Weekly Math Problem #80

Equation of a Circle. We're definitely keeping our algebra skills sharp with this week's problem. 🧠 As the saying goes, "Repetition is the mother of all learning". So, you will definitely see skills being repeated in the problems as well the combination of them to solve the problems. The equation of a circle is part of a larger topic called conic sections. Let's  go!  🏃🏿‍♀️

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

       ✔️     Substitution
       ✔️     Completing the square technique
       ✔️     How to solve a quadratic equation

            

WMP #80 wants us to...

Happy solving!

Check back on Saturday, April 9th 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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Part a.

To determine the center and radius of the circle, the completing the square technique needs to be used on the given equation. To start that process, the constant needs to be isolated. Once the equation is in standard form, then the center and radius can be identified.

The center of the circle is (1, -1) and its radius is 1 unit. This was figured out without graphing it. We'll view the graph later in this post.

Part b.

To show that the point (1, -2) is a point of intersection for circle C and the given line, the substitution method was used. The equation of the line was substituted for y in the equation of the circle. The equation of the circle was then simplified into a factorable quadratic equation. This allows for values of x to be solved for...one of which is the x-value in the given point. It is then shown that the corresponding y-value is indeed the y-value in the given point.

Now that we've completed both parts of the problem, let's view the graph:

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

 

▪️ Did you use the same methods above to solve the problem? If so, please share.

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

Thank you for solving with me this week. ✏️
Let's move on to WMP! #81. 💪🏿

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

Weekly Math Problem! #25

Basic Probability. I believe this is the first probability problem I'm doing on the blog. I've had a love/hate relationship with probability in the past. Like a lot of other things in life, repetition helped over the years.Let's not talk about Probability Theory. 😣 When I was learning it, my brain took a long while to grasp it. When that course was over, I breathed a sigh of relief. Some things really do take time. In the the case of my brain and probability theory, it was taking more time than the semester would allow. 😅

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

        ✔️ How to use basic probability formulas

Yeah, that's it. Here is WMP! #25:

Happy solving!

Check back on Friday, October 30th for the solution, which will be posted below ⬇️.

Shameless plug: Follow me on Instagram @TheYoungeLady

✏️📓 Solution Time! 📓✏️

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Well, once you get the correct formulas, you just need to make sure that you put the given values in the correct places in the formulas. (I can't tell you how many times I've seen that kind of mistake.) Here's how I worked out the questions:

Notice in part (iv), I gave an explanation why the events are independent, even though the question didn't ask, "why or why not?" It's not a coincidence that the answer from part (iv) is the same as the answer from part (i). When events are independent, one has no effect on the other. So, the probability of both events occurring is the same as multiplying their individual probabilities. Read more about independent events from MathisFun's page, Probability: Independent Events. 

 

▪️ Did you find these problems easy to solve??

▪️ How do you feel about probability??

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

Thanks for solving with me this week!

See you next week for WMP! #26

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Cheers!

The Younge Lady