The normal monthly temperatures (°F) for Omaha, Nebraska, are recorded below.

Month

Jan Feb Mar

Apr May

Jun

Jul

Aug

Sep

Oct

Nov

Dec

1

2

3

4

5

6

7

8

9

10

11

12

Temp.

21°

27°

390520620

720

770

740

650

53°

39°

25°

a. Write a sinusoidal function that models Omaha's monthly temperature variation

b. Use the model to estimate the normal temperature during the month of April.

Answers

Answer 1

Answer

[tex]y = 28 \sin(\frac{\pi}{6} - \frac{2\pi}{3}) + 49[/tex]

Step by Step Explanation

Given

See attachment for table

Required

Determine the sinusoidal function

The sinusoidal function is represented as:

[tex]y = A \sin(Bx + C) + D[/tex]

Where

[tex]|A| = Amplitude[/tex]

And it is calculated as:

[tex]A = \frac{1}{2}[Highest - Least][/tex]

From the table:

Highest = 77 and Least = 21

So:

[tex]A = \frac{1}{2}[77 - 21][/tex]

[tex]A = \frac{1}{2}[56][/tex]

[tex]A = 28[/tex]

B is calculated as:

[tex]Period = \frac{2\pi}{B}[/tex]

The period is 12 i.e. 12 months

So:

[tex]\frac{2\pi}{B} = 12[/tex]

[tex]B = \frac{2\pi}{12}[/tex]

[tex]B = \frac{\pi}{6}[/tex]

C is calculated as:

[tex]\frac{C}{B} = -4[/tex]

[tex]C = -4 * B[/tex]

[tex]C = -4 * \frac{\pi}{6}[/tex]

[tex]C = -2 * \frac{\pi}{3}[/tex]

[tex]C = -\frac{2\pi}{3}[/tex]

Lastly, D is calculated as:

[tex]D = Least + A[/tex]

So:

[tex]D =21 + 28[/tex]

[tex]D=49[/tex]

So, the function is:

[tex]y = A \sin(Bx + C) + D[/tex]

[tex]y = 28 \sin(\frac{\pi}{6} - \frac{2\pi}{3}) + 49[/tex]

The Normal Monthly Temperatures (F) For Omaha, Nebraska, Are Recorded Below.MonthJan Feb MarApr MayJunJulAugSepOctNovDec123456789101112Temp.2127390520620720770740650533925a.
Answer 2

Answer:

y=28 sin (pi/6 t - 7pi/6)+49

Step-by-step explanation:


Related Questions

What was first the fruit orange or the color orange
And how did the first people kill an animal with what
If a bow then where did they get the string from

Answers

Answer:

The orange (fruit) definitely got named first.

In ancient time, people hunt animals with old hunt tools. We can see some examples of old hunting tools.

And if they used bow, then I think they made string from raw materials like tree's branded peels.

Step-by-step explanation:

The perimeter of an equilateral triangle is 60 centimeters. The length of the altitude of the triangle is XV3 centimeters. What is the value of x? ​

Answers

9514 1404 393

Answer:

  x = 10

Step-by-step explanation:

Half of the triangle makes a 30°-60°-90° "special" triangle. We know the side ratios of that are 1 : √3 : 2. The long side is 1/3 of the perimeter, so is 60/3 = 20 = 10×2. Then the altitude is 10 times the middle ratio value: 10√3 ≈ 17.32.

Comparing this with x√3, we find x = 10.

Answer:

X = 25

Step-by-step explanation:

To solve this question, we'll first of all find determine the side length of the triangle from the perimeter.

Perimeter of an equilaterial triangle = 3 * s

S = side length

Perimeter = 150cm

150 = 3s

S = 150 / 3

S = 50cm

The side lengths are 50cm each since they are all equal.

To find x,

We have to divide the triangle equally into two different part.

Check the first attachment for better illustration on how the equilaterial triangle is.

Check the second attachment for better illustration on the triangle when its divided into a right angle triangle.

From the right angle triangle, we can use pythagorean theorem to solve for x

a² = b² + c²

a = 50cm

b = 25cm

c = x√(3)

50² = [x√(3)]² + 25²

2500 = x² * 3 + 625

2500 - 625 = 3x²

1875 = 3x²

X² = 1875 / 3

X² = 625

X = √(625)

X = 25

HOPE THIS HELPS

if so please give me a brainlist

How can you compare two rates graphically?

Answers

Answer:

Step-by-step explanation:

In Quadrants I and III, a larger rate has a steeper slope; for example, the line that climbs faster has the steeper slope.

NEED HELP ASAP (will give 10 points)

Answers

Answer:

Overuse of natural resources would not be a benefit, since it isn't a good to overuse something

1. Find the area of the figure above in square inches


2. Find the perimeter of the figure above in inches

Answers

The area is: 1,375 inches and the perimeter is: 197 inches

Find the value of a. 19 km 19 km Perimeter = 57 kilometers​

Answers

Answer:

19km

Step-by-step explanation:

The formula for the perimeter of a triangle is: S+S+S.

So;

19km+19km+a=57km

a=57km-19km-19km

=19km

What is the volume, in cubic centimeters, of a rectangular prism with a height of 7 centimeters, a width of 6 centimeters, and a length of 14 centimeters?

Answers

Answer:

588

Step-by-step explanation:

multiply length x width x height 7×6×14

Step-by-step explanation:

multiply 7,6,14

=588

therefore the answer in cubic centimeters is= 588

The equation A= 1750(1.04)t represents an account balance t years after the account was created. Which statement is correct?
A. The account balance will decrease 0.04% each year.
B. The account balance will increase 0.04% each year.
C. The account balance will decrease 4% each year.
D. The account balance will increase 4% each year.

Answers

Answer:

D. The account balance will increase 4% each year.

Step-by-step explanation:

Given the equation :

A= 1750(1.04)t

This is an exponential growth rate equation which has it's general format as :

A = A0 * (1 + r)^t

A0 = initial value,

Since (1 + r) is greater Than 1 ; then we conclude that it is a growth relation.

1 + r = 1.04

The rate, r = (1.04 - 1) = 0.04

r = 0.04 = (0.04 * 100%) = 4%

Hence, The account balance will increase 4% each year.

What is i^34?
A. -1
B. -i
C. 1
D. 1

Answers

Answer:

A.-1 all you had to do was look up the answer

Step-by-step explanation:

The answer to the question is A.

1. is a hanger a/an right,acute, or obtuse triangle?
2. is it a/an equilateral, scalene or isosceles triangle? please put an explanation for both, thanks :)

Answers

Answer:

1. acute 2. isosceles

Step-by-step explanation:

1. Acute means less then a 90 degree angle a hanger has a degree of about 60.

2. isosceles means it has 2 sides the same length a hanger has 2 sides the same length.

please help


will mark brainlist

Answers

Answer:

(-2, 4)

Step-by-step explanation:

Reflection over the x-axis would mean the point would flip upwards, this would affect the y coordinate.

I'LL GIVE BRAINLIEST PLEASE ANSWER ALL FOUR PLEASE

Answers

Answer:

i would need to see all four to be able to answer ?

Step-by-step explanation:

2/x-2+15/x=2/x-2 what is the LCD

Answers

Answer:

im not sure

Step-by-step explanation:

hy

Answer:

what butt to not answer

Step-by-step explanation:

Could someone please give the answer to this question.?

Answers

Answer:

25

Step-by-step explanation:

v^2 - 10v + __ : what number when added to itself gives you -10 ? -5

what's -5 x -5 ? 25

(v-5)^2 is a perfect square

could someone help me please? 13 points!!

Answers

Answer:

0.13

Step-by-step explanation:

it's not that hard all you have to do is add the shaded blocks, then make it a decimal

Answer:

Your answer would be 13%.

Step-by-step explanation:

Their is 100 squares and 13 squares are

shaded therefore it would be 13%.

Hope this helps!

Which of these expressions would be the best estimate of the quotient 15 1/2 ÷ 3 2/3?
A. 15÷3
B. 15÷4
C. 16÷3
D. 16÷4

Answers

Answer:

D

Step-by-step explanation:

Because 15 1/2 ÷ 3 2/3 equals 4.22727272727 and 15 divided by 3 is 5, 15 divided b 4 = 3.75 16 divided by 3 is 5.33333333333 and 16 divided by 4 equals 4 so thats the closest answer

Hope this helps

A survey of 11 students showed that 8 liked science, 7 liked mathematics, and 4 liked both. How many students just liked science

Answers

Answer:

4 I guess..........not sure but my answer is 4

Pleaasseee helppppp.

Answers

Answer:

180+12x

Step-by-step explanation:

Could someone give me a hand?

Answers

Answer:

30

Step-by-step explanation:

Look at the image I attached for reference as I explain. (I only labeled the angles that are relevant to the problem)

These triangles are congruent, as shown by the first equation.

When triangles are congruent, it means that the sides and angles are the same.

We can see that angles ∠ABC and ∠DEC are corresponding, which means that they have the same value.

We don't know ∠DEC, but we have two angles in that triangle that we do know. Since the angles in a triangle add up to 180, we have this equation:

180-65-55=∠DEC

60 = ∠DEC

So now we know that ∠DEC is 60 degrees.

Since ∠ABC and ∠DEC are equal:

2x=60.

Divide both sides by 2, and we get x =30.

