Let u solve cu = 0. Show that any derivative, say w = uxt, also solves cw = 0. In cu = 0, u = u(t, x) do the change of variables
(ξ, η) specified below, to find the equation for v(ξ, η). Is it vξξ − c 2vηη = 0? (a) Translation ξ = t − T, η = x − y where y, T are fixed. (b) Dilation ξ = at, η = ax for any constant a. (c) Find the change of variables (ξ, η) = (?, ?) such that v(ξ, η) satisfies 1v = vξξ −vηη = 0
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Answer: x = 780
Step-by-step explanation: Well <u><em>percent</em></u> means <em>over 100</em> so we can set up an equation for this problem by reading it from left to right.
So we know that <u><em>10%</em></u> means <em>10/100</em>, <u><em>of</em></u> means times, <em><u>what</u></em> <em><u>number</u></em> means <em>x</em>, <u><em>is</em></u> means <em>equals</em>, and <em><u>12</u></em> means 12.
Notice that <em>10/100</em> can be reduced to 1/10.
So rewriting our problem we have <em>X/10 = 78</em>.
To get rid of the fraction, we multiply both sides of the equation by 10 and we have <em>x = 780</em>. So, 10% of 780 is 78.
Now let's check our answer back in the original problem to see if it makes sense.
We have <em>10% of 780 is 78</em>. Well we know that 100% of of 780 would be 780 so 10% of 780 should be alot less than 780 so 78 seems to make sense.
Image provided showing my work.
