Answer:
(x, y) = (1, -1)
Step-by-step explanation:
We'll write these equations in general form, then solve using the cross-multiplication method.
43x +67y +24 = 0
67x +43y -24 = 0
∆1 = (43)(43) -(67)(67) = -2640
∆2 = (67)(-24) -(43)(24) = -2640
∆3 = (24)(67) -(-24)(43) = 2640
These go into the relations ...
1/∆1 = x/∆2 = y/∆3
x = ∆2/∆1 = -2640/-2640 = 1
y = ∆3/∆1 = 2640/-2640 = -1
The solution is (x, y) = (1, -1).
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<em>Additional comment</em>
The cross multiplication method isn't taught everywhere. The attachment explains a bit about it. Our final relationship changes the order of the fractions to 1, x, y from x, y, 1. That way, we can use the equation coefficients in their original general-form order. (The fourth column in the 2×4 array of coefficients is a repeat of the first column.)
Let's assign some random values to it, and say 1 unit of petroleum costs 100 bitcoins, because we all know bitcoins are the best currency :P
If the price goes up by 10%, it is now 100*1.1 = 110bitcoins for 1 unit.
However he's only getting 0.9 units now, so multiplying 110 by 0.9 gives us 99 bitcoins. His petroleum bill used to be 100 (which is why I picked 100 as it's easier), and now it is 99. Therefore his petroleum bill has reduced by 1%
The numbers are 30 and 15. Length is 15 and width is 30.
That is the slope at f(1)
one way is to just take the derivitive
f'(x)=2x+(1/x)
for ti-89, do calc then derivitive then input "x^2+ln(x),x)" and click enter to get the derivitive
you would get f'(x)=2x+(1/x)
an easier way would be to have
click calc then differntiate then type x^2+ln(x),x)|x=1 then click enter
you get f'(1)=3
answer is 3
