A ball is thrown from an initial height of 2 meters with an initial upward velocity of 15/ms . The ball's height h (in meters) a
fter t seconds is given by the following. =h+2−15t5t2 Find all values of t for which the ball's height is 7 meters. Round your answer(s) to the nearest hundredth. (If there is more than one answer, use the "or" button.)
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We have to find the" ratio of the area of sector ABC to the area of sector DBE".
Now,
the general formula for the area of sector is
Area of sector= 1/2 r²θ
where r is the radius and θ is the central angle in radian.
180°= π rad
1° = π/180 rad
For sector ABC, area= 1/2 (2r)²(β°)
= 1/2 *4r²*(π/180 β)
= 2r²(π/180 β)
For sector DBE, area= 1/2 (r)²(3β°)
= 1/2 *r²*3(π/180 β)
= 3/2 r²(π/180 β)
Now ratio,
Area of sector ABC/Area of sector DBE =
= 4/3
We will use u-substitute:
Then for substitution:dx=u du. and integral becomes:
=u-ln(u+1)=
. Now we will change the values of limits: 
=4-ln(5)-2+ln(3)=2+ln(0,6)=2-0.51=1.49