Weekly Math Problem #51

Differentiation. Coming back to a calculus classic this week--the derivative! I feel like calculus helps my mind to feel nice. 😌

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

        ✔️     How to find the derivative of a polynomial

WMP! #51 says...

Happy solving!

Check back on Friday, May 28th 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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We've been asked to find the derivative of a polynomial written in product form. This lends itself very easily to the product rule for differentiation. (Also, this is the way to do it because, expanding the polynomial is too time consuming. 😩) This requires us to identify the factors of the polynomial so that we can tag them accordingly. The formula below has f and g in it but, other identifiers can be used. After identifying the factors, I find the derivative for each one, then plug in all components into the formula.

As soon as you complete the substitution, you have found the derivative. The remaining work that's done is for simplification and better presentation of the derivative. 

▪️ Were you able to find the derivative??

▪️ Let me know what you thought about this week's problem in the comments section.

Thanks for solving with me this week!

Up next, WMP! #51. 👍🏿

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

Weekly Math Problem! #9

Solving A Rational Equation. I definitely get why people don't like fractions. They can be super annoying to deal with, especially when the fractions have variables in them. 🙄 Plus, mathematics has a few stipulations concerning fractions that must not be ignored--like the denominators having to be the same before being able to add/subtract them. I guess...🤷🏿...lol.

If you don't like basic fractions, then you're surely not gonna like this week's problem. And you know what? You have every right not to like it. L👀k below to see why I said what I said.

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

    ✔️  Methods for solving rational equations

    ✔️  Factoring polynomials

    ✔️  Multiplying binomials

Alrighty...here is WMP! #9...

Happy solving! 

Check back on Friday, July 3rd for the solution, which will be posted below ⬇️.

Shameless plug: Follow me on Instagram @TheYoungeLady

✏️📓 Solution Time! 📓✏️

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I'm definitely a fan of getting rid of fractions when solving rational equations. As you can see, the original equation was reduced to solving a quadratic equation, which yielded distinct roots. ⚠️ CHECK YOUR SOLUTION(S)! ⚠️ Even though the quadratic yielded two roots, there is no guarantee that those roots will be the solutions for the original rational equation. They are potential solutions, awaiting your check for them to be verified solutions. My check is below. You don't have to check "by hand" like I did below. (I did it like that to keep my skills sharpened.) Feel free to use a calculator or mathematics software to aid you in checking the solution. (Of course, the tool you choose to use will depend on the situation you're in.) 

However you choose to check the potential solutions, you should find that both of them satisfy the original rational equation. 👍🏿

◾️ How you handle rational equations??

◾️ When was the last time you even solved an equation like this??

◾️ Comment below with your responses and let me know what you thought about this week's problem.

Wow...we're close to WMP! #10 😲

Cheers!

The Younge Lady