Answers
By direct substitution and simplification, the trigonometric function z = cos (2 · x + 3 · y) represents a solution of the partial differential equation \(\frac{\partial^{2} t}{\partial x^{2}} - \frac{\partial^{2} t}{\partial y^{2}} = 5\cdot z\).
How to analyze a differential equation
Differential equations are expressions that involve derivatives. In this question we must prove that a given expression is a solution of a differential equation, that is, substituting the variables and see if the equivalence is conserved.
If we know that \(z = \cos (2\cdot x + 3\cdot y)\) and \(\frac{\partial^{2} t}{\partial x^{2}} - \frac{\partial^{2} t}{\partial y^{2}} = 5\cdot z\), then we conclude that:
\(\frac{\partial t}{\partial x} = -2\cdot \sin (2\cdot x + 3\cdot y)\)
\(\frac{\partial^{2} t}{\partial x^{2}} = - 4 \cdot \cos (2\cdot x + 3\cdot y)\)
\(\frac{\partial t}{\partial y} = - 3 \cdot \sin (2\cdot x + 3\cdot y)\)
\(\frac{\partial^{2} t}{\partial y^{2}} = - 9 \cdot \cos (2\cdot x + 3\cdot y)\)
\(- 4\cdot \cos (2\cdot x + 3\cdot y) + 9\cdot \cos (2\cdot x + 3\cdot y) = 5 \cdot \cos (2\cdot x + 3\cdot y) = 5\cdot z\)
By direct substitution and simplification, the trigonometric function z = cos (2 · x + 3 · y) represents a solution of the partial differential equation \(\frac{\partial^{2} t}{\partial x^{2}} - \frac{\partial^{2} t}{\partial y^{2}} = 5\cdot z\).
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Related Questions
When a product fails to perform as warranted, this is called a) contractual liability. O b) product malfunction. c) malicious manufacture. d) breach of warranty
Answers
Answer:
When a product fails to perform as warranted, this is called breach of warranty.
how do you Simplify 6(x + 3).
Answers
Answer:
6x+18
Step-by-step explanation:
6(x + 3).
Distribute
6x+6*3
6x+18
Select the correct answer. How many solutions for x does the following equation have? A. 4 B. 0 C. infinite D. 1
Answers
The equation 2 (p+ 7) = 4 - 8p has only one solution that is; -9.
We know that solution of an equation refers usually to the values of the variables involved in that equation that if substituted in place of that variable would give a true mathematical statement.
We need to determine the solutions does the equation 2 (p+ 7) = 4 - 8p have;
Now solving for p,
2 (p+ 7) = 4 - 8
Open the bracket,
2p+ 14 = 4 - 8
Combine the like terms,
2p = -4 - 14
2p = -18
p = -18/2 = -9
Therefore, the equation has only one solution which is -9.
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4) A snowboarder descends down a mountain at a rate of 15 feet per second. How far will she travel after 9 seconds?
Answers
A = { 4, 6, 8, 9 } B = { 3, 5, 8 } A ⊕ B =
Answers
Answer:
37 pls brain list me pls.
What is this? Please answer if u know what you are doing thank you
Answers
Answer:
y= 8
Step-by-step explanation:
y= k/x
-8= k/4
k= -8×4= -32
y= k/x
y= -32/-4
y= 8
hope it helps!
Answer:
the answer is 8 if y= -8 when x is 4 amd
XYZ company is situated in Ghana. They have been commissioned your organisation to design a database for them. The database is expected to keep data on employees, customers, suppliers, and products. Important records on employees such as employee's ID, date of birth, and dependants are expected to be captured in the database. Products information such as product's ID, name of product, manufacturing and expiring data, and name of supplier are expected to be captured. The company receives suppliers from different organisations, hence, it would like the database to capture relevant details of these suppliers. Each supplier supplies only one type of product for the company. Every customer is assigned one sales representative, yet sales representatives maybe assigned up to ten customers. Customers can order an unlimited number of good. Properly represent all entities, relationships, constraints, and appropriate keys in an E-R diagram that can readily be used in a database.
