Weekly Math Problem #76

Weighted Average. Sometimes, I find problems just by Googling a topic or question type. So, this time I recalled computing a weighted average/mean and wanted to see what worksheets were available. In my search results was a [Weighted Averages Worksheet] from WOU. I've chosen problem 1 from the worksheet.

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

        ✔️     How to compute a weighted average/mean        

            

WMP! #76 says ...

Happy solving!

Check back on Saturday, April 2nd for the solution, which will be posted below ⬇️.

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✏️📓 Solution Time! 📓✏️

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Computing a weighted average is something that, I find, students don't know how to do. When they are looking at grading distribution from a syllabus for a course, they're, sometimes, not too sure how to compute it. Hopefully the solution below is helpful.

When computing a weighted average, you should convert the each percent to its decimal equivalent, before multiplying it by the score or the average score for the specific category.

Student X's grade, using all of the scores, works out to be about 82.2%.

o------------------------------------o

Student X's grade, after dropping the missed homework assignment (grade of 0/10), works out to be about 87.5%--a 5.3% increase.

▪️ Have you ever calculated a weighted average before?

▪️ Did you get the same averages I got?

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

Thank you for solving with me this week. ✏️
We're on to WMP! #77. 🤓

Cheers!

The Younge Lady

Weekly Math Problem #75

1st Order ODE. This week's problem type was inspired by a student who just wanted to review and be more familiar with differential equations (of the ordinary type). I rarely get a student who needs assistance with differential equations, so you know I was excited to help the student. 🤩 These types of sessions are great for me because they force me to remember concepts and topics I don't use often. It also allows me to stay sharp. 🔪

Check out WMP #2 and WMP #47 for other problems involving differential equations. 

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

        ✔️     How to solve a 1st order, linear differential equation        

             

WMP! #75 wants us to ...

Happy solving!

Check back on Saturday, February 26th 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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If you've checked out my previous differential equation WMPs, then you're aware that solutions to the problems are not short. 😒 Nonetheless, here we go... 

Once it's been identified that we're dealing with a first order, linear ordinary differential equation, it need to be put in a form that will allow us to move forward with solving it. Make the coefficient of dy/dt 1, then identify p(t) and g(t). 

Now that p(t) has been identified, we can now find the integrating factor.

The integrating factor is crucial in figuring out what the function is. 

Figuring out the function is great, but we're not done yet. We've got to deal with the constant. Now, we'll use the condition provided in the problem.

We have a function, and we have the value of the constant, C, that will yield the specified condition. Let's put it together.

And before we go, let's take a quick look at the function we just found:

** This plot was generated using Geogebra.org's calculator. **

▪️ Were you able to solve for y?
▪️ Let me know what you thought about this week's problem in the comments section. 

Thank you for solving with me this week. ✏️
We're on to WMP! #76. 🤓

Cheers!

The Younge Lady

Weekly Math Problem #74

Profit. As I browse my many materials, I landed upon a word problem. This one has a financial application to it. Nothing to be too concerned about...even if you don't have a financial background, you will be able to understand it. Your algebra background is far more important, in this case. 

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

        ✔️     How to solve a quadratic equation        

             

WMP! #74 says...

Happy solving!

Check back on Saturday, February 19th 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 folks, let's get into this solution... 

Step 1:  Find the profit function

Step 2:  Setup the specified profit condition

This quadratic equation can be solved using two methods.

Step 3a:  Solve via the factoring

Step 3b:  Solve via quadratic formula

Step 4:  Answer the question

With the given conditions of revenue and cost for the company, it is found that a profit of $300 will be generated by producing either 20 or 60 units of product.

Here is plot of the profit function:

** This plot was generated using Geogebra.org's calculator. **

▪️ Were you able to find the two values of x?
▪️ If so, what method did you use?

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

Thank you for solving with me this week. ✏️
WMP! #75 is up next. 🏌🏿‍♀️

Cheers!

The Younge Lady

Weekly Math Problem #73

Exponents. I found this week's problem on the internet. 👍🏿 We'll be working with exponents this week. For some, working with exponents isn't a big deal. For others, it's confusing/annoying, and I can understand why. No judgment here. So let's take it back to simplifying rational expressions, where the answer should have *positive exponents only*.

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

        ✔️     Properties/Laws of exponents        

             

WMP! #73 want us to...

Happy solving!

Check back on Saturday, February 12th 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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One of the cool things about math is...there is more than one way to simplify or solve something. 

When I looked at this week's problem, I realized that there were multiple ways for me to use the exponent rules to simplify the rational expression. I settled on the one below. I color-coded it so that it would be easier to follow.

First, I went inside the parentheses and used the rules to ensure that I had positive exponents. (Having a negative coefficient is fine.) Then I used my skills to deal with the negative exponent on the outside of the expression. Lastly, I "distributed" that outer exponent to every portion of the rational expression and completed my simplification. 

I used five different exponent rules to simplify this rational expression. 👩🏿‍🏫

▪️ Were you able to simplify the expression?
▪️ If so, did you do it a different way?

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

Thank you for solving with me this week. ✏️
Up next...WMP! #74. 

Cheers!

The Younge Lady