Outside temperature over a day can be modelled as a sinusoidal function. Suppose you know the high temperature for the day is 80 degrees and the low temperature of 50 degrees occurs at 5 AM. Assuming t is the number of hours since midnight, find an equation for the temperature, D, in terms of t.

Answers

Answer 1

To find an equation for the temperature, D, in terms of t, we can use the properties of a sinusoidal function to model the temperature variation over the day.

Given:

High temperature: 80 degrees

Low temperature occurs at 5 AM (t = 5)

t is the number of hours since midnight

Let's assume a sinusoidal function of the form:

D = A * sin(B * t + C) + Dc

where:

A represents the amplitude (half the difference between the high and low temperatures)

B represents the frequency (how many cycles occur over a 24-hour period)

C represents the phase shift (how much the function is shifted horizontally)

Dc represents the vertical shift (the average temperature throughout the day)

We can determine the values of A, B, C, and Dc based on the given information.

Amplitude (A):

The amplitude is half the difference between the high and low temperatures:

A = (80 - 50) / 2

= 30 / 2

= 15 degrees

Frequency (B):

Since we want the temperature to complete one cycle over a 24-hour period, the frequency can be calculated as:

B = 2π / 24

Phase Shift (C):

Since the low temperature occurs at 5 AM (t = 5), the function should be shifted horizontally by 5 hours. To convert this to radians, we multiply by (2π / 24):

C = 5 * (2π / 24)

Vertical Shift (Dc):

The average temperature throughout the day is the midpoint between the high and low temperatures:

Dc = (80 + 50) / 2

= 130 / 2

= 65 degrees

Now we can put all the values together to obtain the equation for the temperature, D, in terms of t:

D = 15 * sin((2π / 24) * t + (5 * 2π / 24)) + 65

Simplifying further:

D = 15 * sin((π / 12) * t + (π / 12)) + 65

Therefore, the equation for the temperature, D, in terms of t is:

D = 15 * sin((π / 12) * t + (π / 12)) + 65.

Related Questions

how to draw the 6th term .

Answers

To draw the 6th term, represent it visually within the context of the pattern or sequence from which it is derived.

To draw the 6th term, we need to understand the context or pattern from which the term is derived.

Drawing the term usually involves representing the elements or characteristics of the pattern in a visual form.

Without specific information about the pattern, we can provide a general approach to drawing the 6th term.

Identify the Pattern:

Determine the sequence or pattern from which the 6th term is derived.

It could be a numerical sequence, a geometric pattern, or any other pattern.

For example, if the pattern is a number sequence of multiples of 3, the first few terms would be 3, 6, 9, 12, 15, and so on.

Visualize the Pattern: Based on the identified pattern, visualize how the elements change or progress from term to term.

This could involve drawing a diagram, a graph, or any visual representation that captures the pattern.

Consider using a coordinate grid, a number line, or any other suitable visual aid.

Locate the 6th Term:

Use the information from the pattern and the visualization to determine the specific position or value of the 6th term.

In our example of multiples of 3, the 6th term would be 18.

Draw the 6th Term: Finally, represent the 6th term in your chosen visual form.

This could mean marking the position on a number line, plotting a point on a graph, or incorporating the value into a diagram.

Note that the specific method of drawing the 6th term will depend on the nature of the pattern and the context in which it is given.

Providing more details about the pattern would allow for a more accurate and specific visual representation of the 6th term.

For similar question on sequence.

https://brainly.com/question/28036578

#SPJ8

Which statement about rectangles is true?
1. Only some rectangles are parallelograms.
2. Parallelograms have exactly 1 pair of parallel sides.
3. So, only some rectangles have exactly 1 pair of parallel sides.
1. All rectangles are parallelograms.
2. Parallelograms have 2 pairs of parallel sides.
3. So, all rectangles have 2 pairs of parallel sides.
1. Only some rectangles are parallelograms.
2. Parallelograms have 2 pairs of parallel sides.
3. So, only some rectangles have 2 pairs of parallel sides.
1. All rectangles are parallelograms.
2. Parallelograms have exactly 1 pair of parallel sides.
3. So, all rectangles have exactly 1 pair of parallel sides.

Answers

The correct statement about rectangles is:

1. All rectangles are parallelograms.

2. Parallelograms have exactly 1 pair of parallel sides.

3. So, all rectangles have exactly 1 pair of parallel sides.

A rectangle is a type of parallelogram that has additional properties. By definition, a rectangle is a quadrilateral with four right angles. This means that opposite sides of a rectangle are parallel. Since all four sides of a rectangle are right angles, it follows that a rectangle has exactly 1 pair of parallel sides.

