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Related Rates & Optimization Next Class: Indeterminate Forms & L Agenda Test 2 is this Friday! Today's Topics: Related Rates & Optimization Next class: Indeterminate Forms & L'H^opital'sRule (Watch Videos: 6.5-6.9) Mihai Alboiu MAT137 18 January 2021 1/6 \Just Take a Pebble... ...and cast it to the sea." It produces a circular ripple. When the radius is 2 metres and is increasing at a rate of 10cm=s, at what rate is the area increasing? Mihai Alboiu MAT137 18 January 2021 2/6 Mario Party (3 is the best) Mario, Yoshi, Peach, and DK want to rent a disco ball for their upcoming party, but they could only find a flashlight. At the party, Yoshi is designated the \disco ball." Yoshi stands in the centre of the room pointing the flashlight horizontally (parallel to the ground) and spins at 3 revolutions per second. The room is square with side length 8 metres. At what speed is the light from the flashlight moving across the wall when it is 3 metres away from a corner? Mihai Alboiu MAT137 18 January 2021 3/6 I Want to be a Farmer A farmer has 300m of fencing and wants to fence off a rectangular field and add an extra fence that divides the rectangular area in two equal parts down the middle. What is the largest area that the field can have? Mihai Alboiu MAT137 18 January 2021 4/6 \Space's Loneliness" Find the point on the parabola y2 = 2x that is closest to the point (1; 4). Mihai Alboiu MAT137 18 January 2021 5/6 It's Waluigi Time! Waluigi hears a scream: \Ouch!" He turns and sees that Wario is on fire! Luckily, Waluigi is at the edge of a river. Wario is 10 metres away from the river and Waluigi is 5 metres away from the point P on the river closest to Wario. Waluigi is carrying an empty bucket, and he can run twice as fast with an empty bucket as he can with a bucket full of water. How far from the point P should Waluigi fill his bucket up to reach Wario as quickly as possible? Mihai Alboiu MAT137 18 January 2021 6/6.
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