Hey can you please help me posted picture of question
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Answer:
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Step-by-step explanation:
Question:-
- We are given the following non-homogeneous ODE as follows:
- A general solution to the above ODE is also given as:
- We are to prove that every member of the family of curves defined by the above given function ( y ) is indeed a solution to the given ODE.
Solution:-
- To determine the validity of the solution we will first compute the first derivative of the given function ( y ) as follows. Apply the quotient rule.
- Now we will plug in the evaluated first derivative ( y' ) and function ( y ) into the given ODE and prove that right hand side is equal to the left hand side of the equality as follows:
- The equality holds true for all values of " C "; hence, the function ( y ) is the general solution to the given ODE.
- To determine the complete solution subjected to the initial conditions y (1) = 3. We would need the evaluate the value of constant ( C ) such that the solution ( y ) is satisfied as follows:
- Therefore, the complete solution to the given ODE can be expressed as:
- To determine the complete solution subjected to the initial conditions y (3) = 1. We would need the evaluate the value of constant ( C ) such that the solution ( y ) is satisfied as follows:
- Therefore, the complete solution to the given ODE can be expressed as:
Micah did not explain the last step correctly. You cannot cross out a term from the numerator and denominator unless it is a factor. In other words, x² needed to be multiplied and not added in order to cross it out.
Answer: 0.0667117 * miles
Step-by-step explanation: The Earth is one astronomical unit from the sun i.e.1AU= 93 million miles.The angular speed of the Earth traveling around the sun is approximately 0.9863 degrees per day. If we assume the orbit of the Earth is completely circular, what is the linear speed in miles per hour?
Step-by-step explanation: First, a day has 24 hours. Knowing how far the earth travels in day we can say:
0,9863 degrees/day = 0,9863 degrees/(24 hours)
0,9863 degrees/day = 0.0411 degrees/hours
Also, we know the orbit completely circular, so the total distance on, degrees, is 360°. Also this distance can be know with the formula:
Total Circuference = 360° = 2*pi* R
Because Radius is variable for any circle. It is say that:
360° = 2*pi radians
WIth this relation, we can know how many radians are 0.0411 degrees
360/0.0411 = (2*pi)/x
x = (2*pi*0.0411)/(360)
X = 0.00071733032
X is how much the Earth travels per hour in Radians.
Multiplying per Radius:
Earth distance traveled per hour = 0.0667117 * miles