Find th midopint
the mindpoint of 2 points (x1,y1) and (x2,y2) is
((x1+x2)/2,(y1+y2)/2)
so midpoint is ((4+2)/2,(1-5)/2)=(6/2,-4/2)=(3,-2)
now find the slope of the line
it is perpendicular to the line with (4,1) and (2,-5)
find the slope of th eline passing through (4,1) and (2,-5)
slope between (x1,y1) and (x2,y2) is
(y2-y1)/(x2-x1)
so the slope between (4,1) and (2,-5) is
(-5-1)/(2-4)=-6/-2=3
perpendicular lines have slopes tha tmuliplty to get -1
3 times what=-1
what=-1/3
so what is the equation of a line that passes through the point (3,-2) and has a slope of -1/3
the equation of a line that has a slope of m and passes through (x1,y1) is
y-y1=m(x-x1)
so
y-(-2)=-1/3(x-3)
y+2=-1/3(x-3)
if we want slope intercept form
y+2=-1/3x+1
y=-1/3x-1
if we want standard form
1/3x+y=-1
x+3y=-3
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subtract equations to form the equation of:
2x + 2y = 8
rearrange first equation to make x the subject:
x = 4 - 2y
subsitute into 2x + 2y = 8
2 (4 - 2y) + 2y = 8
8 - 4y + 2y = 8
collect like terns
-2y + 8 = 8
8s cancel out
-2y = 0
divide by -2
<u>y</u><u> </u><u>=</u><u> </u><u>0</u>
substitute y value into x + 2y = 4
x + 2 (0) = 4
solve for x
x + 0 = 4
<u>x</u><u> </u><u>=</u><u> </u><u>4</u>
therefore, the solutions are:
<h3>
<u>x</u><u> </u><u>=</u><u> </u><u>-</u><u>4</u></h3><h3>
<u>y</u><u> </u><u>=</u><u> </u><u>0</u></h3>
254.47cm^2
Step-by-step explanation:
A= pi x 3x3
= 9pi
x2 (there is 2 circles)
18pi
C=pi x D
= pi x 6
= 6pi
Width of rectangle wrap perfectly around the circle, so the circumference of 6pi will become the width of the rectangle
Rectangle:
A=lxw
= 10.5 x 6pi
= 63pi
Add up:
63pi + 18pi = 81pi
81pi = 254.469.....
Round to nearest 100th would be 254.47cm^2
(100th is 1/100= 0.01)
Hope this helps!
399,713 rounded to the nearest thousand is 400,000