HELPPPPPPPPPPPP MEHHHHHHHHHHHHHHHHHHHHHHHHH PLZZZZZZZZZZZZZZZZ GRADES GO OUT TOMMORROW AND I NEED THIS SO I CAN GET MY GRADE UP FROM A D+ PLZZZZZZZZ MY PARENTS WILL MURDER ME

Answers

Answer:

6.48

Step-by-step explanation:

17*-.36= -6.12

-6.12+12.6= 6.48

The sum of 10 and twice a number
(an equation)

Answers

Answer:

10+2x= the sum (anything could be put here)

Step-by-step explanation:

Well sum is automatically addition

Doubleing a number is basically multiplying it by 2

so

10+2x= whatever youw ant to put here

7) Usain Bolt is almost 7 foot tall. What is this height (approximately) in meters?​

Answers

Answer:

since 7 feet is 2.1336

aproximatly would be 2.08 rounded 2 meters

Step-by-step explanation:

f(x)= 3x - 5x + 2x – 3

Answers

There is no x-intercept/zero

Shanice's school is selling tickets to a play. on the first day of ticket sales the school sold 11 adult tickets and 6 student tickets for a total of $154. The school took in $145 on the second day by selling 3 adult tickets and 11 student tickets. find the price of a student ticket.

Answers

Answer:

$319

Step-by-step explanation:

add the money and then what u get for the money add it to the other numbers u have.

Use a net to find the surface Area of the square pyramid The height of the pyramid is 9 yes and the base sides are all 2.5 yrds and its a square as a base

Answers

Answer:

[tex]Area = 51.68yd^2[/tex]

Step-by-step explanation:

Given

[tex]h = 9yd[/tex] -- height

[tex]a = 2.5yd[/tex] --- base sides

Required

Determine the surface area

The net is not given. So, I will solve directly.

The surface area is calculated as:

[tex]Area = a^2 + 2a\sqrt{\frac{a^2}{4} + h^2}[/tex]

So, we have:

[tex]Area = 2.5^2 + 2*2.5\sqrt{\frac{2.5^2}{4} + 9^2}[/tex]

[tex]Area = 6.25 + 5\sqrt{\frac{6.25}{4} + 81}[/tex]

[tex]Area = 6.25 + 5\sqrt{1.5625 + 81}[/tex]

[tex]Area = 6.25 + 5\sqrt{82.5625}[/tex]

[tex]Area = 6.25 + 5* 9.086[/tex]

[tex]Area = 51.68yd^2[/tex]

You need to know how far you are away from the lighthouse.
You use a range finder to find the distance from the sailboat to the lighthouse light is 245 yards.
For angle B, chose an angle measure between 25° and 45°: __________
Based on the above information, find the distance from the sailboat to the island where the lighthouse is located.

Answers

Answer:

The distance from the sailboat to the island where the lighthouse is located is approximately 212.2 yards

Step-by-step explanation:

The distance between the sailboat and the lighthouse is found using trigonometric ratios as follows;

The given parameters are;

The distance from the sailboat to the lighthouse's light = 245 yards

The angle of elevation of angle B = An angle chosen between 25° and 45°

For simplicity, we chose, B = 30°

A right triangle formed with the height of the light house and the horizontal distance of the sailboat from the lighthouse as legs and angle B is the angle adjacent to the horizontal distance of sailboat from the light house

The hypotenuse length = The distance from the sailboat to the lighthouse's light = 245 yards

By trigonometric ratio, in the we have;

[tex]cos\angle B = \dfrac{Adjacent\ leg \ length}{Hypotenuse \ length}[/tex]

The adjacent leg length = The horizontal distance of sailboat from the light house

[tex]\therefore cos (30^{\circ}) = \dfrac{The \ horizontal \ distance \ between \ the \ sailboat \ and \ the \ lighthouse }{245 \ yards}[/tex]

The horizontal distance between the sailboat and the light house = 245 × cos(30°) ≈ 212.176223927

Therefore;

The horizontal distance between the sailboat and the lighthouse ≈ 212.2 yards

Therefore, the distance from the sailboat to the island where the lighthouse is located ≈ 212.2 yards.

someone help me with this

Answers

Answer:

C

Step-by-step explanation:

the middle line is the median you can see that they are the same

x/12-5>-2 please help

Answers

Answer:

Your math problem

1

2

5

>

2

can i get brainliest plz :)

Find the slope and y intercept

Answers

slope: 5/1 (5 if simplified)
y-intercept: 10

There is a bag filled with 4 blue and 5 red marbles.
A marble is taken at random from the bag, the colour is noted and then it is replaced.
Another marble is taken at random.
What is the probability of getting 2 blues?

Answers

Answer:

17/55 if simplified otherwise 34/110

Step-by-step explanation:

Answer:

16/81

Step-by-step explanation:

this is the answer that came up on hegarty

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