How could you use cross products to check the solution to this proportion #12/30=5/x#?

↳Redirected from "Suppose that I don't have a formula for #g(x)# but I know that #g(1) = 3# and #g'(x) = sqrt(x^2+15)# for all x. How do I use a linear approximation to estimate #g(0.9)# and #g(1.1)#?"
1 Answer
EZ as pi
Oct 27, 2016

#12 xx12.5 = 30xx5#
#" "150=150#

Explanation:

You will have to have a solution first ..

Cross multiplying is a way of finding the solution, but we will use that to check later. Let's use another method to find #x#

#12/30 = 5/x#

Notice that #12 div 2.4 =5 #

#(12 div 2.4)/(30 div 2.4) = 5/12.5" " rarr x = 12.5#

To check whether this is correct: cross-multiply...

#color(lime)(12)/color(blue)(30) = color(blue)(5)/color(lime)(12.5)#

Is #color(lime)(12 xx 12.5) = color(blue)(30xx5)?#

We find: #color(lime)(150) = color(blue)(150)#

Therefore we have the correct solution for #x#

This is true for any equivalent fractions:

#7/5 = 21/15" " 4/11 = 20/55#

#105 =105" "220 = 220#

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