Let R be the region bound by the equations y = 2 + cos(x) and y = csc(x) in the first quadrant on the interval 0 ≤ x < π.

a) Write, but do not solve, an equation involving integral expressions whose solution is the area of

the region R.

b) Write, but do not solve, an equation involving integral expressions whose solution is the volume

of the solid generated when R is revolved around the x-axis.

c) Write, but do not solve, an equation involving integral expressions whose solution is the volume

of the solid generated when R is revolved around the line x = –1.

answer: c, the green line

step-by-step explanation:

there is no black line, eliminate b.

simple interest implies periodic payments, but the red line shows no payments, eliminate d.

simple interest has equal payments. if paid say every day, the graph is about a straight line (actually a stairstep).

the yellow line is not straight, eliminate a.

check: the green line is straight, answer is c.

simple interest with positive interest rate gives a straight line sloping up to the right. green line:

g(t) = $100 + ($200-$100) ÷ (20 years) × (t years)

= $100 + (4%/year) × ($100)(t years)

incidentally, the yellow line curving upward represents continuously compounded interest

y = $100 × 2^(t years / (14 assuming the yellow line hits $200 at 14 years. 2^0 is 1, so y(0) = $100; 2^(14/14) is 2, so y(14) = $200.

6 cm

step-by-step explanation:

answer: y = -2.5x - 15

              (-6,0)

step-by-step explanation: