First, we convert the rate to \(\displaystyle\frac{{m}^{{3}}}{{h}}{r}\): \((16)\)

Question

asked 2021-05-16

Where does the helix

\(r(t)=<\cos(\pi t), \sin( \pi t), t >\)

intersect the paraboloid

\(z = x^2 + y^2\)?

(x, y, z) =

What is the angle of intersection between the helix and the paraboloid?

\(r(t)=<\cos(\pi t), \sin( \pi t), t >\)

intersect the paraboloid

\(z = x^2 + y^2\)?

(x, y, z) =

What is the angle of intersection between the helix and the paraboloid?

asked 2021-06-10

Here’s an interesting challenge you can give to a friend. Hold a $1 (or larger!) bill by an upper corner. Have a friend prepare to pinch a lower corner, putting her fingers near but not touching the bill. Tell her to try to catch the bill when you drop it by simply closing her fingers. This seems like it should be easy, but it’s not. After she sees that you have released the bill, it will take her about 0.25 s to react and close her fingers-which is not fast enough to catch the bill. How much time does it take for the bill to fall beyond her grasp? The length of a bill is 16 cm.

asked 2021-05-12

Your town is installing a fountain in the main square. If thewater is to rise 25m(82feet)above the fountain,how much pressuremust the water have as it moves slowly toward the nozzle thatsprays it up into the air?

Rather than putting a pump in the fountain(previous question)the engineer puts a water storage tank in a nearby high risebuilding.How high up in that building should the tank be for itswater to rise 25m when spraying out thefountain?(neglect friction)

Rather than putting a pump in the fountain(previous question)the engineer puts a water storage tank in a nearby high risebuilding.How high up in that building should the tank be for itswater to rise 25m when spraying out thefountain?(neglect friction)

asked 2021-03-07

A family is canoeing downstream (with the current). Their speed relative to the banks of the river averages 2.75 mi/h. During the return trip, they paddle upstream (against the current), averaging 1.5 mi/h relative to the riverbank.

a. Write an equation for the rate of the canoe downstream.

b. Write an equation for the rate of the canoe upstream.

c. Solve the system to find the family’s paddling speed in still water.

d. Find the speed of the current of the river.

a. Write an equation for the rate of the canoe downstream.

b. Write an equation for the rate of the canoe upstream.

c. Solve the system to find the family’s paddling speed in still water.

d. Find the speed of the current of the river.