The area of a rectangle is 35 ft squared , and the length of the rectangle is 3 ft more than twice the width. find the dimension
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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:
The polynomial that represent twice the sum of - x +6 and 7
+ x -1 is : 4
+10
<h3>What is a polynomial?</h3>
A polynomial is any algebraic expression that has the least value of the power of its variable as 2.
When the highest value of the polynomial is 2, it is a called a quadratic expression.
Analysis:
2( -5 -x +6 + 7
+x -1)
2( 2 + 5) =
4 + 10
In conclusion, the polynomial that represents the above expressions is 4 + 10
Learn more about polynomials: brainly.com/question/2833285
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