X is the radius of the slice. So we must find the equation of the side of the cone.
y=mx+b, so now we must use two points to solve for the slope, or "m".
m=(y2-y1)/(x2-x1)
m=(0-15)/(5-0)
m=-15/5
m=-3 so our line so far is:
y=-3x+b, b=y-intercept=value of y when x=0, which we can see is 15 ft so:
y=-3x+15
Now the radius is x, so we must solve for x from the equation above...
-3x+15=y subtract 15 from both sides
-3x=y-15 divide both sides by -3
x=(15-y)/3
And area of this circle is:
A=πx^2, and using x found above:
A=(π/9)(15-y)^2
A=(π/9)(225-30y+y^2), so when y=6 ft
A=(π/9)(225-30*6+6^2)
A=(π/9)(81)
A=9π or if we let π=pi
A=9pi ft^2
Width = 45 inches
Height = 36 inches
Area = 45 • 36 = 1620 inches squared
(7.5 x 10^-3) + (5.8 x 10^-3 )
= (7.5 x 1/1000) + (5.8 x 1/1000) OR decimal form --> (7.5 x 0.001) +(5.8 x 0.001)
0.0075 + 0.0058 = 3/400+29/5000
0.0133 = 133/10000
Hope it helps.
Frogs are at the pond = 12.
Given,
There are some frogs and some lily pads at a pond. If lily pads with frogs on them have two frogs each, then there are 3 lily pads with no frogs on them. If each lily pad has exactly one frog on it, then there are 3 frogs with no lily pad.
= 2( n-3) = n+3
= 2n -6 = n+3
=> n = 9
9 pads, 12 frogs.
Hence, Frogs are at the pond = 12.
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8). x=(-1+√22)/2 , x=(-1-√22)/3
9). x=(1+√5)/2 , x=(1-√5)/2
10). x=3 , 1/4
11). x=1/3 , -1
12). x=2+2√3 , 2-2√3