Answers
By answering the presented question, we may conclude that Sales Rep: expression This entity maintains information about sales reps such as SalesRepID and SalesRepName.
what is expression ?An expression in mathematics is a collection of representations, numbers, and conglomerates that mimic a statistical correlation or regularity. A real number, a mutable, or a mix of the two can be used as an expression. Mathematical operators include addition, subtraction, fast spread, division, and exponentiation. Expressions are often used in arithmetic, mathematic, and form. They are used in the representation of mathematical formulas, the solution of equations, and the simplification of mathematical relationships.
The ER diagram above depicts the database entities and their connections. Here's a quick rundown of each entity and its characteristics:
Employee: This object contains information on employees such as EmployeeID, Name, DateOfBirth, and Dependents.
ProductID, ProductName, ManufacturingDate, ExpiryDate, and SupplierID are all stored in this object.
Supplier: This entity holds supplier-specific information such as SupplierID, SupplierName, ContactPerson, and ContactNumber.
CustomerID, CustomerName, ContactPerson, and ContactNumber are all stored in the Customer entity.
Sales Rep: This entity maintains information about sales reps such as SalesRepID and SalesRepName.
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Help me please, I’m very confused on what to do
Answers
Just add the powers while it is multiply
-1+(-3)
= -1 - 3
= -4
So it is \(2^{-4}\)
Mr. Baker is making pancakes and reads the recipe on the back of the van key box use the information in the table to determine the ratio of the cups of pancake mix 2 cups of water a what is the constant ratio
Answers
A constant ratio is that the ratio is the same for all the points that's are given.
How to illustrate the information?Your information is incomplete. Therefore, an overview will be given.
It should be noted that constant ratio simply means the ratio is the same for all the points that's are given.
It should be noted the ratio will be constant is when the output and the input stays the same sand doesn't change.
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Give one word for the following.
To find the way, carefully and safely
Answers
GPS.....................GPS..............................................................................................
5. Jamal is taking a road trip. He plans to travel a total of 350 miles over the course of 8 days. If he plans on driving an equal amount each day, how far will he travel each day? Solve and check!
Answers
Answer: 43.75 miles per day.
Step-by-step explanation: All you have to do is divide 350 by 8, when you divide you basically just split the number evenly 8 times, which is what 350 divided by 8 is. He will have to drive 43.75 miles a day.
√-100 = + i
DONE
+
i
Answers
Answer:
10i
Step-by-step explanation:
We can separate \(\sqrt{-100}\) into \(\sqrt{100*-1}\). This equals \(10*\sqrt{-1}\), and since \(\sqrt{-1}=i\), it is \(10i\).
Answer:0 + 10i
Step-by-step explanation:
Terrell sells clay pots. He sells 2 clay pots for $6, 3 clay pots for $9, and 4 clay pots for $12. What is the unit rate of dollars per clay pot?
A
1
B
2
C
3
D
4
Answers
if you double a number and then add 36, you get 4 over 11 (4/11) of the original number,
what is the original number?
Answers
Answer:
The original number is -22
Step-by-step explanation:
We'll label our mystery number x.
2x + 36 = 4x/11
Multiply both sides by 11
4x = 22x + 396
Isolate x to one side (for this I subtract 4x from both sides, but you can also subtract 22x if you'd like)
0 = 18x + 396
Isolate x pt 2
18x = -396
Divide both sides by 18 to find your answer!
x = -22
Plug in to confirm
-44 + 36 = -88/11S
8 = 8
What is the best description of the relation in item 2
Answers
Answer:
Step-by-step explanation:
One input(x-value) can only have one output(y-value) in order to be a function
Calculate the loss on selling 50 shares of stock originally bought at 13 3/4 and sold at 12
Answers
The loss on selling 50 shares of stock would be 87.50.
To calculate the loss on selling 50 shares of stock originally bought at
\(13\frac{3}{4}\) and sold at 12, we need to determine the difference between the purchase price and the selling price, and then multiply it by the number of shares sold.
First, let's convert the purchase price from a mixed fraction to a decimal. \(13\frac{3}{4}\) can be expressed as 13.75.
Next, we calculate the difference between the purchase price and the selling price:
\(13.75 - 12 = 1.75.\)
Finally, we multiply the difference by the number of shares sold:
\(1.75 \times50 = 87.50.\)
Therefore, the loss on selling 50 shares of stock would be 87.50.
