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 ⬇️.

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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 #70

Eigenvalues. This week, linear algebra came to mind. The last time I did a linear algebra related problem on this blog was in WMP #45. Check it out...it may help you with this week's problem. 👀 *clears throat*. Anyhow, eigenvalues are cool and have lots of applications. For more info, check out the Applications of Eigenvalues and Eigenvectors page from Interactive Mathematics website. 

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

        ✔️     How to find the determinant of a 2x2 matrix
        ✔️     How to solve a quadratic equation
             

WMP! #70 wants us to...

Happy solving!

Check back on Saturday, January 22nd 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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🎶Let's get it started...🎶

The process to finding the eigenvalues of a 2x2 matrix requires working with a polynomial called the characteristic polynomial. Ours will be a quadratic polynomial generated from finding the determinant of (Y - λI2), where I2 is the 2x2 identity matrix.

Now that we have the characteristic polynomial, we need to find it roots. The roots of the characteristic polynomial are the eigenvalues of the matrix. Set the characteristic polynomial equal to zero and solve. Ours is factorable, but if it wasn't, then you'd have the option to use other methods for solving a quadratic equation.

The eigenvalues have been found!

▪️ Hopefully you haven't found the process to finding the eigenvalues of a 2x2 matrix daunting.

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

Thank you for solving with me this week. 😊
📗 WMP! #71 is up next. 

Cheers!

The Younge Lady

Weekly Math Problem #60

Logarithmic Equation. Honestly, I don't want to lose momentum this week. I want to say more but...I...am...tired! 😩😩

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

        ✔️     Properties of Logarithms
        ✔️     Methods to solve a quadratic equation

     

WMP! #60 want us to...

Happy solving!

Check back on Saturday, October 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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If you've solved the problem above, then you would've seen that, indeed, solving a quadratic equation was required. There are options to solving a quadratic equation. How many options you have available to you depends on the type of quadratic equation you have. Below, you will see that I chose to use the completing the square method to solve the resulting quadratic equation. 

Did you forget that I like visuals? (I don't blame you if you did. 😅) The graph below shows the intersection where the LHS of the equation meets the RHS of the equation. As you can see, the intersection occurs when x=2...our solution! 👏🏿

**This plot was created using Geogebra's Graphing Calculator. Click image to enlarge.

▪️ Were you able to solve this week's equation??

▪️ 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! #61. 👍🏿

Cheers!

The Younge Lady