Algebra I question ((5y-)-(-4y+6)=3) by Marquitta

Hi, Marquitta.


I’m assuming your question is how to solve this problem for y. Let me give you a similar question to walk you through the challenging parts of this equation.

Consider:                                                 (3x)-(-8x+2)=4, solve for x

The first thing I’d want to do is eliminate that irritating double negative. So, I’m going to rewrite the problem.

                                                                       (3x)-1(-8x+2) = 4

When you recognize that there is really a (-1) multiplying the expression (-8x-2), you can see that we can go ahead and use the distributive property to make those negatives go away:



                                                     (3x)-1(-8x+2)=4            -1( -8x) = 8x

                                                                                          -1(2) = -2
                                                     3x + 8x -2 = 4

Now, we can combine like terms and solve:

                                         3x + 8x -2 = 4         3x + 8x = 11x 
                                                                 
                                         11x -2 = 4              add 2 to both sides

                                         11x=6                   divide by the coefficient of x, 11

                                           x = 6/11            fractional answer!

Your problem is very similar. If you get stuck, just do what I did. The numbers are different, but the process is exactly the same.

Let me know if you need more help! Thanks for the question!



Mrs. Young

higher order derivatives question by Unknown

Question: I'm trying to solve for t given:


y''''(t)-10y'''(t)+35y''(t)-50y'(t)+24y(t) = e^(5t)

and that

y'''(0) = y''(0) = y'(0) = y(0) = 0



any hints??



Answer:
Thank you for your question. I don’t get a lot of cal. questions…so this will be fun!

In general, when we’re dealing with finding higher order derivatives, it is important to simplify the process in your mind by only thinking in terms of first order derivatives. In other words,

f'' (x) = f ' (f ' (x) )

Or in words, “the 2nd derivative of x is the derivative of the first derivative”

“the 3nd derivative of x is the derivative of the 2nd derivative”

Etc…

Also, look at the given information:

y'''(0) = y''(0) = y'(0) = y(0) = 0

Why was this given? What information does this give you that is necessary to solve for t?

Next, the exponential term is a real headache. How could you eliminate it?



I hope this helps. If you need further help, you can email me or leave a comment to this post. I can provide a sample problem.



Thanks.



Mrs. Young