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A data set is made up of the values 5, 6, 9, 12, and 18.
The table shows the distance between each value and the mean of 10.
Data value
Distance between
value and mean
5
5
6
4
9
1
12
2
18
8
Sum of distances 20
What is the mean absolute deviation (MAD) of the data set?
Answers
Answer:
4
Step-by-step explanation:
a p e x its correct
Find the x - and y -intercepts of the following equation: 3x-2y=5 ?
Answers
The x-intercept will be (5/3, 0) and the y-intercept will be (0, -5/2).
The x-intercept of an equation is the point at which the graph of the equation intersects the x-axis, which means that the y-coordinate of that point is 0. To find a x-intercept, we can set y = 0 in equation and solve for x.
Given the equation: 3x - 2y = 5
Setting y = 0, we get;
3x - 2(0) = 5
3x = 5
x = 5/3
So, the x-intercept is (5/3, 0).
The y-intercept of an equation is the point at which the graph of the equation intersects the y-axis, which means that the x-coordinate of that point is 0. To find y-intercept, we can set x = 0 in equation and solve for y.
Setting x = 0, we get;
3(0) - 2y = 5
-2y = 5
y = -5/2
So, the y-intercept is (0, -5/2).
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bonsoir pouvez vous m'aidez
Answers
Answer:
Treatment for HIV/AIDS involves taking highly effective medicines called antiretroviral therapy (ART) that work to control the virus [1][2]. ART involves taking a combination of HIV medicines (called an HIV regimen) to suppress the virus and stop the progression of the disease [1]. The goal of treatment is to reduce the amount of HIV in the body and keep it at a low, undetectable level to help prevent further damage to the immune system and reduce the risk of transmitting HIV to others.
In a certain Algebra 2 class of 28 students, 7 of them play basketball and 5 of them play baseball. There are 18 students who play neither sport. What is the probability that a student chosen randomly from the class plays both basketball and baseball?
Answers
Answer:
2 students play both
Step-by-step explanation:n(u)=28
n(b)=7,n(b)=5,n(who play neither sport)=18
HERE,
n(u)=n(b)+n(b)-n(BnB)+n(who play neither sport)
28=7+5-n(BnB)+18
28=30-n(BnB)
n(BnB)=30-28
=2 answer
Find the area of the triangle. Round to the
nearest tenth.
8 yd
98 percent
3 yd
Answers
Answer:
i NEED A PICTURE.
Step-by-step explanation:
First if is an Eigenvector of the matrix A with Eigenvalue 4, will also be an Eigenvalue for any linear combination of the matrix A.
Answers
When the matrices A and B commute, or when they fulfill AB=BA, this is a significant exception.
What is matrix?
A matrix is a rectangular array or table of numbers, symbols, or formulae used to represent mathematical objects or qualities of such things. It is often arranged in rows and columns. For instance, a matrix contains two rows and three columns. a group of integers organized in a rectangular array in rows and columns. Matrix elements or entries refer to numbers. In several disciplines of engineering, physics, economics, statistics, and mathematics, matrices have a wide range of applications.
The eigenvalues and eigenvectors of the sum of two matrices are typically not the same as the sums of the eigenvalues and eigenvectors of the individual matrices. In actuality, there is no way to separate the eigenvalues of A and B from one another.
When a vector v is an eigenvector of both A and B, it is also an eigenvector of A+B, with an eigenvalue equal to the sum of its eigenvalues for A and B, respectively. There is, however, no reason to anticipate that two matrices will share an eigenvector in general. There is no method to create an eigenvector of A+B from two random eigenvectors of A and B alone.
When the matrices A and B commute, or when they fulfill AB=BA, this is a significant exception. In this situation, their invariant spaces coincide, and if both of them are diagonalizable, they are concurrently diagonalizable, which means that their eigenvectors do as well. As was already noted, in this specific instance, the eigenvectors of A+B are likewise the same.
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What is the horizontal distance from the origin to the point (1,4)
Answers
Answer:
given ,
a point , let's say , A( 1 , 4 ) on the cartesion plane.
to find - the horizontal distance of the point from the origin.
