5.
For the expression 2x - 4 - 1 + x
2x + x -4 - 13x - 5For the expression -x + x + x-1-1-1-1-1
2x - 5
For the expression 3x+(-5)
= 3x - 5
Hence the expressions that is equivalent to 3x - 5 are 2x - 4-1 + x and 3x+(-5)
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