The region inside one leaf of r the area of the region is pi.20.
r =cos5θ
cos5θ =0
5θ=pi/2 ,5θ=3pi/2
θ=pi/10,θ=3pi/10
area of one leaf = ∫[pi/10 to 3pi/10](1/2)r2dθ
= ∫[pi/10 to 3pi/10](1/2)(cos5θ)2dθ
= ∫[pi/10 to 3pi/10](1/4)(1+cos10θ)dθ
=[pi/10 to 3pi/10](1/4)(θ+ (1/10)sin10θ)
=(1/4)((3pi/10)+ (1/10)sin3pi) -(1/4)((pi/10)+ (1/10)sinpi)
=(1/4)(3pi/10) -(1/4)(pi/10)
=(1/4)(2pi/10)
=pi/20
area of one leaf =pi.20.
Region area (calculus) Region area. The non-negative function given by y = f(x) represents a smooth curve on the closed interval [a, b].The area through the curve of f(x), the x-axis, and the perpendicular lines x = a and x = b The bounding region shown in Figure 1 is given by.
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We know that
the equation of the line in standard form is
Ax+By=C
the equation of the line <span> in the slope-intercept form is
</span><span>y +1 = 2/3 (x - 8)-----> y+1=(2/3)x-(16/3)----> y-(2/3)x=(-16/3)-1
</span>y-(2/3)x=(-19/3)----> multiply by 3-----> -2x+3y=-19
the answer is
-2x+3y=-19
<span>I verify that the points belong to the given line
for the point (8,-1)
-2*8+3*(-1)=-19--------> -16-3=-19-----> -19=-19------> is ok
for the point (2,-5)
-2*2+3*(-5)=-19------> -4-15=-19------> -19=-19-----> is ok</span>
Answer:
3/10
Step-by-step explanation:
There are 2 red, 2 blue, 1 orange, 2 purple and 3 green stones. = 10
P( green) = number of green / total
= 3/10
Answer:
vertex = (3, 2 )
Step-by-step explanation:
The vertex is the turning point of the graph.
This occurs at (3, 2 ) ← vertex
