Weekly Math Problem #48

Radical Equation. I was in a pinch and decided to look to the topic of solving radical equations for this week's problem. Based on my observations from working with others, mistakes tend to happen after the radical disappears--meaning students seem to understand the mechanism by which the radical should "disappear" and stumble to solve the resulting equation. Let's see how solving this one goes.

To solve this week's problem in completion, you need to recall the following math skills:

        ✔️     How to use exponent rules
        ✔️     How to factor a trinomial

WMP! #48 says to:

Happy solving!

Check back on Friday, May 7th for the solution, which will be posted below ⬇️.

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Buy Me a ☕️ Coffee: TheYoungeLady ( I'm gonna need it this year. 😆 )

✏️📓 Solution Time! 📓✏️

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Solving this equation is straight forward. The radical expression is already isolated so, you can make the radical "disappear" and solve the resulting cubic equation. The factor by grouping method was used to solve the equation, after it was fixed to be equal to zero. 

Checking the potential solutions above wasn't too bad so, it was done below.  

Here is a graph of the two functions involved in the original equation, with the intersection points in black.

If you stuck around to this point, you're a star!

▪️ Let me know what you thought about this week's problem.

Thanks for solving with me this week!

Up next, WMP! #49. 👩🏿‍🏫

Cheers!

The Younge Lady

Weekly Math Problem! #47

2nd Order ODE. Sometimes, topics just come to mind and I say to myself, 🤔 "Haven't done that in a while. I should do it so I don't forget." That's pretty much it. Well, sometimes I can see the problem or parts of the problem and not quite remember the name of the topic. Then I'll have a little digging to do so that I can get the name of the topic. Well, 2nd order ode (second order ordinary differential equation) is the order for this week. 😅 Specifically, we're looking at a non-homogenous equation with constant coefficients.

⚠️Many steps involved.⚠️To solve this week's problem in completion, you need to recall the following math skills:

        ✔️     How to factor a trinomial
        ✔️     How to use the method of undetermined coefficients
        ✔️     How to find derivatives

WMP! #47 says to:

Happy solving!

Check back on Friday, April 23rd for the solution, which will be posted below ⬇️.

Shameless 🔌 Plug: Follow me on Instagram @TheYoungeLady
Buy Me a ☕️ Coffee: TheYoungeLady ( I'm gonna need it this year. 😆 )

✏️📓 Solution Time! 📓✏️

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You can't say I didn't warn you about the many steps involved in the solution to this problem. Why did I do it? Well...because it's good practice and I want to make sure that I can remember math at this level. As I challenge my myself, I challenge you. 

🧐 Let's get it!

I did my best to organize my solution and color code it so that it would be understood a little better.

The general solution to the equation can be broken down into two parts--the homogeneous solution and the particular solution.

I worked on the homogenous solution, before tackling the particular solution. Once I got bot parts, I put them together to complete the general solution to the equation.

This one was quite a bit of work but, it got done! 🤔 I think I'll do another one like this sooner than later. 

▪️ Have you ever encountered this kind of problem when learning about differential equations?

▪️ Leave your responses down below and let me know what you thought about this week's problem.

Thanks for solving with me this week!

Up next, WMP! #48. 👩🏿‍🏫

Cheers!

The Younge Lady

Weekly Math Problem! #35

Polynomial Division. Alright folks. I think I've mentioned this before but, I'm not sure. So, I am mentioning it now. I do my best to make sure I am mixing up the type of problems I post every week. I have learned different types and levels of math over the years and have liked most of it. (Although, I possess a bias for calculus.) As a tutor, I want to make sure that I can help others with various levels of math, especially at the college level. One of the things I have to consider when choosing a problem is making sure that I am able to type the question and it's solution. This week's problem is good. 👍🏿 (I don't know if that's a hint or not. 🤷🏿‍♀️)

To solve this week's problem in completion, you need to recall the following math skills:

        ✔️     How to divide a polynomial by a binomial

Ready? Great! WMP! #35 says:

Happy solving!

Check back on Friday, January 29th for the solution, which will be posted below ⬇️.

Shameless 🔌 Plug: Follow me on Instagram @TheYoungeLady
Buy Me a ☕️ Coffee: TheYoungeLady ( I'm gonna need it this year. 😆 )

✏️📓 Solution Time! 📓✏️

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Jumping right in, the numerator in the problem (which is also the dividend) is prime--it cannot be factored. Since, it cannot be factored and reduced, this division needs to be completed the long way...literally ---> via long division. 🥴 Sorry...

Unfortunately, I couldn't show each individual step of the long division process. (A video is needed for that.) What I've done, instead, is just showed the completed long division in two forms--the first with the undistributed negative sign and the second with the distributed negative sign. **Notice that the dividend lacks a cubic term. So, to proceed with the long division method, a place holder must be used:  0x3 

 

    

As you can see there is a reminder. The reminder should be written as a fraction, with the divisor as the denominator. Putting that along with the quotient shows the final answer as follows: 

Wait...not so fast. Let's check it! (That's one of the things that I like about math--you can check your work). To check, we'll multiply the quotient and the divisor, adding the reminder to it.

Now, you're free to go. The check works out and I am satisfied. 

▪️ Did your solution work out?

▪️ Leave your response down below and let me know what you thought about this week's problem.

Thanks for solving with me this week!

Onward to WMP! #36

Cheers!

The Younge Lady