Math 1300 Section 004 Calculs I 3. A hot air balloon is inflated with hot air an

Question

Math 1300 Section 004 Calculs I 3. A hot air balloon is inflated with hot air and the change in the radius of the balloon over time is give by the table below. t (minutes) 0 257 11 12 r(t) (feet per minute) 5.74.0 2.012 06 0 (a) (2 points) The radius of the balloon at t-5 is 30 feet. Estimate the radius of the balloon whe t-54 using the tangent line approximation att (b) (2 points) Use the right Riemann sum with give subintervals to appronimate the area under the Notice that the subintervals are not all the same graph of ) on the interval o, 12 Ti length. (e)(1 point) Give a physical interpretation of the quantity you found in part (b) Make sure to indiate units in your answer

Explanation / Answer

(a) Here r'(t) at t = 5 minute is 2 feet per minute

Here radius at t = 5.4 minute

r = r'(t) (t1 -t0 ) + R5 = 30 + 2 * (5.4 - 5.0) =  30.8 feet

(b) Riemann sum = here we build 5 trepozids here

Area of trepozid = (a + b)h/2 where h is the height and a and b are parellal sides

sum = (5.7 + 4.0) * (2-0) /2 + (4 + 2) * (5-2)/2 + ( 2 + 1.2) * (7-5)/2 + (1.2 + 0.6) * (11 - 7)/2 + (0.6 + 0.5) * (12-11)/2

sum = 26.05 Feet

(c) Here the are tells us the total increase in the radius of the baloon over 12 seconds tme interval.

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