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Svet_ta [14]
2 years ago
10

I would like help with the question. It's part of my assigment, but I have trouble with this type of math. If someone understand

s, can you explain it to me as well? For future reference?
In Panama City in January, high tide was at midnight. The water level at high tide was 9 feet and 1 foot at low tide. Assuming the next high tide is exactly 12 hours later and that the height of the water can be modeled by a cosine curve, find an equation for water level in January for Panama City as a function of time (t).,

Mathematics
1 answer:
nata0808 [166]2 years ago
7 0
The cosine function cos(x), as you know, has a peak at x=0, a minimum at x=π, and another peak at x=2π. That is, its period is 2π. Its amplitude is 1, meaning the peak is +1 and the minimum is -1.

Problems where sine or cosine functions are used to model periodic behavior are problems in scaling. You need to match the period and amplitude of your scaled cosine function to the period and amplitude of the phenomenon you are modeling.

Here, high tides are 12 hours apart, so we need to scale x by a factor that turns 12 hours into 2π. That might be x ⇒ 2πx/12 or (π/6)x.

The high tide is 9 ft, and the low tide is 1 ft, so we need to do vertical offset and scaling to make the peak of our transformed cosine function be 9 and its minimum be 1. That difference is 8, so has an amplitude of ±4 around a midline of (9+1)/2 = 5.

Then our tide model is
.. water level = 5 +4*cos((π/6)t)

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Answer: The correct option is first, the number of basketball hoops did the company previously produce to make the same profit is 1.3 million hoops.

Explanation:

Let the number of basketball hoops did the company previously produce to make the same profit be x.

Total Revenue = Price * Quantity

The total revenue in million dollars is,

\text{Total Revenue}=(50-5x^2)x

\text{Total Revenue}=50x-5x^3

The total cost in million dollars is,

Total Cost = One unit cost * Quantity

\text{Total Cost}=30x

Profit = Total Revenue - Total Cost

\text{Profit}=50x-5x^3-30x

The profit is 15 million.

15=20x-5x^3

5x^3-20x+15=0\\x^2-4x+3=0\\(x-1)(x^2+x-3)=0

The value of x is 1 and \frac{-1\pm \sqrt{13}}{2}.

The production is always positive therefore the value of x either 1 or 1.3. Since 1 million is not available in the options therefore the the correct optin is 1.3 million hoops.

4 0
2 years ago
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Two parallel lines are crossed by a transversal. Parallel lines x and y are cut by transversal w. On line x where it intersects
oee [108]

Answer:

(A)56.5^\circ

Step-by-step explanation:

From the diagram attached:

Angle 1 and Angle 6 are Co-Interior Angles.

The sum of co-interior angle is 180 degrees.

Therefore:

m\angle 1+ m\angle 6=180^\circ\\\\m\angle 6=123.5^\circ,$ therefore:\\m\angle 1+ 123.5^\circ=180^\circ\\m\angle 1=180^\circ-123.5^\circ\\m\angle 1=56.5^\circ

The measure of angle 1 is therefore 56.5 degrees.

The correct option is A.

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2 years ago
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Four tomatoes cost $3.40. What is the unit rate?
77julia77 [94]

Answer:

$0.85 per tomato

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A unit rate is the cost for one item. Like $0.99 for this one bag of skittles.

So $3.40 divided by four is $0.85.

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tim estimates that 60÷5.7 is about 10. Will the actual quotient be greater then or less than 10? explain
lana66690 [7]
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2 years ago
Sections of prefabricated fencing are each 4 1/3 feet long. how long are 6 1/2 sections placed end to end
zalisa [80]

we know that

4\frac{1}{3}= \frac{(4*3+1)}{3} =\frac{13}{3}

6\frac{1}{2}= \frac{(6*2+1)}{2}=\frac{13}{2}

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\frac{13}{2} *\frac{13}{3} =\frac{169}{6}\ ft

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<u>the answer is</u>

28\frac{1}{6} \ ft


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