(LC)

The depth of the water at the end of a pier changes periodically along with the movement of tides. On a particular day, low tide

Valentin [98]

Draw a diagram to illustrate the problem as shown in the figure below.

The minimum depth of 2.5 m occurs at 12:00 am and at 12:30 pm.
Therefore the period i0s T= 12.5 hours.
The maximum depth of 5.5 m occurs at 6:15 am and at 6:45 pm. Therefore the period of T = 12.5 hours is confirmed.

The double amplitude is 5.5 - 2.5 = 3 m, therefore the amplitude is a = 1.5 m.
The mean depth is k = (2.5 + 5.5)/2 = 4.0 m

The model for tide depth is
$d=-1.5cos( \frac{2 \pi t}{12.5})+4$

That is,
d = -1.5 cos(0.5027t) + 4
where
d = depth, m
t = time, hours

A plot of the function confirms that the model is correct.

8 0

3 years ago

Read 2 more answers

Help me! I'm the most stupidest person ever!

vovangra [49]

Alright here's the breakdown:
your trying to find how many miles per day
so
take the miles (290) and the days it took (5)
and
divide the miles by the days it took (290/5)
and the answer is
58 mi. per day

6 0

3 years ago

Read 2 more answers

1. The mechanics at Lincoln Automotive are reborning a 6 in deep cylinder to fit a new piston. The machine they are using increa

Firdavs [7]

Answer:

$0.0239\frac{in^{3}}{min}$

Step-by-step explanation:

In order to solve this problem, we must start by drawing a diagram of the cylinder. (See attached picture)

This diagram will help us visualize the problem better.

So we start by determining what data we already know:

Height=6in

Diameter=3.8in

Radius = 1.9 in (because the radius is half the length of the diameter)

The problem also states that the radius will increase on thousandth of an inch every 3 minutes. We can find the velocity at which the radius is increasing with this data:

$r'=\frac{1/1000in}{3min}$

which yields:

$r'=\frac{1}{3000}\frac{in}{min}$

with this information we can start solving the problem.

First, the problem wants us to know how fast the volume is increasing, so in order to find that we need to start with the volume formula for a cylinder, which is:

$V=\pi r^{2}h$