23 5 uuepn the values of a b and c Draw a picture 2 A cylin

#2,3 & 5

uuepn the values of a, b, and c. Draw a picture 2. A cylindrical can uwith both a top and a lootlom has the sane of the can surface area as a cub with edge 50 mm. The height is o em. Find the nadius of the can to the nearest thounandth 3. Solve the equatonm tos 2x+ sin x O on the intlerval E, 2rl. Hint : use the appropriate trig identity for the doube angle of ensine .1 4. Given o) x5x 3x+using your graphing calculater a) Find the zeroes to the nearest thousand-th b) Name the intervals on ohch f is decreasing Be sure to include a 5. An isosceles +ni amgle has a verlex at the origin and the ends e on + ress the area of triangle as a fumchon of the length ofs base. Assume its base lies above the x-axis. Draw a picture. 6. A line tangent to y=3X3+ 2x2+10 at x-c has a slope of 4c-e. Find the eguation of the tangent line to 7. Express a in factored form. Then determine the signs of q)

Solution

there seems to be something missining in 2nd problem like \"cub\" doesn\'t make any sense. so i\'m going to solve #3

Ans(3):
cos(2x)+sin(x)=0

1-2sin^2(x)+sin(x)=0   {using formula cos(2x)=1-2sin^2(x)}

-2sin^2(x)+sin(x)+1=0

2sin^2(x)-sin(x)-1=0

(2sin(x)+1)(sin(x)-1)=0

(2sin(x)+1)=0   or   (sin(x)-1)=0

sin(x)=-1/2 or   sin(x)=1

which gives solution in given interval [-pi, 2pi]

as {-5pi/6, -pi/6, pi/2, 7pi/6, 11pi/6}