Outside temperature over a day can be modeled as a sinusoidal function. Suppose you know the temperature is 80 degrees at midnight and the high and low temperature during the day are 89 and 71 degrees, respectively. Assuming t is the number of hours since midnight, find an equation for the temperature, D, in terms of t.

Answers

Answer 1

Answer:

The equation is given by:

[tex]D(t) = 80 + 9\sin{0.2618t}[/tex]

Step-by-step explanation:

Sine function:

Has the following format:

[tex]y = A\sin{bx}[/tex]

In which A is the amplitude and [tex]\frac{2\pi}{b}[/tex] is the period.

Suppose you know the temperature is 80 degrees at midnight and the high and low temperature during the day are 89 and 71 degrees

This means that the amplitude of the sinusoidal variation function is 89 - 80 = 80 - 71 = 9. This means that [tex]A = 9[/tex]

During a 24-hour day, which means that the period is 24. So

[tex]\frac{2\pi}{b} = 24[/tex]

[tex]24b = 2\pi[/tex]

[tex]b = \frac{2\pi}{24}[/tex]

[tex]b = 0.2618[/tex]

So the variation is:

[tex]V(t) = 9\sin{0.2618t}[/tex]

Assuming t is the number of hours since midnight, find an equation for the temperature, D, in terms of t.

Initial temperature of 80, so:

[tex]D(t) = 80 + V(t) = 80 + 9\sin{0.2618t}[/tex]


Related Questions

It takes Josephine 60 minutes to walk 7 1/2 blocks.At This Rate How Many Blocks Can He Walk In 4 Hours.

Answers

Answer:

30 blocks

Step-by-step explanation:

60 minutes = 1 hour

For one hour, she will walk 7.5 blocks.

The rate is 7.5blocks per hour.

Multiply this by 4 hours, and you will get 30 blocks.

(7.5)4 = 30

If 4/5 of comcrete covers 5/6 of a bridge, how many tons if concrete is required to cover the entire bridge

Answers

Answer:

Write and solve an equation of proportions:

Step-by-step explanation:

4/5 ton 5/6 bridge

-------------- = ------------------

x 1 bridge

Then (4/5) * (1 bridge) = (5/6 bridge)x.

Solve this for x by mult. both sides of the equation by 6/5:

(6/5)(4/5) = x

24/25 tons of concrete are needed to complete the entire bridge.

100 people went to a picnic. 32 people got sick with food poisoning. The Public HealthDepartment narrowed it down to either the chicken salad or the cream pie. They determined that80 people ate chicken salad, 75 people ate cream pie, 33 people ate chicken salad cream pie anddid not get sick, 5 ate neither food and did not get sick, 40% of the people who ate chicken saladgot sick, and 36% of the people who are cream pie got sick. Was it the chicken salad or thecream pie

Answers

Answer:

It was the chicken salad.

Step-by-step explanation:

If you multiply each amount of people that ate one or the other and how many got sick, you get:

Chicken salad: 32

Cream pie: 27

And 32 people got sick so it must be the chicken salad.

Please help




thx thx thx thx

Answers

Answer: Alabama Alaska Arizona Arkansas California Colorado Connecticut Delaware Florida Georgia Hawaii Idaho Illinois Indiana Iowa Kansas Kentucky Louisiana Maine Maryland Massachusetts Michigan Minnesota Mississippi Missouri Montana Nebraska Nevada New Hampshire New Jersey New Mexico New York North Carolina North Dakota Ohio Oklahoma Oregon Pennsylvania Rhode Island South Carolina South Dakota Tennessee Texas Utah Vermont Virginia Washington West Virginia Wisconsin Wyoming or all of the US states in alphabetical order

What does circumference mean?


Distance around a circle


Space a circle takes up


Line from one side of a circle to another


Line from center of circle to side

Answers

Answer: Distance around a circle
are you in college?

Work out
3/8 x 11

Give your answer as a mixed number.​

Answers

Answer:

4.125 in decimal form and 4 1/8 in simplified fraction form

Step-by-step explanation:

The value of multiplication of an improper fraction 3/8 and a whole number 11 as a mixed number is 4 1/8.

To calculate 3/8 × 11 as a mixed number, we can follow these steps:

Step - 1:

Multiply the whole number by the numerator of the fraction:

11 × 3 = 33

Step - 2:

Divide the result by the denominator of the fraction:

33 ÷ 8 = 4 with a remainder of 1

Step - 3:

The whole number part of the mixed number is the quotient from the division:

The whole number part is 4.

Step - 4:

The fractional part of the mixed number is the remainder divided by the original denominator:

The fractional part is 1/8.

Therefore, the answer to 3/8 × 11 as a mixed number is 4 1/8.

To learn more about the fractions;

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For parallelogram ABCD, find m<1

Answers

Answer:

b

Step-by-step explanation:

the answer is

the angel m<1= 36°

The measure of angle m<1= 36°.

What is a parallelogram?

That quadrilateral in which opposite sides are parallel is called a parallelogram.

Thus, a parallelogram is always a quadrilateral but a quadrilateral can or cannot be a parallelogram.

