answer.
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
kirill
16 days ago
9

Antonio's toy boat is bobbing in the water under a dock. The vertical distance HHH (in \text{cm}cmstart text, c, m, end text) be

tween the dock and the top of the boat's mast ttt seconds after its first peak is modeled by the following function. Here, ttt is entered in radians. H(t) = {5}\cos\left({\dfrac{2\pi}{3}}t\right) - {35.5}H(t)=5cos( 3 2π ​ t)−35.5H, left parenthesis, t, right parenthesis, equals, 5, cosine, left parenthesis, start fraction, 2, pi, divided by, 3, end fraction, t, right parenthesis, minus, 35, point, 5 How long does it take the toy boat to bob down from its peak to a height of -35\text{ cm}−35 cmminus, 35, start text, space, c, m, end text? Round your final answer to the nearest tenth of a second.
Mathematics
2 answers:
Inessa [9K]16 days ago
4 0

Response:

0.7 seconds

Detailed explanation:

Zina [9.1K]16 days ago
3 0

Answer: The elapsed time t equals 33.0 seconds.

Detailed explanation:

We start with the equation modeling the vertical distance H between the dock and the boat's mast at time t seconds after the first peak:

H(t) = 5cos( 2π/3 ​t) − 35.5H

The maximum height is 5 units.

When the mast is at its lowest point, H(t) equals 0.

5cos( 2π/3 ​t) − (35.5/100)H = 0

5cos( 2π/3 ​t) − 0.355 × 5 = 0

5cos( 2π/3 ​t) − 0.1775 = 0

Thus, 5cos( 2π/3 ​t) = 0.1775

From there, we find: cos( 2π/3 ​t) = 0.1775/5

Which simplifies to cos( 2π/3 ​t) = 0.355

To solve for t, we compute: 2π/3 ​t = cos^{-1}(0.355)

This yields: 2π/3 ​t = 69.2

Therefore, by multiplying both sides by 3, we have: 2πt = 69.2 × 3

Which results in 2πt = 207.6

Finally, solving for t gives: t = 207.6/2π

This results in t = 33.0 seconds.

You might be interested in
pat made a total of 48 pottery plates and cups if she made twice as many plates as cups how many plates did she make?
tester [8842]
48 divided by 3 equals 16 (cups)
Adding 16 and 16 gives 32 (which is double the number of cups)
Thus, the number of plates is 16.
5 0
1 month ago
Select the correct answer. What is the greatest common factor of this expression? 12m + 18m2 A. 6m B. 6 C. 2m D. 2
Svet_ta [9500]
Regardless of the value of M, it will correspond to 18m squared.
7 0
8 days ago
Read 2 more answers
Which function has no horizontal asymptote? F (x) = StartFraction 2 x minus 1 Over 3 x squared EndFraction f (x) = StartFraction
tester [8842]

Response:

f(x)=\frac{2x^2}{3x-1}

Detailed explanation:

The function  f(x)=\frac{2x-1}{3x} features a horizontal asymptote which is y=\frac{2}{3}

The function  f(x)=\frac{x-1}{3x} presents a horizontal asymptote which is y=\frac{1}{3}

One function f(x)=\frac{2x^2}{3x-1} lacks a horizontal asymptote  because the degree of its numerator surpasses that of the denominator,

The function  f(x)=\frac{3x^2}{x^2-1} displays a horizontal asymptote which is y=3

3 0
14 days ago
Read 2 more answers
Five thousand tickets are sold at​ $1 each for a charity raffle. Tickets are to be drawn at random and monetary prizes awarded a
babunello [8412]

Response:

the expected value of this raffle if you purchase 1 ticket = -0.65

Breakdown of the calculation:

Details:

5,000 tickets are sold at​ $1 each for a charitable raffle

Winners will be chosen at random with cash prizes as follows: 1 prize of ​$500​, 3 prizes of ​$300​, 5 prizes of ​$50​, and 20 prizes of​ $5.

Therefore, the value and its respective probability can be calculated as follows:

Value                              Probability

$500 - $1 = $499              1/5000

$300 - $1 = $299              3/5000

$50 - $1 = $49                    5/5000

$5 - $1 = $4                     20/5000

-$1                           1 - 29/5000 = 4971/5000

The expected value of the raffle when buying 1 ticket is computed as follows:

E(x) = \sum x * P(x)

E(x) = (499 * \dfrac{1}{5000} + 299 *\dfrac{3}{5000} + 49 *\dfrac{5}{5000} + 4 * \dfrac{20}{5000} + (-1 * \dfrac{4971}{5000} ))

E(x) = (0.0998 + 0.1794+0.049 + 0.016 + (-0.9942 ))

E(x) = (0.3442 -0.9942 )

\mathbf{E(x) = -0.65}

So, the expected value of this raffle when one ticket is purchased = -0.65

7 0
7 days ago
A gazebo is being built near a nature trail. An equation of the line representing the nature trail is y = 13x−4. Each unit in th
PIT_PIT [9117]

Respuesta:

126 pies

Explicación paso a paso:

Dado que:

Ecuación de la línea que representa el sendero de naturaleza:

y = 13x - 4

Distancia del gazebo respecto al sendero de naturaleza:

Cada unidad en el plano de coordenadas = 10 pies

Por lo tanto,

y = 13(10) - 4

y = 130 - 4

y = 126 pies

6 0
9 days ago
Other questions:
  • The mapping diagram shows a functional relationship. A mapping diagram shows a relation, using arrows, between domain and range
    15·2 answers
  • must a function that is decreasing over a given interval always be negative over that same interval explain
    15·2 answers
  • If the roads leading to an arena can together handle 3,500 vehicles/hour of arena-only traffic, at what time should the roads be
    9·1 answer
  • Last year the cost of a season ticket for a Rugby club was £370
    9·2 answers
  • The basketball team scored 82 points from 2- points anf 3-points baskets. They make 38 baskets altogether. Let a represent the n
    14·2 answers
  • Beth wants to earn $500 to purchase a new phone. She earns $11 an hour at her job. The function B(h)=11h represents the amount o
    6·1 answer
  • What is 7/12 of a full rotation
    15·2 answers
  • The Gades Foundation and HBM Corporation are eager to donate generously to their favorite charities.
    5·2 answers
  • Here is the five-number summary for a group of 100 runners in a 5-kilometer race. the variable is the time to complete the race.
    6·1 answer
  • To reduce wear and tear on the family vehicle, you decide to rent a car. Happy Harry’s Rentals has a $500 fee for any rental up
    6·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!