Find the circulation and flux of the field Bold Upper F equals negative 3 x squared Bold i minus 3 y squared Bold j around and across the closed semicircular path that consists of the semicircular arch Bold Bold r 1 (t )equals (a cosine t )iplus (a sine t )j, 0 less than or equals t less than or equals pi, followed by the line segment Bold r 2 (t )equals t Bold i, negative a less than or equals t less than or equals a.

0

Step-by-step explanation:

CPdx+Qdy=C1Pdx+Qdy+C2Pdx+Qdy=circulation

C1:x=acost,dx=−asintdty=asint,dy=acostdt.C2:x=t,dx=dt,y=0,dy=0.

P=−y=−asint.Q=x=acost

circulation=π0[−asint(−asint)+acost(acost)]dt+a−atdt=a2π0dt+t22a−a=πa*2

Flux=CPdy−Qdx=C1Pdy−Qdx+C2Pdy−Qdx=π0[−asint(acost)−acost(−asint)]dt+a−a0dt=0

17

step-by-step explanation:

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.