Answer:
Step-by-step explanation:
We are given the equation of the line y=3x and a point, say Q(60,0) outside of that line.
We want to find the point on the line y=3x which is closest to Q.
Let P(x,y) be the desired point. Since it is on the line y=3x, it must satisfy the line.
If x=a, y=3a, so the point P has the coordinates (a,3a).
Distance between point Q and P
To minimize D, we find its derivative
Therefore, the y-coordinate for P is 3*6=18.
The point P=(6,18).
Next, we calculate the distance between P(6,18) and (60,0).
Answer:
15
Step-by-step explanation:
4×3=12 15-12=3 3+12=15
Answer:
go everything youve learnt from grade 3 come right up
Step-by-step explanation:
sometimes its knowing the simply formulas thatll get you through
Answer:
132ft
Step-by-step explanation:
add all the sides
47+47+19+19=132
Answer: Choice A
g(x) = sqrt(2x)
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Explanation:
"sqrt(x)" is shorthand for "square root of x"
f(x) = 3x^2 is given
g( f(x) ) = x*sqrt(6) is also given
One way to find the answer is through trial and error. This would only apply of course if we're given a list of multiple choice answers.
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Let's start with choice A
g(x) = sqrt(2x)
g( f(x) ) = sqrt(2 * f(x) ) .... replace every x with f(x)
g( f(x) ) = sqrt(2 * 3x^2 ) .... plug in f(x) = 3x^2
g( f(x) ) = sqrt(6x^2 )
g( f(x) ) = sqrt(x^2 * 6)
g( f(x) ) = sqrt(x^2)*sqrt(6)
g( f(x) ) = x*sqrt(6)
We found the answer on the first try. So we don't need to check the others.
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But let's try choice B to see one where it doesn't work out
g(x) = sqrt(x + 3)
g( f(x) ) = sqrt( f(x) + 3)
g( f(x) ) = sqrt(3x^2 + 3)
and we can't go any further other than maybe to factor 3x^2+3 into 3(x^2+1), but that doesn't help things much to be able to break up the root into anything useful. We can graph y = x*sqrt(6) and y = sqrt(3x^2 + 3) to see they are two different curves, so there's no way they are equivalent expressions.
