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
deff fn [24]
3 years ago
11

Antonio's toy boat is bobbing in the water next to a dock. Antonio starts his stopwatch, and measures the vertical distance from

the dock to the height of the boat's mast, which varies in a periodic way that can be modeled approximately by a trigonometric function. The vertical distance from the dock to the boat's mast reaches its highest value of -27 \text{ cm}−27 cmminus, 27, space, c, m every 333 seconds. The first time it reaches its highest point is after 1.31.31, point, 3 seconds. Its lowest value is -44\text{ cm}−44 cmminus, 44, space, c, m. Find the formula of the trigonometric function that models the vertical height HHH between the dock and the boat's mast ttt seconds after Antonio starts his stopwatch. Define the function using radians.

Mathematics
1 answer:
Firlakuza [10]3 years ago
7 0

Answer:

Step-by-step explanation:

Since we're given a time at which the height is maximum, we can use a cosine function for the model.

The amplitude is half the difference between the maximum and minimum: (-27 -(-44))/2 = 8.5 cm.

The mean value of the height is the average of the maximum and minimum: (-27 -44)/2 = -35.5 cm.

The period is given as 3 seconds, and the right shift is given as 1.31 seconds.

This gives us enough information to write the function as ...

  H(t) = (amplitude)×cos(2π(t -right shift)/period) + (mean height)

  H(t) = 8.5cos(2π(t -1.31)/3) -35.5 . . . . cm

You might be interested in
Kathryn draws three pairs of intersecting lines. In each figure, she measures a pair of angles. What is a reasonable conjecture
denis23 [38]
<span>Inductive reasoning is that when two lines intersect you will always have a pair of congruent angles considering an exception when all the angles are congruent. According to this,
1) Vertical angles (or opposite angles) are congruent. In this case, vertical angles could be acute or obtuse depending on the position of the lines.

2) The second case is the exception when all the angles are equal. It means that the lines are perpendicular.

3) Again back to the first case, vertical angles are equal or congruent in other words.

4) And again back to the second case when the lines are perpendicular, then all the angles that formed are equal to each other.

You can observe all the cases in the picture attached below.</span>

3 0
3 years ago
Read 2 more answers
What is the value of the x in the equation 2x +3y = 36, wheb y = 6?
ddd [48]

Answer:

x = 9

Step-by-step explanation:

5 0
3 years ago
Read 2 more answers
If 1900 square centimeters of material are available to make a box with a square base and an open top, find the largest possible
Evgen [1.6K]

Answer:

Volume = 7969 cubic centimeter

Step-by-step explanation:

Let the length of each side of the base of the box  be A and the height of the box be H.

Area of material required to make the box  is equal to  is A^2 + 4*A*H.

A^2 + 4*A*H = 1900

 Rearranging the above equation, we get -  

`H = \frac{(1900 - A^2)}{(4*A)}

Volume of box is equal to product of base area of box and the height of the box -  

V = A*A* H

Substituting the given area we get -

\frac{A^2*(1900 - A^2)}{4A} = \frac{(1900*A - A^3)}{4}

For maximum volume

\frac{dV}{dA} =0

\frac{ 1900}{4} - \frac{3*A^2}{4} = 0

A^2 = \frac{1900}{3}

Volume of the box

= \frac{\frac{1900}{3}*(1900 - \frac{1900}{3}) }{4 * \sqrt{\frac{1900}{3} } }

= 7969 cubic centimeter

3 0
2 years ago
2. A university class had two recitation sections. The Monday recitation had 64 students and
grin007 [14]

Answer:

22

Step-by-step explanation:

64+20= 84 (number of students in total)

84/2= 42 (number of students each session)

Moving 22 students to Monday will result in equal number of students.

4 0
3 years ago
13u - v + 8 Coefficients.​
Aleks04 [339]

Answer:

the coefficient in the equation is 13

Step-by-step explanation:

a coefficient is a number that is in front of a variable. 13 is in front of the variable u so it is the coefficient.

6 0
3 years ago
Read 2 more answers
Other questions:
  • Find two consecutive whole numbers that 74 lies between.
    12·1 answer
  • What should be done to both sides of the equation in order to solve w - 9 = 15? Add 15. Subtract 15. Add 9. Subtract 9.
    6·1 answer
  • What kind of triangle has angles 35,110,35
    13·1 answer
  • Use the diagram and equations below to match the following angles with their correct measures.
    5·1 answer
  • How do u do this it's something about solving proportions and I have no idea how to do this plz help
    6·1 answer
  • Reflect triangle ABC over the x-axis. Then translate the new triangle 5 units to the left. What are the coordinates of the verti
    14·2 answers
  • Help me to get brainest everyday if u friend me
    13·2 answers
  • Dave's father is paying him to paint the storage
    7·1 answer
  • (1 point for work, 1 point for correct answer) PLEASE HELP BEFORE WINTER BREAK​ NO LINKS HURRY
    6·2 answers
  • 5. Find the equation of the line that goes through the points (4,7) and (-2,-5)
    6·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!