The function y=60+25sin(pi/6)t, where t is in months and t=0 corresponds to April 15, models the average high temperature in degrees Fahrenheit in Centerville.

b.) What is the maximum high temperature and when does this occur?

NOTE: I found the answer online, I just don't understand how to get there. It's July 15, 85 degrees.

Answers

Answer 1

Answer:

The maximum temperature will be of 85 degrees, on July 15.

Step-by-step explanation:

Sine function:

The sine function oscilates between -1 and 1, and it's maximum value is:

[tex]\sin{(\frac{\pi}{2})} = 1[/tex]

y=60+25sin(pi/6)t

The maximum value will occur when [tex]\sin{(\frac{\pi t}{6}}) = 1[/tex], and it will be of 60 + 25 = 85 degrees.

When will it occur?

First we find the value of t for which the value inside the function sine is [tex]\frac{\pi}{2}[/tex]. So

[tex]\frac{\pi t}{6} = \frac{\pi}{2}[/tex]

[tex]\frac{t}{6} = \frac{1}{2}[/tex]

[tex]2t = 6[/tex]

[tex]t = \frac{6}{2} = 3[/tex]

That is the number of months after April 15, which is 3 months. So July 15.


Related Questions

Practice
In the figure, a || 6. What is the value of x?

Answers

Answer:

x = 40

Step-by-step explanation:

3x + 9 = 129 Alternate Exterior Angles Theorem

-9 -9

3x = 120 divide by 3

x = 40

quick i’m almost done

Answers

Answer:

Step-by-step explanation:

[tex]\sqrt{12^{2}+6^{2} } = \sqrt{144 + 36} = \sqrt{180} = \sqrt{36*5}= 6\sqrt{5} = 13.4[/tex]

answer is A

Need some help on this question??

Answers

Step-by-step explanation:

I am sorry I didn't know the answer

Answer:

2nd option

Step-by-step explanation:

The secant- secant angle CAD is half the difference of the intercepted arcs, that is

∠ CAD = [tex]\frac{CD-GE}{2}[/tex]

5. In order to figure out who will go first in a game, your friend asks you to
pick a number between 1 and 25.
a. What are the possible outcomes?
b. What are the favorable outcomes of choosing an even number?
c. What are the favorable outcomes of choosing a
number less than 20?

Answers

Answer:

a. - Any number 1-25

b. - 12/25

c. - 20/25

Given that
5x : 8 = 7:2
Calculate the value of x
Give your answer in its simplest form.

Answers

Answer:

Step-by-step explanation:

Given

5x : 8 = 7 : 2

[tex]\frac{5x}{8} =\frac{7}{2}\\cross , multiply\\\\10x = 56\\x = \frac{56}{10}\\x =\frac{28}{5}[/tex]

hope it helps :)

Please help me on this for my quiz: Which equation represents an inverse variation with a constant of 56?
A: y/x=56
B: 7/y=8/x
C: 1/4y=14x
D:xy/2=28

Answers

Answer:

D) xy/2 = 28

Step-by-step explanation:

Inverse Variation:

y = k/x

Given:

k = 56

Work:

y = k/x

y = 56/x

xy = 56

xy/2 = 28

xy = 28 * 2

xy = 56

Braelyn is writing an equation to represent the perimeter of a rectangle with the width equal to half the length. She knows that the perimeter is equal to 18 units and needs to find the length and width of the rectangle. Which equations represent this relationship? Select the four correct answers.
x + one-half x = 18
2 x + x = 18
2 (x) + 2 (2 x) = 18
x + one-half x + x + one-half x = 18
2 (x + one-half x) = 18
2 x + one-half x = 18

Answers

Answer:it’s the middle 4. First and last choices are wrong

Step-by-step explanation:

Answer:

it’s the middle 4. First and last choices are wrong

Step-by-step explanation:

The probability that you randomly select a red marble from a group of 40 marbles is 7/20 . How many are red marbles?

Answers

There are 14 red marbles
14 i think. Since 7/20 is 35%, it’s 40-65%(100%-35%) and so it is 14 red marbles.