WE are given that angle CAD = 36 degree

So, we know that parallelogram has parallel opposite sides.

Thus according to alternate interior angle we can say that;

angle CAD = angle m<1 = 36

therefore, the measure of angle m<1= 36°

Learn more about parallelogram;

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What is the y intercept of the line?

-3


-1


4


2

Answers

Answer:

2

Step-by-step explanation:

2 because the line goes through the y intercept at 2

X^2- 2x - 54 = 0

I need the answer to this please

Answers

x = 1 + √ 55 , 1 − √ 55 or

x = 8.41619848 , − 6.41619848

Solve for n. 35 = 9n - 10
Please don’t put a random answer for points.

Answers

Answer:

5

Step-by-step explanation:

First, you would add 10 to both sides to get 45 = 9n. Then, you would divide both sides by 9 to get n = 5. I hope this helps :)

Answer:

n = 5

Step-by-step explanation:

35 = 9n - 10

First, add 10 to each side.

35 + 10 = 9n - 10 + 10

45 = 9n

Divide both sides by 9

9n/9 = 45/9

n = 5

Hope this helps! Feel free to ask any questions

1 to the 10 power is what

Answers

Answer:

all u have to do is add a 0 to the end of 1 so it is 10

Step-by-step explanation:

88% of the light aircraft that disappear while in flight in a certain country are subsequently discovered. Of the aircraft that are discovered, 72% have an emergency locator, whereas 86% of the aircraft not discovered do not have such a locator. Suppose a light aircraft has disappeared.
A) If it has an emergency locator, what is the probability that it will not be discovered?B) If it does not have an emergency locator, what is the probability that it will be discovered?C) If we consider 10 light aircraft that disappeared in flight with an emergency recorder, what isthe probability that 7 of them are discovered?

Answers

Answer:

a) [tex]P(D'/L)=0.03[/tex]

b) [tex]P(D/L')=0.7[/tex]

Step-by-step explanation:

From the question we are told that

Probability of discovered [tex]P(D)=0.88[/tex]

Probability of aircraft with locator [tex]P(L/D)=0.72[/tex]

Probability of lost aircraft without locator [tex]P(L'/D')=0.86[/tex]

Generally the probability that aircraft are not discovered is mathematically given as

[tex]P(D')=1-0.88[/tex]

[tex]P(D')=0.12[/tex]

Generally the probability that aircraft with locator are discovered is mathematically given as

[tex]P(L'/D)=1-0.72[/tex]

[tex]P(L'/D)=0.28[/tex]

Generally the  Probability of lost aircraft without locator mathematically given as

[tex]P(L/D')=1-0.86[/tex]

[tex]P(L/D')=0.14[/tex]

Generally the  Probability of having a locator mathematically given as

[tex]P(L)=P(L/D)*P(D)+P(L/D')*P(D')[/tex]

[tex]P(L)=0.72*0.88+0.14 *0.12[/tex]

[tex]P(L)=0.6504[/tex]

a)Generally the  Probability of getting lost even with locator mathematically given as

[tex]P(D'/L)=\frac{P(L/D')(P(D')}{P(L)}[/tex]

[tex]P(D'/L)=\frac{0.14*0.12}{0.6504}[/tex]

[tex]P(D'/L)=0.0258302583[/tex]

[tex]P(D'/L)=0.03[/tex]

b)Generally the  Probability of getting lost even with locator mathematically given as

[tex]P(D/L')=\frac{P(L'/D)(P(D)}{P(L')}[/tex]

[tex]P(D/L')=\frac{0.28*0.88}{1-0.6504}[/tex]

[tex]P(D/L')=0.704805492[/tex]

[tex]P(D/L')=0.7[/tex]

Help me please guys .
What is the answer?


4.3

4.2

4.1

4.4

Answers

Cosine = adjacent/ hypotenuse
cos(53) = x/7
7 * cos(53) = x
x = 4.2

Sine = opposite / hypotenuse
sin(53) = y/7
7 * sin(53) = y
y = 3.2

what is the slope of a line that passes through the point (3,29.25)

Answers

Answer:

The slope is 9 3/4 or 9.75

Step-by-step explanation:

slope= rise/run or y/x

29.25/3=9.75 or 9 3/4

What is the value of x?
Enter your answer in the box.

Answers

Answer:

136

Step-by-step explanation:

68 * 2 = 136

Write an expression in the simplest form that represents the perimeter of the following shape

Answers

Perimeter is adding all 4 sides together:

8 + 8 + 9x + 9x

Simplify by coming like terms to get:

18x + 16

The answer is d. 18x + 16

What is the constant of proplity?
O 0.75
O 0.8
01.25
O 1.5

Answers

the answer to the problem- 1.5

i need help asap due tonight

Answers

Answer:

The top right one 3(x+4)=30

Step-by-step explanation:

Answer:

The answer should be the one on the top right.

