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Solve the given problems.The volume $V$ (in $\mathrm{m}^{3}$ ) of water used each day by a community during the summer is found to be $V=2500+480 \sin (\pi t / 90)$ where $t$ is the number of the summer day, and $t=0$ is the first day of summer. On what summer day is the water usage the greatest?

Calculus 1 / AB

Chapter 27

Differentiation of Transcendental Functions

Section 4

Applications

Derivatives

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Lectures

03:09

In mathematics, precalculu…

31:55

In mathematics, a function…

02:03

A fountain sends a stream …

01:31

Solve each problem.Vol…

01:32

02:45

A conical paper cup with d…

01:57

Volume of Water Between $0…

02:10

Solve each problem.Wav…

05:23

Water flows into a conical…

01:14

03:15

A faucet is filling a hemi…

04:16

A rectangular swimming poo…

so we have a stream and this stream is pushing water up like this. So the water gun comes down and vertical high treason by the water is 5.0 meters. So at this highest point, we know that the final speed off the water is you. So we have to figure out what is the speed with which the water is coming out after street. So we have Ah, we squared minus we not. Square is equal to two times eight times s and he final speed is zero minus. We're trying to figure out the initial speed is equal to two times negative, 9.8 times five. So solving this for Lena gives us 9.9%. So the water is coming out after scream at the speed off 9.9 meters per second. Now the water inflow rate Q is equal to a country. So the area off the pipe is given as five points year old times 10 to the negative four and then you multiply that with 9.9 that gives you the valiant flow rate is equal to 5.0 times 10 to the negative. A three meter cubed per second, So the next thing we need to do is be it need to be able to change that to gallons per minute. So we have. Q. Is incredible fireplace your own times 10 to the negative three Working group for a second. So we time stacked with one gallon over 3.79 times 10 to the negative three meter cube and then times that with one second of 60 seconds, which is equal to one minute. So having the calculator, this comes out to be 1 to 79 gallons per minute.

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In mathematics, precalculus is the study of functions (as opposed to calculu…

In mathematics, a function (or map) f from a set X to a set Y is a rule whic…

A fountain sends a stream of water straight up into the air to a maximum hei…

Solve each problem.Volume of Water $\quad$ A water tank in the shape of …

A conical paper cup with diameter 4 inches and height 4 inches is initially …

Volume of Water Between $0^{\circ} \mathrm{C}$ and $30^{\circ} \mathrm{C},$ …

Solve each problem.Wave Action The vertical position of a floating ball …

Water flows into a conical tank with cross-sectional area $\pi x^{2}$ at hei…

A faucet is filling a hemispherical basin of diameter 60 $\mathrm{cm}$wi…

A rectangular swimming pool $10 \mathrm{ft}$ wide by $20 \mathrm{ft}$ long a…

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The number 2 is also the smallest & first prime number (since every other even number is divisible by two).

If you write pi (to the first two decimal places of 3.14) backwards, in big, block letters it actually reads "PIE".

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