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sukhopar [10]
3 years ago
5

A swimming dock oscillates up and down as waves go by. At time (in seconds) t = 0 the dock is 15 feet above the bottom of the la

ke. It takes ten seconds to move one cycle (from its highest point at t = 0 back to its next high point at t = 10) It moves down 3.6 feet from high point to low point. In other words it is 11.4 feet above the bottom of the lake at t = 5 seconds.
Mathematics
1 answer:
OLEGan [10]3 years ago
6 0

Answer:

The motion, y of the dock with time , t can be represented as a cosine function as presented in the following equation;

y = 1.8 \times cos(\frac{2\pi }{10} \cdot t) + 13.2

Step-by-step explanation:

Here we approximate the motion of the dock as a cosine function as follows

y = a·cos(b(x - c)) + d

a = Amplitude

The period = 2π/b

d = Vertical shift

c = Horizontal shift

Here we have the period given as the time to complete one cycle = 10

The vertical shift, d, is the height above the bottom of the lake + amplitude = 11.4 ft + 3.6 ft/2 =13.2 ft

The amplitude is the distance from the highest point to the neutral point = 3.6/2 = 1.8 ft

Therefore, a = 1.8 ft

Again, we have that at t = 0, we have the dock is at its highest point, therefore, the dock agrees well with the cosine function that has the highest value at 0, therefore c = 0

The cosine function representing the motion of the dock is thus;

y = 1.8·cos(2π/10·t) + 13.2.

You might be interested in
Which numbers are between -7 and 2 on a number line? Circle all that apply.
sukhopar [10]

Answer: See below

Step-by-step explanation:

A. 2.1       No (2.1>2)

B. -1         Yes

C. 0         Yes

D. -7.5     No (-7.5<-7)

E. 3.5       No (3.5>2)

F. -6.4      Yes

G. -8         No (-8<-7)

5 0
2 years ago
Read 2 more answers
can anyone help tech me how to solve for tax and tip. im going to 6th grade and trying to get into the advanced group but I don'
baherus [9]

If something isn't clear or you're still confused about, let me know in the comments.

Step-by-step explanation:

Okay, here's my best try.

Suppose you have a bill for $8.45

If you are asked to add, say, 8% tax, you must calculate 8 percent of 8.45 and then add it to 8.45.

Begin by converting 8% to decimals by dividing by 100.

\frac{8}{100}=0.08 8% is 0.08 in decimal form.

To calculate a percentage of a number, you multiply the decimal percent by the number; example:

0.08(8.45) 8.45 is being multiplied by 0.08. The result is: 0.676. (this is the tax; however you have to round up to two decimal places: $0.68)

After finding the tax amount, if you are asked to add it to the bill, you have to add it to the original bill; in this case, $8.45

This would be: 0.68+8.45=9.13.

Therefore, the total bill after tax is for $9.13

----------------------------------------------------------------------------------------------------

With tips is the same thing, however, you can have 2 situations.

Situation 1: You are asked to calculate 15% tip of total bill.

In this situation, you can do the same we do to calculate tax.

Convert the percentage to decimal by dividing by 100.

\frac{15}{100}=0.15

and multiply it by the original bill.

0.15(8.45)=1.2675. Rounding up, this would be $1.27 for tip.

If you were to add it to the original bill, simply sum.

8.45+1.27=9.72

The total bill after tips is for $9.72

Situation 2: You are asked to calculate 15% tip of the total bill with a tax of 8% included.

In this situation, you must first calculate the total bill with the tax added, like we did above; we got a bill for $9.13 (Tax included)

Then you can calculate 15% tip of this new bill that has tax included.

Convert

\frac{15}{100}=0.15

Multiply by the new bill (because this is the one that includes tax)

0.15(9.13)=1.3695 Round up.... $1.37 for tips.

If you are asked to give a total amount of money including tax and tips, add this to the bill.

9.13+1.37=10.50

This bill would be for $10.50

3 0
3 years ago
PLEASE i need help
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1. 8^3 * 8^2, 8^5, and (2^3)^5
2. 6^9, and 6^5 x 6^4
6 0
3 years ago
Is inches allowed to be used in science when measuring?
Dima020 [189]
Typically in science, centimeters are used when measuring.
8 0
2 years ago
Help me with my aleks its due June 30th
Alex

Answer:

5 divided by 2 = 2.5         2.5 is the answer because you split the bigger number in half and in order to do that you need to divide by 2.

Step-by-step explanation:

                                   Hope this helps you!!!!!!!!!! :) :) :) :) :)

                                   SORRY IF IT'S WRONG!!!!! :) :) :) :) :)

6 0
3 years ago
Read 2 more answers
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