See images for the following problem
Answers
Related Questions
Writing Describe another methodfor solving the expression inExercise 1. Does this method alwayswork? Explain.
2. What is the value of 6x – 3y if x = 5 and y = 1F.11. G.33 H.6 with an exponent of 5 I.65
7 decreased by nThe expression is
The soccer team is making pizzas for a fundraiser. They put1/4 of a pound of cheese on each pizza. If they have 12 one-pound packages of cheese, how many pizzas can they make?
2. A unique solution exists in the entire xy-plane.
3. A unique solution exists in the region y ≤ x.
4. A unique solution exists in the region consisting of all points in the xy-plane except the origin.
5. A unique solution exists in the region x2 + y2 < 1.
Answers
A unique solution exists in the region consisting of all points in the xy-plane except the origin.
The correct option is 4.
The given differential equation is:
(x² + y²)y' = y²
The equation can be rewritten as:
We need to determine a region of the xy-plane for which the differential equation would have a unique solution whose graph passes through a point (x₀, y₀) in the region.
To determine the region, we can use the existence and uniqueness theorem for first-order differential equations.
According to the theorem, a unique solution exists in a region if the differential equation is continuous and satisfies the Lipschitz condition in that region.
To check if the differential equation satisfies the Lipschitz condition, we can take the partial derivative of the equation with respect to y:
dy/dx = y / (x² + y²)
The partial derivative is continuous and bounded in the entire xy-plane except at the origin (x=0, y=0).
Therefore, the differential equation satisfies the Lipschitz condition in the entire xy-plane except at the origin.
Since the differential equation is continuous in the entire xy-plane, a unique solution exists in any region that does not contain the origin. Therefore, the correct answer is:
A unique solution exists in the region consisting of all points in the xy-plane except the origin.
To learn more about the Lipschitz condition;
#SPJ12
Final answer:
The differential equation will have a unique solution in the entire xy-plane except at the origin, as both the function and its partial derivatives are continuous and well-defined everywhere except at that point.
Explanation:
To determine a region of the xy-plane where the differential equation (x2 + y2)y' = y2 has a unique solution passing through a point (x0, y0), we need to consider where the function and its derivative are continuous and well-defined. According to the existence and uniqueness theorem for differential equations, a necessary condition for a unique solution to exist is that the functions of x and y in the equation, as well as their partial derivatives with respect to y, should be continuous in the region around the point (x0, y0).
We note that both the function (x2 + y2)y' and its partial derivative with respect to y, which is 2y, are continuous and well-defined everywhere except at the origin where x = 0 and y = 0. Therefore, a unique solution exists in the region consisting of all points in the xy-plane except the origin.
From the given options, the correct answer is:
4. A unique solution exists in the region consisting of all points in the xy-plane except the origin.
Learn more about Differential Equations here:
#SPJ3
Answers
Answer: y/10
Step-by-step explanation: step 1 = simplify y/100
step 2 = (5/32 x 64) x y/100
step 3 = simplify 5/32
step 4 = (5/32 x 64) x y/100
step 5 = The answer is y/10
Answers
Answer:
=(m2p+−2r7)(m+−5p4r2)
=(m2p)(m)+(m2p)(−5p4r2)+(−2r7)(m)+(−2r7)(−5p4r2)
=m3p−5m2p5r2−2mr7+10p4r9
=10p4r9−5m2p5r2−2mr7+m3p
Step-by-step explanation:
:D
Answers
Answer:
In multiplication the answer is called PRODUCT and in division the answer is called quotient.
Step-by-step explanation:
I hope that helps and you get a good grade :)
The answer to a multiplication problem is called a Product. The answer to a division problem is called the quotient.
Answers
Answer:x=−8 and y=8
Step-by-step explanation: Do you want it solved step by step?
Answer:
One solution, (-8,8)
x = -8
y = 8
Step-by-step explanation:
-6x + 3y = 72 then 3y = 72 + 6x, y = 24 + 2x
5x + 8y = 24
substitute for y:
5x + 8(24 + 2x) = 24
5x + 192 + 16x = 24
21x = -168
x = -8
y = 24 + 2(-8) = 8
Answers
Answer: We should reject the null if the test statistic is greater than 1.895.
Step-by-step explanation:
We assume the population to be normally distributed.
Given: Sample size : , which is asmall sample (n<30), so we use t-test.
We always reject the null hypothesis if the absolute t-value is greater than critical value.
Therefore, We should reject the null if the test statistic is greater than 1.895.