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

Weekly Math Problem! #8

Solving A Trigonometric Equation. So, I kind of like trigonometric equations. When you're learning College Algebra/Precalculus, the trigonometric equations you get pretty much work out nicely--having the same trigonometric functions in them or allowing you to use trig identities to force your equation to have the same trig functions in them...for the most part. Also, the values for the angle(s) you're solving for tend to be those "special" angle values. This week's trig equation is one I don't recall learning in school, but was exposed to while tutoring. 

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

    ✔️  General form of a trigonometric equation

    ✔️  Pythagorean Theorem

    ✔️  Trigonometric identities

I present to you WMP! #8...

Happy solving! 

Check back on Friday, June 26th for the solution, which will be posted below ⬇️.

Shameless plug: Follow me on Instagram @TheYoungeLady

✏️📓 Solution Time! 📓✏️

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I preface my solution by saying that the my use of colors is more for me as much as it is for you. I hope that makes sense. 🤷🏿

Here's the thing...in solving this problem, the thing that tripped me up the most is moving from the form of the solution to using the appropriate trigonometric addition identity, denoted in blue towards the top of my solution. May I also point out when solving for Φ (phi), that it is best to use both the sine and cosine functions. If not, you run the risk of possibly solving for a slightly incorrect value of Φ by using just one of the functions. For example, if you used arccos( ), to solve for Φ, you would have gotten a positive value, instead of the negative value needed to substitute in the expression to finish solving for x.

One thing I can surely say is, I feel more comfortable solving a problem that looks like this one. This was good for my brain. Oh, and before I forget...I solved for x in radian measure because it's something that I'm not used to doing. I can think a bit more easily in degrees, so I decided not to solve for x in degrees.

◾️ Are you used to solving these types of trigonometric equations??

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

Moving right along to WMP! #9 👍🏿

Cheers!

The Younge Lady

Weekly Math Problem! #7

Solving A Quadratic Equation. This week's problem is related to WMP! #6. We're working with another quadratic equation, except this time we don't have to come up with it. So, no word problem here. What does happen sometimes, which can be highly annoying, is being forced to solve a problem using a specific method when you have other options that you'd prefer to use. You can definitely see this in textbook exercises across various types/levels of mathematics. Lots of professors do this. I am guilty as charged, myself. At least when I've done it, it wasn't to torture my students...I promise. 👀 It was really to expose them and push their abilities, so that they wouldn't be caught by surprise. 😁

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

    ✔️  How to solve rational equations

    ✔️  How to solve quadratic equations

    ✔️  Completing the square method

Ready? If not, here goes WMP! #7 anyway...

Happy solving! 

Check back on Friday, June 19th for the solution, which will be posted below ⬇️.

Shameless plug: Follow me on Instagram @TheYoungeLady

✏️📓 Solution Time! 📓✏️

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I don't really have much to say. So...without further ado, here's my solution:

Here is a graph of the quadratic with the solution (roots) identified:

*This graph was generated on Geogebra.org.*

◾️ How do you feel about this method for solving quadratics?? Love it? Hate it?

◾️ What's your go-to method for solving quadratic equations?? 

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

Up next...WMP! #8 😏

Cheers!

The Younge Lady

Weekly Math Problem! #6

Quadratic Function Application. One of the things that people cannot stand in mathematics, next to fractions is...dare I say it...⚠️word problems⚠️. 🙄 Trust me I get it! 😒 I've encountered hundreds, if not a few thousand, words problems over the years I've been doing mathematics. I'm talking about word problems from algebra, geometry, precalc, calc, differential equations, linear algebra, statistics, standardized tests such as the SAT and GRE, not to mention word problems from the sciences. And still, when I see a word problem, my insides jump just a little bit. It can definitely be tricky to relate the words you're seeing in a problem to some math formula/techniques that you'll need to solve the word problem. If you're super annoyed with word problems, leave a comment down below 👇🏿 and vent a bit.

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

    ✔️  How to convert words/phrases to algebraic expressions

    ✔️  How to solve a quadratic equation

    ✔️  How to find the minimum/maximum value of a quadratic function

You will also need to know a little finance vocabulary, which can be easily looked up. Here goes WMP! #6... 

Happy solving! 

Check back on Friday, June 12th for the solution, which will be posted below ⬇️.

Shameless plug: Follow me on Instagram @TheYoungeLady

✏️📓 Solution Time! 📓✏️

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One of the things that will be helpful when solving a problem is identifying and marking the words/phrases that can be translated into algebraic expressions/equations. In the solution, the key phrases are denoted in blue. 

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Below is the graph of R(x): 

*This graph was generated on Desmos.com.*

The graph of the function isn't part of the original question, however it's great if you can have a visual to confirm or deny the answers you came up with. I showed the point on the graph where no revenue is generated, which is one of the roots (or "zeros") of the function. I also showed the point on the graph where maximum revenue is generated, which is the maximum point (or turning point).

◾️ How did you find this word problem?? Easy? Hard? In between? 

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

See you again, soon, for WMP! #7 🤓

Cheers!

The Younge Lady