SAT Math Part 16 - Direct Variation Problems - By The Organic Chemistry Tutor
Transcript
| 00:00 | 56 . Why varies directly with X ? If y | |
| 00:06 | is 21 when X is nine , What is the | |
| 00:09 | value of ? Why ? When X is 15 ? | |
| 00:13 | So what do we have to do here in this | |
| 00:14 | problem ? Well first we need to come up with | |
| 00:20 | an equation why varies directly with X . So this | |
| 00:24 | tells us that why is equal to K . X | |
| 00:26 | or K is a constant . Let's say if it | |
| 00:29 | stated that why varies indirectly with X or is inversely | |
| 00:34 | proportional to X . Then the equation that we will | |
| 00:37 | use is y . Is equal to K over X | |
| 00:41 | . Yeah . Now we need to use the information | |
| 00:46 | here to calculate K . Once we have the value | |
| 00:50 | of K We can calculate the value of Y when | |
| 00:53 | X is 15 . So we know that why is | |
| 00:57 | 21 when X is not . So to solve for | |
| 01:02 | K . We need to divide both sides by nine | |
| 01:07 | . So Kay is 21/9 . Now 21 We can | |
| 01:12 | write that as seven times street nine . We can | |
| 01:15 | write that as three times street . And if we | |
| 01:19 | cancel it three we could see that K . It's | |
| 01:25 | 7/3 . So that's we have the formula Y . | |
| 01:31 | Is equal to 7/3 times x . So now we | |
| 01:37 | could answer the second part of the problem . What | |
| 01:40 | is the value of why When X is 15 ? | |
| 01:44 | So why is going to be 7/3 times 15 ? | |
| 01:50 | 15 is basically five time stream . Yes . And | |
| 01:54 | so we could cancel a three and then all we | |
| 01:57 | have left over Is seven times 5 which is 15 | |
| 02:03 | . And so this . No I take that back | |
| 02:06 | seven times five is not 15 . That is a | |
| 02:08 | big mistake . seven times 5 is 35 and therefore | |
| 02:14 | see is the right answer . Now for those of | |
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| 02:54 | . So let's get back to the video 57 . | |
| 02:59 | Why varies inversely with the square of X ? If | |
| 03:03 | y equals two . When access to what is the | |
| 03:07 | value of Why ? When access for ? Well first | |
| 03:13 | let's write an equation . And the last example we | |
| 03:16 | saw that when why vary directly with X or proportional | |
| 03:20 | with X . It was simply chaos if why varies | |
| 03:24 | inversely with facts . Acts on the bottom . But | |
| 03:28 | Kay is always on the top . Now in this | |
| 03:31 | example why varies inversely with the square vax ? So | |
| 03:34 | it's going to be K over X squared the square | |
| 03:38 | of axes X squared . So we're going to follow | |
| 03:41 | the same process that we use in the last example | |
| 03:45 | . Yes . Using this part of the problem we | |
| 03:48 | are going to calculate kate and then once we have | |
| 03:51 | the value of K we can plug in for In | |
| 03:54 | two X and calculate the value of Y . Yeah | |
| 03:59 | . So why is to when X is too So | |
| 04:03 | what is K two squared is basically for now let's | |
| 04:10 | write to over one and we can cross multiply . | |
| 04:13 | So we have one times K which is K And | |
| 04:16 | that's equal to two times 4 which is eight . | |
| 04:19 | So thus Replacing K . a . we have the | |
| 04:24 | equation why is equal to eight over X squared . | |
| 04:29 | Yeah , that was that in mind . Let's see | |
| 04:32 | what why is going to be when access for . | |
| 04:35 | So this is going to be eight over four squared | |
| 04:39 | Now . four square to 16 . And we can | |
| 04:43 | write 16 As eight times 2 And eight . You | |
| 04:47 | can write that as eight times one . So if | |
| 04:50 | you cancel an eight we can clearly see that . | |
| 04:53 | Why is one half . And so e . Is | |
| 04:58 | the answer for this problem . By the way , | |
| 05:01 | for those of you who want more examples on these | |
| 05:03 | type of problems . Go to Youtube and type in | |
| 05:07 | direct variation organic chemistry tutor . And the video should | |
| 05:11 | come up with more harder problems related to this topic | |
| 05:16 | . So feel free to take a look at that | |
| 05:18 | when you get a chance . |
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