\(\underline\bold{using \: Distance \: formula \:} \\ \\ d(AO) = \sqrt{( x_{2} - x_{1}) {}^{2} +( y_{2} - y_{1}) {}^{2} } \\ \\ d(AO) = \sqrt{(1 - 0) {}^{2} + (4 - 0) {}^{2} } \\ \\ d(AO) = \sqrt{1 + 4} \\ \\ d(AO) = \sqrt{5} units \)
hope helpful :D
1. The circumference of a circle is 5811 cm. Find the diameter (D), the radius (r), and the
length of an arc (a) with measure of 140°
A. D: 116 cm:r: 29 cm; a: 160 cm
B. D: 58 cm; r: 29 cm; a: 22.6 cm
C. D: 29 cm; r: 58 cm: a: 11.37 cm
D. D: 58 cm; r: 116 cm: q: 11.37 cm
Answers
Radius = Circumference ÷ 2π
Diameter = 2•Radius
half a number is 21 less than double the number find the number.
Answers
Answer:
14
Step-by-step explanation:
let the number be x
2x is larger than half of x by 21: 2x = 0.5+21
Solve:
2x = 0.5+21
1.5x = 21
x = 14
Write the trigonometric ratio as a simplified fraction.
10. sin B
C9
A
C
6
15 C
B
11. cos A
12. tan A
10.
11.
12.
Answers
The value of the trigonometric ratios are;
sin A = 2/5
cos A = 3/5
tan A = 2/3
How to determine the ratiosIt is important to note that there are six different trigonometric identities and their ratios.
We have;
sine cosinetangentcotangentsecantcosecantFrom the diagram shown, we have;
sin θ = opposite/hypotenuse
cos θ = adjacant/hypotenuse
tan θ = opposite/adjacent
Then,
sin A = 6/15 = 2/5
cos A = 9/15 = 3/5
tan A = 6/9 = 2/3
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The value of the trigonometric ratios are;
sin A = 2/5
cos A = 3/5
tan A = 2/3
How to determine the ratiosIt is important to note that there are six different trigonometric identities and their ratios.
We have;
sine cosinetangentcotangentsecantcosecantFrom the diagram shown, we have;
sin θ = opposite/hypotenuse
cos θ = adjacant/hypotenuse
tan θ = opposite/adjacent
Then,
sin A = 6/15 = 2/5
cos A = 9/15 = 3/5
tan A = 6/9 = 2/3
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2x + (-2x) when simplified is: ?
Answers
Answer:
Hello!
___________________
2x + (-2x) = 0
Step-by-step explanation: Simplify the expression.
Hope this helped you!
5/8 plus2/5 simplest form
Answers
Answer:
1.025 is the anwser in decimal form
Answer:
1 1/40
Step-by-step explanation:
so change 5/8 and 2/5 to have a common denominator, which would be 40, so it would change into 25/40 + 16/40, which is 41/40, just add the numerators and simplify. hope this helped a bit
How many subsets does the set D={c,a,t} have?
Answers
Answer:
There's a constraint in the question. A and B should be and G shouldn't be in the subset. Then A, B and G actually don't have any choices.
Step-by-step explanation:
4. Prove the following identities:
(a) (a ÷cos A+b ÷sin A)²+(a ÷ sin A-b ÷ cos A)²=a²+b²
Answers
By algebra properties and trigonometric formulas, the trigonometric expression (a · cos A + b · sin A)² + (a · sin A - b · cos A)² is equivalent to the algebraic expression a² + b².
How to prove a trigonometric expression
In this problem we must prove that the trigonometric expression (a · cos A + b · sin A)² + (a · sin A - b · cos A)² is equivalent to the algebraic expression a² + b², this can be done both by algebra properties and trigonometric formulas. First, write the given expression:
(a · cos A + b · sin A)² + (a · sin A - b · cos A)²
Second, expand the expression by algebra properties:
a² · cos² A + 2 · a · b · cos A · sin A + b² · sin² A + a² · sin² A - 2 · a · b · cos A · sin A + b² · cos² A
(a² + b²) · cos² A + (2 · a · b - 2 · a · b) · cos A · sin A + (a² + b²) · sin² A
(a² + b²) · (cos² A + sin² A)
Third, use the fundamental trigonometric formula:
a² + b²
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