1st video : Dead Poets Society
This video tells us about look at something in a different way. We shouldn't look something in a common way because we can't be creative. We must look our own way.
2nd video : Believe
In this video, there is a boy. That boy said on the stage. First, he asked audiences, "Do you believe in me?" And the audiences answered,"Yes!!". Then, the little boy replied, "Because I believe in me." This video tell us to believe in ourselves. Because we can do anything, say anything, think anything, and become anything if we can believe in ourselves.
3rd video : What You Know about Math
4th video : Solving Differential Equation
Let dy over dx is equal to four times x square. To find variable y, first, we can multiply both sides by dx. So, we get dy is equal to four times x square times dx. Now, we must integrate both sides. We get integral dy is equal to integral four times x square times dx. Now, we can solve it. We get that y is equal to three fourth times x cube plus c. c is constant.
5th video : Solving Linear Equation with One Variable
1. Let x – 5 = 3, Find the value of x!
To get the value of x, we can add both sides with five. It will be x minus five plus five is equal to three plus five. So we get x is equal to eight.
2. Let 7 = 4a – 1, Find the value of a!
We can add both sides with one. It will be seven plus one is equal to four a minus one plus one. We get eight is equal to four a. Then, we divided both sides by four. So, we get two is equal to a.
3. Let 2/3 x = 8, Find the value of x!
To get the value of x, we can multiply both sides by three second. It becomes three second times two third x is equal to eight times three second. So, we get the value of x is eight times three second, that is twelve.
4. Let 5 – 2x = 3x + 1, Find the value of x!
First, we can subtract both sides by three x. It becomes five minus two x minus three x is equal to three x plus one minus three x. We get five minus five x is equal to one. Then, we can subtract both sides by five. That equation becomes negative five x is equal to negative four. Now, we can divide both sides by negative five. So, we get x is equal to four fifth.
5. Let 3 – 5(2m – 5) = -2, find the value of m!
First, we should multiply negative five by two m minus five. The equation becomes three minus ten m plus twenty five is equal to negative two. We get twenty eight minus ten m is equal to negative two. Then, we can add both sides by negative twenty eight. We get negative ten m is equal to negative thirty. Last, we can divide both sides by negative ten. So we get m is equal to three.
6. Let ½ x + ¼ = 1/3 x + 5/4, find the value of x!
First, we should subtract both sides by a quarter. It becomes a half x is equal to one third x plus one. Then, we can subtract both sides by one third x. We get one sixth x is equal to one. Last, we can multiply both sides by six. So we get x is equal to six.
7. Let 0,35 x - 0,2 = 0,15 x + 0,1, find the value of x!
6th video : Proof Log Base x of A is Equal to Log Base x Minus Log Base x of B
Let say that logarithm base x of A is equal to B (logx A = B). We can say that it is same to x to the B is equal to A (xB =A). If we multiply log base x of A with C, we get C times log base x of A is equal to B times C (C logx A = BC).
Go back to x to the B equal to A. If we rise x to the B to the power of C, we get x to the B to C power is equal to A to the C. We can say that x to the BC is equal to A to the C (xBC = AC).
Then, write x to the BC is equal to A to the C in logarithm expression. So, it becomes logarithm base x of A to the C is equal to BC (logx AC = BC).
Now, we can see that C times logarithm base x of A is equal to logarithm base x of A to the C (C logx A = logx AC).
We know that C times logarithm base x of A is equal to logarithm of A to the C and we just learn that logarithm base x of A plus logarithm base x of B is equal to logarithm base x of A times B (logx A + logx B = logx AB).
What happens if we change the addition with a subtraction?
Let say that:
1. Log base x of A is equal to l, it says that x to the l is equal A.
2. Log base x of B is equal to m, it says that x to the m is equal B
3. Log base x of A over B is equal to n, it says that x to the n is equal to A over B.
Now, we change A over B with x to the l over x to the m. We can write that x to the l over x to the m is equal to x to the l times x to the negative m or that also equal to x to the l minus m. We can see that x to the n is equal to x to the l minus m. So, n is equal to l minus m.
Then, log base x of A over B is equal to l minus m. That also equal to log base x of A minus log base x of B (because log base x of A is equal to l and log base x of B is equal to m). So, log base x of A over B is equal to log base x of A minus log base x of B.
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