Answer:
y has a finite solution for any value y_0 ≠ 0.
Step-by-step explanation:
Given the differential equation
y' + y³ = 0
We can rewrite this as
dy/dx + y³ = 0
Multiplying through by dx
dy + y³dx = 0
Divide through by y³, we have
dy/y³ + dx = 0
dy/y³ = -dx
Integrating both sides
-1/(2y²) = - x + c
Multiplying through by -1, we have
1/(2y²) = x + C (Where C = -c)
Applying the initial condition y(0) = y_0, put x = 0, and y = y_0
1/(2y_0²) = 0 + C
C = 1/(2y_0²)
So
1/(2y²) = x + 1/(2y_0²)
2y² = 1/[x + 1/(2y_0²)]
y² = 1/[2x + 1/(y_0²)]
y = 1/[2x + 1/(y_0²)]½
This is the required solution to the initial value problem.
The interval of the solution depends on the value of y_0. There are infinitely many solutions for y_0 assumes a real number.
For y_0 = 0, the solution has an expression 1/0, which makes the solution infinite.
With this, y has a finite solution for any value y_0 ≠ 0.
Answer:
1. -32
2. -46
Step-by-step explanation:
1. When muliplying a number with a postive number and a negative number the answer will be a negative number
2. When you have a negative number and when you have a postive number and you are subtracting your answer has to be a negative answer
Answer:
Remote interior angle
Step-by-step explanation:
<Y is a remote (non-adjacent) interior angle for <w.
Answer:
The Proof is given below.
Step-by-step explanation:
Given:
P is the center of Circle
∠ONE ≅ ∠TEN
To Prove:
∠5 ≅ ∠6
Proof:
Exterior Angle Theorem:
Exterior Angle Property of a Triangle states that measure of exterior angle of a triangle is equals to the sum of measures of its interior opposite angles.
STATEMENT REASON
1. So In ΔONE,
1. Exterior Angle Property of a Triangle.
2. Similarly In ΔTEN,
2. Exterior Angle Property of a Triangle.
3. But , ∠ONE ≅ ∠TEN 3. Given
4. And P is the center of circle So
4.radius of same circle
5. ΔPEN is an Isosceles triangle,
∴ ∠ 1 ≅ ∠ 2 5. Isosceles triangle property
6. ∴ ∠5 ≅ ∠6 6. From 3 and 5 Transitive Property.........Proved
4cm I think, because it’s usually a even and equal number. But don’t take my word for it.
