34.no 3 do like example given solution Example 13:assume that x and y vary with time.dp dxdt di andrelated ?dta) How areb) If x increases at a constant rate of ft/sec, and y decreases at a constant rate ofi fl/sec, how fast is the size of the diagonal changing when x = 3 ft and y = 4 fi2Solution:a)x2ydy2ydtdp2xdt2pdtdyy dtdpdt%3Db) 3() + 4 (-)5-dtdpdt10 ft/secExample 14:The radius of the base of a right circular cone is decreasing at the rate of 4 cm/min, and theheight is increasing at the rate of 6 cm/min. At what rate is the volume changing when theheight is 12 cm and the radius is 6 cm ?Solution:drdh4,= 6dtdtdVdt= ?, h = 12,r= 6V =dVdt[6° (6) + 2 (6) (-4) ( 12 ) ]- 120n%3D MAT A34 RELATED RATESTUTORIAL 34Suppose that h =At a certain instant when x = 1 and y = 3, x is increasing at the rate of2x'y, where both x and y are changing with time.instant? State whether h is decreasing or increasing.2.The area of a rectangle is fixed at 200 cm?. The sides x and y vary with timey dxx dtdya) Show thatb) If x increases at a rate of 2 cm/s, what is the rate of change of y at theinstant x = 25 ?Suppose that z = 9x* - 2x2 + 3x, where both z and x are both functions of tiGiven that x is increasing at the rate of 2 units sHow fast is z changing when x = 2? Is z increasing or decreasing ?Let 0 (in radians) be an acute angle in a right triangle. x and y are the lengths of thesides adjacent and opposite to0 respectively. Assume that x and y vary with time.4.dydea) Show thatdtdxtan 0 + x sec 0dtdtb) At a certain instant, x = 4 m and is increasingat 1 ms , while y = 4 m and is decreasingat 0.6 ms. How fast is 0 changing at that instant?Is 0 increasing or decreasing at that instant?Let V be the volume of a cylinder having height h and radius r, and assume thath and r vary with time.dV drdt' dtdhanddta) How arerelated ?b) At a certain instant, the height is 6 cm and increasing at 2 cm/sec,while the radius is 10 cm and decreasing at 2 cm/sec.How fast is the volume changing at that time?Is the volume increasing or decreasing at that instant?6. The height of a cone is decronui

Question

Accepted Answer

Answered: Image /qna-images/answer/9570973f-bda6-4198-93de-0a0810850374.jpg

inst /3. 2x2 + 3x, where both z and x are both functions Suppose that z = 9x Given that x is increasing at the rate of 2 units s How fast is z changing when x = 2? Is z increasing or decreasing ? %3D