Weekly Math Problem #57

Derivative. Derivatives are so versatile! I couldn't believe the various ways derivatives were used in Calculus 1. When we got to a "new" topic in the course, it was the same derivative in a new light. It was quite interesting to me. Once you learn how to find a derivative, you that for the majority of the course. This did involved lots of word problems, especially when it came its various types of applications. 😩 Luckily for us, this week's problem isn't that kind of word problem. 

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

        ✔️     Derivative rules
        ✔️     Substitution and evaluation
        

WMP! #57 says the following:

Happy solving!

Check back on Friday, October 1st 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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And we're back to look at the solution to this week's problem!

The function we've been given is a rational function, and the quotient rule for derivatives is needed to find its derivative. The cool thing about this problem is that we do not need to know what f(x) or g(x) are equal to, to find the solution. 😉

First, let's find get the derivative of h(x): 

Now that we have the derivative of h(x), we can use the given information to see what h'(2) is:

That's all folks! Without knowing what what f(x) and g(x) are, we're able to figure out what h'(2) is. Nice. 😎

▪️ How did you solve this problem??

▪️ Did you get the same answer??

▪️ 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! #58. 👩🏿‍🏫

Cheers!

The Younge Lady

Weekly Math Problem #56

Box-and-Whisker Plot. You know I like my visuals. I don't come from Missouri but, when it comes to math, I need you to show me. 😉 (You see what I did there?) Box-and-whisker plots (box plots) are cool because they show you characteristics of the data you're working with that may be very useful to you. You can definitely see whether or not the data set is skewed. Also, you may be able to tell what the distribution of the data is. These days, software is used to create boxplots by those who need to use such information. Once a data set isn't too crazy, doing a box plot by hand isn't too bad. So, that's what we'll be doing this week. 

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

        ✔️     How to find the five-number summary of a data set
        ✔️     How to construct a box plot
        

Here is what WMP! #56 says...

Happy solving!

Check back on Friday, September 24th 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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Are you ready? I think I am so...let's go! I think a good way to tackle this problem is to outline steps to take.

Step 1. Order the values from least to greatest.

It's super important to put your data ascending order. If not, then the values in the five-number summary will be incorrect. 

Now that the data has been put in order, we can get the five-number summary needed to help us produce the boxplot. 

Step 2. Identify the extreme values.

The extreme values are two of the five numbers needed to construct the boxplot. These values are the minimum and maximum values and they are used to make sure the whiskers are the right length. Since the data set is in order, those values are on either end of it. 

Step 3. Find the median.

The median is the middle number in an ordered data set and is the third number we're finding in the data set. This data set has twenty values in it, which means there are two numbers in the middle. When this happens, the median is computed by taking the average of the two middle numbers. (The median is also known as the second quartile, Q2)

Step 4. Find the first and third quartiles.

The remaining two numbers part of the five-number summary are the first and third quartiles, Q1 and Q3 respectively. To find these, the ordered data set needs to be broken into two subsets--the lower half and the upper half. Since the data set has twenty values in it, the lower and upper halves will have 10 values each. 

Q1 is the median of the lower half, while Q3 is the median of the upper half.

Step 5. Construct the box plot.

Time to draw! We've found all the numbers part of the five-number summary and here they are listed in ascending order: 

Minimum = 32

          Q1 = 56

      Median = 74.5

             Q3 = 82.5

Maximum = 99 

We'll construct an appropriate timeline for the plot, place a marker at the appropriate places over the number line, then draw the whiskers and box. 

...And there you have it--a box plot for the test scores data set we worked with!

(I checked my work using Microsoft Excel and Google Sheets but kept getting a different value for Q3. 🤷🏿‍♀️ Not sure why. Share any insights you have. I checked to see if I had any errors in my work. Not sure if I missed any errors I may have. 🤷🏿‍♀️)

▪️ Did you get the same values for the five-number summary??

▪️ Did you use technology to check your work??

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

Thanks for solving with me this week!

On to WMP! #57. 🤸🏿‍♂️

Cheers!

The Younge Lady

Weekly Math Problem #55

System of Linear Equations. I know it has been a while since the last problem (of which I still owe you my solution 🥴...it's coming, it's coming). Please don't disown me. When life throws you curveballs, you learn how to catch 'em. ⚾️🤷🏿‍♀️ ...And, I'm still learning how to catch. 

So, to get my feet wet, I'm starting with the problem below. To solve this week's problem in completion, you need to recall the following math skills:

        ✔️     Methods for solving a system of linear equations
        

WMP! #55 says to...

Happy solving!

Check back on Friday, September 17th 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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I went through my blog to see which WMPs already involved this week's topic. So,  check out WMP! #4 and WMP! #28 to how I solved those systems. WMP! #4 is more similar to this week's problem than WMP! #28 is. 

Just as a reminder, you have multiple options to use when deciding how to solve the system--addition/elimination method, substitution method, and Guassian elimination (if you're feeling fancy 😉). I am going to go ahead and do the substitution method. The first thing I do is label my equation. This helps me to keep track of things.

Next, I need to examine the equations to see which methods I want to move forward with. For the fun of it, I've decided to do the substitution method. Equations (A) and (B) both possess variables with "1" coefficients. Since equation (A) has a variable with a positive 1 coefficient, I'll just work with that. 

I isolate the variable and label the rearranged version of the equation:

Now, I will substitute this equation into the other two original equations (B) and (C). This allows me to reduce the variables--going from three variables down to two. 

After substituting and simplifying, I have a system of two linear equations in two variables. I examine this system and proceed with the substitution method again. Repeating a similar process from above.

Once this round of substitution is complete, I have come up with a value for one of the variables. Moving forward with with backward substitution...lol...I am able to find the values for the remaining variables and present my solution.

As you may know with mathematics, getting an answer doesn't mean that it's correct. So, I checked my solution in the original system to make sure that it works completely.

Thanks for hanging with me this week. It feels good to get back into the swing of things. 

▪️ What is your preferred method for solving a system like the one from this week's problem??

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

Thanks for sticking around and solving with me this week!

Up next, WMP! #56. 👍🏿

Cheers!

The Younge Lady