Option 1 states that only some rectangles are parallelograms, which is incorrect. All rectangles are parallelograms because they have opposite sides that are parallel.

Option 2 states that parallelograms have 2 pairs of parallel sides, which is also incorrect. Parallelograms have exactly 2 pairs of parallel sides, not 4. A rectangle is a special type of parallelogram that has additional properties such as all angles being right angles.

Option 3 states that only some rectangles have 2 pairs of parallel sides, which is incorrect. All rectangles have exactly 1 pair of parallel sides, not 2. Having 2 pairs of parallel sides would make a shape a parallelogram, not a rectangle.

Therefore, the correct statement is that all rectangles are parallelograms and have exactly 1 pair of parallel sides. 1,2,3 are correct.

For more suhc questions on rectangles visit:

https://brainly.com/question/25292087

#SPJ8

the drawing shows an isosceles triangle

40 degrees

can you find the size of a

Answers

Angle "a" in the given isosceles triangle is 40 degrees.

To find the size of angle "a" in the isosceles triangle with a 40-degree angle, we can use the properties of isosceles triangles. In an isosceles triangle, the two equal sides are opposite the two equal angles.

Since the given angle is 40 degrees, we know that the other two angles in the triangle are also equal. Let's call these angles "b" and "c." Therefore, we have:

b = c

Since the sum of the angles in a triangle is always 180 degrees, we can write the equation:

40 + b + c = 180

Since b = c, we can rewrite the equation as:

40 + b + b = 180

Combining like terms, we have:

2b + 40 = 180

Subtracting 40 from both sides, we get:

2b = 140

Dividing both sides by 2, we find:

b = 70

Therefore, both angles "b" and "c" are 70 degrees.

Now, we can find angle "a" by subtracting the sum of angles "b" and "c" from 180 degrees:

a = 180 - (b + c)

= 180 - (70 + 70)

= 180 - 140

= 40

For more such questions on isosceles triangle visit:

https://brainly.com/question/29793403

#SPJ8

Other Questions

A municipal discount bond is promising to pay $2,150 next year. It is selling for $2,000 today. A treasury bond also promises to pay $2,150 next year, after tax. If the average income tax rate faced by bond market investors in 25 percent, due to arbitrage, the interest rate on the Treasury bond will be X percent and its price will equal Y dollars, where: a. X=10 percent &Y=$2,000 b. X=12 percent &Y=$2,000 c. X=12 percent &Y=$2,200 d. X=10 percent &Y=$2,200 Consider an object that at one time has energy E1 and momentum p1 and at a later time has energy E2 and momentum p2. Use the relativistic energy-momentum equation E2=p2c2+m2c4 to find the value of E22E21. Express your answer in terms of p1, p2, m, and c. Which product is considered a major source of polyunsaturated fat? When a small child says, "You can get me any toy as long as it is pink," she is using: External information Heuristics Consideration set Which particular incident sparked off the civil rights movement in USA? Mittal Companies bought a machine at the beginning of the year at a cost of $35,000. The estimated useful life was five years and the residual value was $2,000. Assume the estimated productive life of the machine is 16,500 units. Expected annual production was year 1, 3,300 units; year 2, 4,300 units; year 3, 3,300 units; year 4, 3,300 units; and year 5, 2,300 units.Complete a depreciation schedule for the units-of-production method.Prepare the journal entry to record Year 2 depreciation. "The Fall, namely, the broken relation between human and God manifests itself in many ways in business. Men and women in business have often lost a sense of meaning about their work." Why does Van Duzer argue this contention? What are some things and business situations can you find be examples of this first type of broken relation? Prove that |1-wz| -|z-w| = (1-|z|)(1-|w|). 7. Let z be purely imaginary. Prove that |z-1|=|z+1). In addition to bikes, Nord wants to produce and sell CartsNord provides us with the following additional information:Bike; Cart:Selling Price -- $500: $400Variable costs -- $300:$250Contribution Mar ( ) ( )Current Units sold: 750: 250Nords total fixed costs (common fixed costs) is $200,000, which cant be separated to neither bike nor cart.Calculate Sales Mix and Unit Contribution Margin of each product. Calculate Break-Even in units and in sales dollars for each products. first part1--The cost of inventory that a business has sold to its customers is called _____________________.2--What inventory system uses a computer system to keeping a running record of inventory on-hand?3--Where is the Recovery Asset reported in accordance with GAAP?4--Explain how sales are to be recorded under the new revenue recognition standard.5--Lesley's Apparel offers its customers the right to return any products purchased up to 45 days after the sale, for any reason. Last Thursday, Lesley's Apparel sold 100 blue cardigans to a variety of customers. Historically (based on experience), Lesley (owner of Lesley's Apparel) expects 20 of those cardigans to be returned for a full refund. On average, Lesley sells a cardigan for $125 and pays $50 to produce a cardigan. Prepare the entries to record the sale of the cardigans and expected refund liability and corresponding asset in accordance with GAAP. You may use traditional journal entries or the accounting equation to illustrate your entries. Please support your answer with well-labeled computations so that we can understand how you determined the amounts posted here. Gravitational force between two masses m, and m, is represented as F Gm m 7 where = xi+yj + zk and Irl=x + y + z G,m,, m are nonzero constants and let's assume that I 0 a) Calculate curl of and divergence of F (4 points) b) Show the integral ffdf is path independent and calculate following (4 points) (11) . vector function (9.10.11 ), . Suppose that the number of atoms of a particular isotope at time t (in hours) is given by the exponential decay function f(t) = e-0.88t By what factor does the number of atoms of the isotope decrease every 25 minutes? Give your answer as a decimal number to three significant figures. The factor is yc9034 avataryc903404/14/2021HistoryHigh SchoolansweredWhich statement best describes urban areas during the late 1800s?Urban areas were often sparsely populated with few employment opportunities.Many cities were overcrowded with limited housing and few sanitation services.Urban areas were designed to encourage people to commute to work and live in suburbs.Many cities were often free of political corruption with few limitations on who could vote. what kind of experience for becoming sultan did suleiman have what is hcf of 180,189 and 600 Story #1 Suppose you found an investment that earns 8.0% each year. Suppose you invest 12,000 dollars today. How many dollars will you have at the end of year five? A Between 12,000 and 14,000 B Between 14,000 and 15,000 C Between 15.000 and 16,000 D Between 16,000 and 18,000 Story #2 Suppose you found an investment that earns 8.0% each year. Suppose you invest 25,000 dollars at the end of year two. How many dollars will you have' at the end of year five? A Between 25,000 and 28,000 B Between 28,000 and 29.000 C Between 29,000 and 30,000 D Between 30.000 and 32.000 Story #3 Suppose you found an investment that earns 8.0% each year. Suppose you invest 12,000 dollars today. Suppose you also invest 25,000 dollars at the end of year two. How many dollars will you have at the end of year five? A Between 39,000 and 42,000 B Between 42,000 and 44,300 C Between 44,300 and 46,400 . D Between 46,400 and 50.000 Jayden and Tiana are saving for their daughter Kiara's college education. Kiara just turned 10 (at t = 0), and she will be entering college 8 years from now (at t -8). College tuition and expenses at State U. are currently $16,000 a year, but they are expected to increase at a rate of 2.5% a year. Kiara should graduate in 4 years--if she takes longer or wants to go to graduate school, she will be on her own. Tuition and other costs will be due at the beginning of each school year (at t -8, 9, 10, and 11). So far, Jayden and Tiana have accumulated $10,000 in their college savings account (at t = o). Their long-run financial plan is to add an additional $4.500 in each of the next 4 years (at t-1, 2, 3, and 4). Then they plan to make 3 equal annual contributions in each of the following years, t = 5, 6, and 7. They expect their investment account to earn 9%. How large must the annual payments at t= 5, 6, and 7 be to cover Kiara's anticipated college costs? a. $6,241.36 b. $6,803.08 Oc$8,036.66 Od. $7,373.08 e $5,754.83 The Wisconsin Lottery will pay a lottery winner a lump sum payment of $29,612,813 as the final payment of her winnings in four years. If the appropriate discount rate for the payment is 7.6% what is the present value of the payment? You are a South Dakota resident and want to get a $500 "Pay Day" loan from www.paydayone.com (yes, this is real). To borrow $500, you need to pay back $612.50 two weeks later. What is the APR and EAR of this loan? (There are 26 2-week periods in a year.)a) 585.0% APR and 19,467.6% EAR.b) 22.5% APR and 22.5% EAR.c) 270.0% APR and 1,041.9% EAR.d) 5.85% APR and 6.02% EAR. An open system of internal recruitment can be expected to minimize _________.A. competition among employeesB. scrutiny of job qualificationsC. overlooking talentD. low morale among those not advanced