Weekly Math Problem #52

Truth Table. Part of the reason I like math is because it's like solving a puzzle. I like puzzles and puzzle-type games. One official definition of puzzle--as a noun--is "a question, problem, or contrivance designed for testing ingenuity" (Merriam-Webster online dictionary). 🤔 Interesting. I mean...math definitely does that. One area of math that definitely gives me that puzzle vibe is logic. So, that's what we're doing this week. Logic was part of the NYS math curriculum when I attended high school. I vividly remember being tested on truth tables and logic proofs. Checkout WMP #26 for a logic proof.

Also, if you're into puzzles and such, check out these Math and Logic Puzzles from MATHisFUN.com.

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

        ✔️     How to use mathematical logical connectives

WMP! #52 wants us to...

Happy solving!

Check back on Saturday, June 5th for the solution, which will be posted below ⬇️.

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✏️📓 Solution Time! 📓✏️

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Here's my truth table. If you found yourself constantly checking the truth tables for the logical connectives to make sure you weren't mixing up the T's and F's, then you're normal. It's easy to get them mixed up. I went over them multiple times.

▪️ Did you truth table have the same results??

▪️ 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! #52. 👍🏿

Cheers!

The Younge Lady

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 #50

Limits. For the most part, I understand limits. It reminds me of integration...where I get the idea but most of the work is knowing the techniques and when to implement them. Such is limits. There are different techniques and knowing when to implement them is important...well...it's important in math. If you're not into math, you most likely don't care. 🤷🏿‍♀️

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

        ✔️     How to find limits involving radical expressions 

Here is WMP! #50:

Happy solving!

Check back on Friday, May 21st 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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Just when you think you have it all figured out...you don't, sometimes. 😩 Let's get into this solution. 

The first thing I did was substitute -1 into the expression to see if a value pops out...but I was met with an indeterminate form.

 

The indeterminate form doesn't help me so, I tried another method--rationalizing the numerator--to see if that would help me with substitution.

With the rationalized form of the expression, I tried substitution again.

Lo and behold...indeterminate form again. 😩 Now, I need another method. This one, I know, won't fail me--L'Hôpital's Rule.

Ahhh...an answer, finally! All of that work to come up with 1/6. 😅🤷🏿‍♀️

▪️ How do you solve this problem??

▪️ Did you go straight to L'Hôpital's Rule??

▪️ 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 #49

Circle Geometry. Good ol' circles. Some really cool items are circular--pizzas, quarters, rings, pies, doughnuts, etc. Yeah...I like circles. So, we'll be working with one this week.

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

        ✔️     How to use circle theorems

Here is WMP! #49:

Happy solving!

Check back on Friday, May 14th 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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Alright y'all...I did the best I could to show my calculations and theorems/rules used. I also labeled the image...and in true Younge Lady fashion, I color-coded stuff. 

😁

▪️ How do you feel about geometry??

▪️ 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! #50. 👍🏿

Cheers!

The Younge Lady

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 ⬇️.

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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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