<h3>
<em>The complete question:</em></h3>
<u><em> </em></u><u>Harold uses the binomial theorem to expand the binomial </u>
<u />
<u>(a) What is the sum in summation notation that he uses to express the expansion?
</u>
<u>(b) Write the simplified terms of the expansion.</u>
Answer:
(a). 
(b).
Step-by-step explanation:
(a).
The binomial theorem says
For our binomial this gives
(b).
We simplify the terms of the expansion and get:
A) √50 = √(25 x 2) =√(5² x 2) = 5√2, what Jacklyn did is the other way round, instead of putting the perfect square out of the radical & keep the 2 inside, she inversed the sens of the operation
b) We have to find the square of the smaller & largest numbers that are near 50:
7² = 49 & 8² = 64==> so 49<50<64 & the number is between the square root of 7 & the square root of 8, but we also notice that 50 is very very near 49, hence let's try 7.1==> 7² = 7.1 x 7.1 = 50.41, which is a very good approximation. Then the approx. to √50 ≈ 50.41
Answer:
Verified
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:
-2.2*2.2*-1.6=7.744
Hope this helps!
