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Interpret proportionality constants

Sal interpret what the constant of proportionality means in a context.

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  • duskpin sapling style avatar for user 2025.pbaker
    I'm still really confused :/
    (12 votes)
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  • leafers ultimate style avatar for user Abe
    This whole concept confuses me. If d=2c, and if d is dollars, and c is cupcakes, the equation directly reads dollar equals two cupcake, which means that one dollar equals two cupcakes, so I should get two cupcakes for one dollar. Even if I divide d by two, I get d/2=c, and if I divide a dollar by two, I get 50 cents equals one cupcake. I just don't understand how Sal got the answer that it is two dollars per cupcake. I saw his formula but the formula doesn't make sense. Can someone please help?
    (8 votes)
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    • piceratops ultimate style avatar for user Marcus
      Necroposting, but maybe my comment will be helpful to others who go through this lesson at a later date. Let d be the amount of dollars to pay and c the number of cupcakes. Then d=2c can be interpreted as the amount of dollars to pay is 2 times the number of cupcakes. Hope this helps.
      (7 votes)
  • blobby green style avatar for user orellanaja
    bruh this is mad confusing.
    (11 votes)
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  • duskpin seedling style avatar for user Monica Juarez
    how would h equal 1/5
    (3 votes)
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    • blobby green style avatar for user velvet.negative
      It took me a while to understand this, too. I was reading the equation as a very direct statement instead of solving for d, which is probably what you are doing, too. Here's a breakdown:

      d=5h
      This seems like 1 of d (1 cm) is equal to 5 of h (5 hours), right? But that's not solving for d - that's assigning a value of 1 to d and then interpreting it as a statement rather than an equation.

      d=5h

      d (whatever this number is) is the equivalent of 5 of h. So, if h has a value of 1 (one hour), then to get the value of d, we have to multiply the value of h by 5. We are not saying literally 5 hours - we are saying the value of the depth in cm is the equivalent of 5 times the value of h.

      So let's give h a value of 1, because each of h is a single hour. That means the equation reads like this: d = 5 x 1. This means the ratio of d to h is 5:1, or that the value of h is 1/5 that of d.

      I hope this helps!
      (6 votes)
  • blobby green style avatar for user Lydia
    All of this makes sense to me, but has anyone encountered the euro/dollar question in practice? I can't figure out how to solve it.

    For those who haven't seen it, e (euro) = 17/20 d (dollar)

    They then ask how many euros we need for one dollar, and vice versa.

    I don't even know where to start... someone explain?
    (2 votes)
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  • hopper cool style avatar for user Malachi
    How does this work with fractions?
    (3 votes)
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  • marcimus pink style avatar for user rennephillips0
    but b kinda makes sense because you can sell cupcakes for a dollar which makes it more difficult and confusing to just pick A for some of ya saying "oh A dosn't makes sense" i know i said it to not putting any words into any bodys mouth just saying not confusing you just saying what comes to mind
    (3 votes)
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  • leaf green style avatar for user Sean Cassidy
    I've been having the hardest time with these. A ratio of 6 books to 21 dollars is a b:d ratio of . But, the algebraic equivalent is not 6b=21d, but the opposite, 21b=6d. It seems counter-intuitive. I think the reason I've been confused is because I got used to doing something like 6/21 x b/d in dimensional analysis. But that's an expression rather than an equation. If I think of it as the equation 6/21 = b/d, then I can divide both sides by one of the units and get the rate/constant=. So, the heart of my confusion seems to be this question: why do I represent this idea of books to dollars as an inverted equation in linear algebra, but multiply quantities directly by their units as an expression in dimensional analysis? I think if I understood why these are opposite, I would stop making this silly mistake.
    (3 votes)
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  • purple pi purple style avatar for user louisaandgreta
    this is confusing because d is already 1d so 1cm therefore it should take 5 hours. 1d=5h.
    (3 votes)
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  • leafers ultimate style avatar for user ssr1004
    Isn't d=2c also equal to 2c=d in the Bettys Bakery problem?
    (2 votes)
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Video transcript

- [Instructor] We can calculate the depth d of snow, in centimeters, that accumulates in Harper's yard during the first h hours of a snowstorm using the equation d is equal to five times h. So d is the depth of snow in centimeters, h is time that elapses in hours. How many hours does it take for one centimeter of snow to accumulate in Harper's yard? Pause this video and see if you can figure that out. All right so we wanna figure out what h gives us a d of one centimeter. Remember d is measured in centimeters. So we really just need to solve the equation one centimeter, when d is equal to one, what is h going to be? And to solve for h we just need to divide both sides by five. So you divide both sides by five, the coefficient on the h, and you are left with h is equal to 1/5. And the unit for h is hours, 1/5 of an hour. So 1/5 of an hour. If they had minutes there, then you would say well 1/5 of an hour, there's 60 minutes, well this is 12 minutes. But they just want it as a number of hours, so 1/5 of an hour. How many centimeters of snow accumulates in per hour? Or this is a little bit of a typo. How many centimeters of snow accumulate in we could say one hour, in one hour, or they could have said how many centimeters of snow accumulate per hour. That's another way of thinking about it. So we could get rid of per hour. So pause the video and see if you can figure that out. Well there's a couple of ways to think about it. Perhaps the easiest one is to say, well what is d when h is equal to one? And so we could just say d when h is equal to one, when only one hour has elapsed, well it's going to be five times one which is equal to five, and our units for d are in centimeters. So five centimeters. Let's do another example. Betty's Bakery calculates the total price d in dollars for c cupcakes using the equation d is equal to two c. What does two mean in this situation? So pause this video and see if you can answer this question. So remember d is in dollars for c cupcakes. Now one way to think about it is, what happens if we take d is equal to two times c, what happens if we divide both sides by c? You have d over c is equal to two. And so what would be the units right over here? Well we have dollars, d dollars, over c cupcakes. So this would be $2, because that's the units for d, per cupcake, dollars per cupcake. This is the unit rate per cupcake. How much do you have to pay per cupcake? So which of these choices match up to that? The bakery charges $2 for each cupcake, yeah $2 per cupcake, that looks right. The bakery sells two cupcakes for a dollar. No that would be two cupcakes per dollar, not $2 per cupcake. The bakery sells two types of cupcakes. No no we're definitely not talking about two types of cupcakes, they're just talking about cupcakes generally, or I guess one type of cupcake, we don't know, but just cupcakes generally is $2 per cupcake.