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This is good but should have used calculus to show monotonic increasing aspect.

Nice presentation. Very clear.

Impressive video, Chris Chappa. Looking forward to your next upload from you. I smashed the thumbs up button on your content. Keep up the fantastic work! Your breakdown of the fundamental identities was incredibly clear. How do you suggest approaching the memorization of these identities for students who struggle with retention?

thank you chris

Excellent explanation. Thank you very much!

I'm starting college in Spring 2025 so I'm just preparing for some of the classes I might struggle with. Your video series really does help and I'm so thankful that you upload these videos for free. You rule man!

I really appreciate the way you explain thing, Prof

That's an awesome explanation.Sets you up for vectors too.Good work teach!!

studying for my calc ii midterm, explaining the relative max/min thing better than my professor could. thank you!!

THANK YOU!!! i watched all 6 parts!! you explained it very well. I was stuck on my homework. now I understand. 😁

Despite what most consumers believe, the Rule of 78s simply determines how much of the total interest (finance) charge is due and payable (earned) at a particular point in time during the loan. Of course the rest of the total interest (finance) charge is unearned. The amount of interest earned and unearned in these types of loans is not calculated as a percentage of the remaining principle, rather it is determined by the Rule. The Rule itself says nothing about having to pay the exact monthly minimum payment or pay off the whole loan in a single lump sump versus making an intermediate payment (i.e. an amount above the minimum but not enough to pay the loan off in full). The Rule simply determines how much interest is earned and unearned at a particular point in time during the loan. The payoff amount at any point in time would always be: Principle + Total Finance Charge + Fees/Late Charges/Etc - Unearned Interest - Payments . . . .

Hello, thank you for these videos I am taking mathematics for teachers 1 and this has been hard to learn with my current professor

tan(θ - 10°) = cot(90° - (θ - 10°)) = cot(80° - θ) that was the answer shown, but shouldn't it be cot(100° - θ) ? cot(90° - (θ - 10°)) cot(90° - θ + 10°) cot(100° - θ)

"cosine of beta is the sine of beta's complement or the complement's sine which is a sine of alpha because that's the complement of beta" I had to laugh at how complex that sounds, even though it's pretty simple lol

My claim is that only 33.33% of your videos in any playlist is in its correct position.

thank you so much

10/10

Hello Professor Chappa, At the 9:06 mark in the video, could I right the and to f-1(x) as 1/3 - 1? or does it have to be written the way you had it as x-1/3?

You are an amazing teacher ! Thank you

Hi Professor, do you know if you had chapter 13.1 voting method posted?

Thank you so much for this video❤

"X"cellent, Professor! We've been going through Transformations for the past two classes where I teach (we meet once a week). Neither does our Pre-Calculus text cover a combined horizontal scaling and shift, for some lame reason.

(p v q)^ ~(p ^ q)

Thanks, Mr. Chris, you really helped me out.

Function f(x) = 0

one to one or one x to one y! Thats brilliants thank you so much!!

thanks pimp

Very helpful to create a tool for work in Excel. Thanks

Nice and clear👏

this really helped me, thankyou so much for the video you saved me some time to revise other topics you're such a great teacher

Hi! great video! I have one question tho. What. does the result at the end tell us about. the association between the two variables?

Thank you!

Amazing work👏

Good luck!!!

I'm working on those skills. Rather than be frustrated over something we can't control. Good job King 👑🤗✈️

You are a saint my good sir and made this so easy to understand. Mind blown

is there any other universal rule for cusp?

6:25

Inclusive or vs. exclusive or is ambiguous in English--we rarely specify which we mean. In informal speech, people usually mean exclusive or in contexts like this--"or else" is assumed.

Thanks. Just saw this on mobius in my class and it wasn't clicking. I feel better about it now.

started playing xordle because of you lol

lol!

you’re my hero other people complicate it on other videos, as soon you said reciprocate my head dumbs it down to opposite and clicks everything, I have no more issues thank you!

Awesome explanation

Well understandable, Thank you!

could've just cancelled out the x?

5:59 Slight clarification: a grey U-shaped region can be formed adjacent to the hypothetical white one, but it has to overlap the 2 clue, violating the clue.

Please start teaching Math 1332, not all Professor are realistic about helping their students. We need more of you.