Step-by-step explanation:

So we know that the whole entire model equals 30, and each of the three sections are s+4. So, in order to get 30, the equation has to have something to do with three times s+4. We can eliminate the one on the top left because the model does not have a 12 involved. We can also eliminate the bottom left because it only represents one of the three s+4s. The bottom right can be taken off because the 3 in that equation is only multiplied to s, and not s+4. The top right works because it is saying that s+4 multiplied by 3 times is equal to 30. There you go! I hope this helps❤️

An urn contains b black balls and r red balls. One of the balls is drawn at random, but when it is put back in the urn c additional balls of the same color are put in with it. Now suppose that we draw another ball.

Required:
Show that the probability that the first ball drawn was black given that the second ball drawn was red is b/(b r c).

Answers

Answer:

Please see the explanation below for proof

Step-by-step explanation:

Probability of choosing black ball from the bag

[tex]\frac{b}{b+r}[/tex]

Probability of choosing red ball from the bag

[tex]\frac{r}{b+r}[/tex]

After the addition of c balls of correspondent color –  

P (R2/B1) [tex]= \frac{r}{(r+b+c)}[/tex]

P (R2/B2) [tex]=\frac{r+c}{(r+b+c)}[/tex]

B1 and B2 are mutually exclusive event

P (B1/R2) = [tex]\frac{\frac{r}{(r+b+c)} *\frac{b}{b+r}}{\frac{r}{(r+b+c)}*\frac{b}{b+r} + \frac{r+c}{(r+b+c)}* \frac{b}{b+r}}[/tex]

P (B1/R2) [tex]=\frac{b}{(r+b+c)}[/tex]

Hence, Proved

Is -2 a whole number

Answers

Answer:

Whole numbers are all natural numbers including 0 e.g. 0, 1, 2, 3, 4… Integers include all whole numbers and their negative counterpart e.g. … -4, -3, -2, -1, 0,1, 2, 3, 4,… Where a and b are both integers.

Step-by-step explanation:

Answer:

No

Step-by-step explanation:

A whole number is any number that does not contain a fraction, decimal, or negative value.

There
are five marbles in
a bag. Three are green and
two are yellow. You draw a
marble, replace it, and then
Draw another. What is the
probability of choosing two
yellow marbles?

Answers

Answer:

like 20 percent

Dufrane buys a new pair of shoes that costs him $186 where the sales tax rate is 7.3%.
What is the total amount he paid after taxes? Round to two decimal places.

Answers

Answer:

$199.58

Step-by-step explanation:

$186 x 0.0730 = 13.578

13.578 + 186 = $199.57

What is the product?

0.4 x 0.6

0.024
0.24
2.4
24.0

Answers

The answer is 0.24 for the question

Round 138.867545518 to 4 decimal places.

Answers

The Answer will be 138.8675

can anyone help me and explain​

Answers

Answer:

so all you have to do is graph the linear equation of y=3x+0. But, the greater than or equals to sign tells us to make a solid line and shade above

result:

Step-by-step explanation:

Plz guys help me plz

Answers

Answer:

B

Step-by-step explanation:

✔️Rate of change using two points on the line, say (2, 60) and (3, 75);

Rate of change (m) = ∆y\/∆x = (75 - 60) / (3 - 2) = 15/1

Rate of change = 15

This means each class costs $15

✔️Initial value is the y-intercept (b). It represents the initial start-up fee.

To find initial value/y-intercept (b), substitute m = 15 and (x, y) = (2, 60) into y = mx + b.

Thus:

60 = 15(2) + b

60 = 30 + b

60 - 30 = b

30 = b

b = 30

Therefore, initial start-up fee is $30.

What are the next three terms in the following sequence 3 6 12 24 plz help

Answers

Answer:

3 6 12 24 48 96 192

Step-by-step explanation:

The answer is 48 96 192

Answer:it equals 96 hope this helps

Step-by-step explanation:

35=7x. please help me fasttt

Answers

Answer:

x=5

Step-by-step explanation:

35 divided by 7 is 5, so in that case, 7 times 5 is 35.

Write an equation of the line passing through the given points.
(3,-25) and (-3,5)

y=

Answers

Answer:

y = -5x -10

Step-by-step explanation:

This is the slope-intercept form:

[tex]y-y_{1} = m(x -x_{1})[/tex]

First, we look for the slope. The slope is found by using the equation:

[tex]m = \frac{y_{2}-y_{1} }{x_{2} -x_{1}}[/tex]

[tex]m = \frac{5 - (-25)}{-3 - 3} = \frac{30}{-6} = -5[/tex]

m = -5.

Now, given the two points, our y₁ is -25, and our x₁ is 3. Therefore, we substitute these values into the equation, and get:

y - (-25) = -5(x - 3)

y + 25 = -5(x - 3)

y + 25 = -5x + 15

y = -5x + 15 -25

y = -5x -10

Answer:

the answer to the problem is y= -5x - 10

At the organic produce store you can buy 3 bags of sweet potatoes for $20.07.
How much would it cost if you were to buy only 2 bags.

Answers

Answer:

$13.38

Step-by-step explanation:

Use proportions to solve this problem:

$20.07 / 3 bags  = X / 2 bags

multiply both sides by "2 bags" to isolate the unknown X

$20.07 * 2 / 3 = X

Therefore, X = $13.38

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