How can you solve a simpler problem to help you find the solution
2 answers:
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So the line that is the limit is where the equation crosses the y axis or where x=0
so
y=(1/2(0)-2)^2+5
y=(-2)^2+5
y=4+5
y=9
at y=9
the upper bound is y=9
alrighty
we will do
let's call the curve that is 6th degree f(x)
and the y=9, g(x)
f(x)=(1/2x-2)^6+5
g(x)=9
find where they intersect
9=(1/2x-2)^6+5
4=(1/2x-2)^6
fancy math
x=8
so the area under the curve will be
because g(x) is above f(x)
so
using our calculator because I can't figure out what
is
or about 21.33333333
so
y=(1/2(0)-2)^2+5
y=(-2)^2+5
y=4+5
y=9
at y=9
the upper bound is y=9
alrighty
we will do
let's call the curve that is 6th degree f(x)
and the y=9, g(x)
f(x)=(1/2x-2)^6+5
g(x)=9
find where they intersect
9=(1/2x-2)^6+5
4=(1/2x-2)^6
fancy math
x=8
so the area under the curve will be
so
using our calculator because I can't figure out what
Answer: Check out the filled out chart below.
Row 1: 1/4, 1/4, -4
Row 2: -2, -2, 1/2
Row 3: 3, 3, -1/3
=========================================
Explanation:
Parallel lines have equal slopes. So if the original line has slope 1/4, then any parallel line will also have slope 1/4. The only thing different is the y intercept.
Perpendicular slopes multiply to -1 assuming neither line is vertical. For row 1, the perpendicular slope is -4 which multiplies with the original slope 1/4 to get -1.
Put another way, the perpendicular slope is the negative reciprocal of the original slope. For row 2, the perpendicular slope is 1/2 because we flip the fraction and the sign for the original slope -2 = -2/1
