The area bounded by the 2 parabolas is A(θ) = 1/2∫(r₂²- r₁²).dθ between limits θ = a,b...
<span>the limits are solution to 3cosθ = 1+cosθ the points of intersection of curves. </span>
<span>2cosθ = 1 => θ = ±π/3 </span>
<span>A(θ) = 1/2∫(r₂²- r₁²).dθ = 1/2∫(3cosθ)² - (1+cosθ)².dθ </span>
<span>= 1/2∫(3cosθ)².dθ - 1/2∫(1+cosθ)².dθ </span>
<span>= 9/8[2θ + sin(2θ)] - 1/8[6θ + 8sinθ +sin(2θ)] .. </span>
<span>.............where I have used ∫(cosθ)².dθ=1/4[2θ + sin(2θ)] </span>
<span>= 3θ/2 +sin(2θ) - sin(θ) </span>
<span>Area = A(π/3) - A(-π/3) </span>
<span>= 3π/6 + sin(2π/3) -sin(π/3) - (-3π/6) - sin(-2π/3) + sin(-π/3) </span>
<span>= π.</span>
Answer:
Small number = 19
Larger no. = 3(19)+14 = 71
Step-by-step explanation:
x + 3x + 14 = 90
4x + 14 = 90
4x = 90 - 14
x = 76 / 4 = 19
Answer:
<u>first graph:</u>
function.
Not one-one
onto
<u>Second graph:</u>
Function
one-one
not onto.
Step-by-step explanation:
We know that a graph is a function if any vertical line parallel to the y-axis should intersect the curve exactly once.
A graph is one-one if any horizontal line parallel to the x-axis or domain should intersect the curve atmost once.
and it is onto if any horizontal line parallel to the domain should intersect the curve atleast once.
Hence, from the <u>first graph:</u>
if we draw a vertical line parallel to the y-axis then it will intersect the graph exactly once. Hence, the graph is a function.
But it is not one-one since any horizontal line parallel to the domain will intersect the curve more than once.
But it is onto, since any horizontal line parallel to the domain will intersect the curve atleast once.
<u>Second graph</u>
It is a function since any vertical line parallel to the co-domain will intersect the curve exactly once.
It is not one-one since any horizontal line parallel to the x-axis does not intersect the graph atmost once.
It is not onto, since any horizontal line parallel to the domain will not intersect the curve atleast once.
Answer:
hope that this helps. the answers are as follows
