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ra1l [238]
3 years ago
9

The motion of a ship riding at anchor can be modeled by y=25-4 cos (pi/6)t, where y is the water depth in feet and t is the time

in hours. Consider a day in which t=0 represents 12:00 midnight. At what time during that day will the water under the ship be the deepest and what time will it be shallowest? What will the water’s depth be at these times?
Mathematics
1 answer:
balandron [24]3 years ago
5 0

Answer: 29 feet (deepest) at 6 am

              21 feet (shallowest) at Midnight & Noon

<u>Step-by-step explanation:</u>

y = -4 cos (π/6)t +25

Amplitude (A) = 4    

-A means it is a reflection over the x-axis (starts at minimum)<em> </em>

Period = 2π/B   →  Period = 12

Phase shift = C/B   →  Phase Shift = 0

Midline (D) = 25

Midline (D) ± Amplitude (A) = Max & Min

Max: 25 + 4 = 29

Min: 25 - 4 = 21

Change the coordinates of y = cos (x) as follows:

  • x-value: Add C then divide by B
  • y-value: Multiply by A then add D

Note that the equation shows: A = -4, B = π/6, C = 0, D = 25

\begin{array}{c|ccc|cl}\underline{\quad x\quad}&\underline{\quad y\quad}&&\underline{\quad (x+C)/B\quad}&\underline{\quad Ay+D\quad}\\0&1&&0&21&minimum\\\pi&0&&3&25&midline\\\pi &-1&&6&29&maximum\\3\pi/2&0&&9&25&midline\\2\pi&1&&12&21&minimum\\\end{array}

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hram777 [196]

Answer:

The inequality for Part A:  −6 °F <  −2 °F

Step by step-

The reason for that us because the -2 is closer to zero on the number line

3 0
2 years ago
Solve the quadratic equation 6x2 + 1 = 5x. Show your work.
Artyom0805 [142]

Answer:

<h2>Factors = (3x - 1) (2x - 1)</h2><h2>values :- x = 1/3 , 1/2</h2>

Step-by-step explanation:

= > 6x^2 + 1 = 5x

• Bring it in the standard form,

= > 6x^2 - 5x + 1 = 0

= > 6x^2 - (3 + 2)x + 1 = 0

= > 6x^2 - 3x - 2x + 1 = 0

• Take out common

= > 3x (2x - 1) - 1 (2x - 1) = 0

= > (3x - 1) (2x - 1) = 0...factors

= > x = 1/3 and 1/2... values of x

<h2>Hope it helps you!! </h2>

7 0
2 years ago
A tour company charges a given price per ticket based on the number, n, of people who take the tour. the maximum number of peopl
UkoKoshka [18]

Harper goes on a tour where the ticket price is $10.50 along with 29 people according to the given expression. Solving the given expression for 'n' results in the required number.

<h3>How to solve an algebraic expression?</h3>

Solving an expression algebraically involves basic operations like addition, subtraction, multiplication, and division.

  • In the expression, add/subtract the constant terms on both sides
  • Multiply/divide the coefficient of the variable on both sides
  • Solve for the variable.

<h3>Calculation:</h3>

Given that,

A tour company charges a given price per ticket based on the number 'n' of people who take the tour.

The maximum number of people who are allowed to take the tour is 35. I.e., n ≤ 35.

The price per ticket is $20 for n < 10 people and the price per ticket is given by the expression 20-(n-10)/2 for n > 10 people.

Harper goes on a tour where the ticket price is $10.50.

Since the price is less than $20, so the number of people who went on this tour is known by the expression 20-(n-10)/2 for n > 10 people.

So, solving the given expression:

20-(n-10)/2 = $10.50

-(n-10)/2 = 10.50 - 20

-(n-10)/2 = -9.5

(n-10) = 9.5 × 2

n -10 = 19

∴ n = 19 + 10 = 29

Therefore, 29 people went on this tour for a ticket price of $10.50.

Learn more about solving an expression here:

brainly.com/question/723406

#SPJ4

3 0
2 years ago
Your friend is graphing the point (5, 3). His first step is to start at the origin and go up 5 spaces. Which statement about his
ddd [48]
He is going up 5 spaces.
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Give pedro jogs every 4 days and Logan jogs every 6 day and I jog together how many days will it take for them to jog again toge
Vinvika [58]

Answer:

8 and 12 days

Step-by-step explanation:

to jog again=double

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7 0
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