1answer.
Ask question
Login Signup
Ask question
All categories
  • English
  • Mathematics
  • Social Studies
  • Business
  • History
  • Health
  • Geography
  • Biology
  • Physics
  • Chemistry
  • Computers and Technology
  • Arts
  • World Languages
  • Spanish
  • French
  • German
  • Advanced Placement (AP)
  • SAT
  • Medicine
  • Law
  • Engineering
sukhopar [10]
4 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]4 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
i think of a number. if i divide the sum of 5 and the number by 3, the result is 2 less than one quarter of the number. find the
Marrrta [24]

Answer:

x = 4.75

Step-by-step explanation:

<u>(5 +X</u><u> )/3</u>  = 2 - <u> X/4</u>

<h3>   <u>(5 +X</u><u> )/3</u>  = 8 - X  </h3><h3>5+ X = 3 (8 - X)   </h3><h3>  5+ X = 24 - 3X transposing terms</h3><h3>X+ 3X= 24 -5</h3><h3>   4X = 19</h3><h3>      X = 19/4 </h3><h3>X = 4.75</h3>
7 0
3 years ago
Jack bought a shirt for $14 because it was discounted 30%. what is the regular price?
Andru [333]

All you have to do is 14*.30 which equals to $4.20


8 0
3 years ago
I need help asapppp!!!!!!!
monitta

Answer:=15x^2+250x

Step-by-step explanation:

8 0
2 years ago
Read 2 more answers
Two payment options to rent a car: You can pay $20 a day plus 25¢ a mile (Option A) or pay $10 a day plus 50¢ a mile (Option B).
BaLLatris [955]

You must drive more than 40 miles to make option A the cheaper plan

<em><u>Solution:</u></em>

Two payment options to rent a car

Let "x" be the number of miles driven in one day

<em><u>You can pay $20 a day plus 25¢ a mile (Option A)</u></em>

25 cents is equal to 0.25 dollars

OPTION A :  20 + 0.25x

<em><u>You pay $10 a day plus 50¢ a mile (Option B)</u></em>

50 cents equal to 0.50 dollars

Option B: 10 + 0.50x

<em><u>For what amount of daily miles will option A be the cheaper plan ?</u></em>

For option A to be cheaper, Option A must be less than option B

Option A < Option B

20 + 0.25x < 10 + 0.50x

Solve the inequality

Add -0.50x on both sides

20 +0.25x -0.50x < 10 + 0.50x - 0.50x\\\\20 - 0.25x < 10

Add - 20 on both sides,

20 - 0.25x - 20 < 10 - 20\\\\-0.25x < -10

\mathrm{Multiply\:both\:sides\:by\:-1\:\left(reverse\:the\:inequality\right)}

0.25x > 10

Divide both sides by 0.25

x > 40

Thus you must drive more than 40 miles to make option A the cheaper plan

7 0
3 years ago
Describe the symmetry of these functions
Oduvanchick [21]
If it was line symmetry it would need to repeat the same shape twice, which the first follows but the second doesn’t.
if it was rotational, you would need to be able to take the shape in the top right and rotate it counterclockwise or clockwise to get the shape that locks in place. that doesn’t follow that.
both line and rotational symmetry is incorrect because the first example would need to lock up inside the right side of that example.

the answer is C
5 0
3 years ago
Read 2 more answers
Other questions:
  • Alex lady sketch for a homemade soccer goal he plans to build . Do you go will be in the shape of a triangular prism . The legs
    14·1 answer
  • Please answer ASAP will mark brainilest ​
    10·1 answer
  • when full, the gas tank of a car can hold 15 gallons. It now contains 12 gallons. What percent represents how full the tank is?
    9·1 answer
  • David’s bowling score is 5 less than 3 times Aaron’s score. The sum of their score is 215. Find the score of each student. Write
    5·1 answer
  • You buy 4 breakfast sandwiches at $2.59 each, 4
    14·1 answer
  • Maxis ordering a salad for lunch. He can choose one of chicken, tofu, hard-boiled eggs, or turkey to have on the salad. He can a
    9·1 answer
  • Can someone pls give me an explanation on how to do this pls
    5·2 answers
  • Find the following ratios. PLEASE HELP QUICK!!
    8·2 answers
  • HURRY PLEASE SOLVE will give brainliest!!!​
    8·1 answer
  • What is the inequality 4x-7&lt;5
    6·2 answers
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!