Troy and Ronnie wrote down how much time they spent at play rehearsal each week for 6
weeks.
Troy spent 6, 4, 8, 5, 10, and 9 hours at play rehearsal.
Ronnie spent 4, 6,3,7,7, and 3 hours at play rehearsal.
How does the range of hours Troy spent compare with the range of hours Ronnie spent at play
rehearsal? Answer the questions to find out.
1. What is the range of hours Troy spent at play rehearsal? Explain how to find the range of a
data set.
Write your answer in the space below.
2. What is the range of hours Ronnie spent at play rehearsal?
Write your answer in the space below.
B. Who had a greater range of hours spent at rehearsal?
Write your answer in the space below.

Answers

Answer:

6 hours. To find the range you arrange the numbers in order from least to greatest, then subtract the largest number in the data set from the smallest.4 hours.

     b. Troy had the greater range because 6 hours is longer than 4 hours.

Step-by-step explanation: To find the range you arrange the numbers in order from least to greatest, then subtract the largest number in the data set from the smallest.

Employees at a company are given £1,200 to spend on items for the office.
They decide to buy a coffee machine and as many bean bags as possible.
Bean bags cost £40 with an offer of "Buy at least 15 get 10% off the price."
The coffee machine costs £280.
How much will they have left over from the £1,200?

Answers

Answer:

100 $

Step-by-step explanation:

Is there a relationship between the percent of high school graduates in each state who took the SAT and the state’s mean SAT Math score? Here is a residual plot from a linear regression analysis that used data from all 50 states in a recent year
A residual plot shows “Percent of high school graduates taking the SAT” along the horizontal axis ranging from 0 to 90 in increments of 10 and “Residual” along the vertical axis ranging from negative 50 to 50 in increments of 25. A horizontal line is drawn at 0 on the vertical axis across the graph. Dots are scattered on the either side of the line across the graph and between negative 30 and 35 on the vertical axis. A dot is shown before 20 on the horizontal axis between negative 70 on the vertical axis.
Explain how the residual plot shows that the Linear condition for performing inference about the slope is, or is not, met.

The variability of the residuals in the vertical direction is roughly the same from the smallest to the largest -value, which suggests that the relationship between mean SAT score and percent taking is not linear.

There is clear curvature in the residual plot, which confirms that the relationship between mean SAT score and percent taking is linear.

There is clear curvature in the residual plot, which suggests that the relationship between mean SAT score and percent taking is not linear.

There is clear curvature in the residual plot, which suggests that the relationship between mean SAT score and residual values is not linear.

The variability of the residuals in the vertical direction is roughly the same from the smallest to the largest -value, which confirms that the relationship between mean SAT score and percent taking is linear.

Answers

Answer:

There is clear curvature in the residual plot, which suggests that the relationship between mean SAT score and percent taking is not linear.

Step-by-step explanation:

Why might it be useful to covert radians to degrees?

Answers

Answer:

Protractor measures degrees

Step-by-step explanation:

what are the lengths of side a and b?​

Answers

Answer:

[tex]a =\frac{\sqrt 2}{2}[/tex] m

[tex]b=\frac{\sqrt 2}{2}[/tex] m

Step-by-step explanation:

Given

The attached triangle

Required

Find a and b

To do this, we make use of the following trigonometry ratio

[tex]\sin(\theta) = \frac{Opposite}{Hypotenuse}[/tex]

So, we have:

[tex]\sin(45) = \frac{a}{c}[/tex]

[tex]\sin(45) = \frac{b}{c}[/tex]

Where

[tex]c = 1[/tex]

So, we have:

[tex]\sin(45) = \frac{a}{1}[/tex]

[tex]\sin(45) = a[/tex]

Rewrite as:

[tex]a =\sin(45)[/tex]

In radical form:

[tex]\sin(45) =\frac{\sqrt 2}{2}[/tex]

So:

[tex]a =\frac{\sqrt 2}{2}[/tex]

Similarly:

[tex]\sin(45) = \frac{b}{c}[/tex]

[tex]\sin(45) = \frac{b}{1}[/tex]

[tex]\sin(45) = b[/tex]

Rewrite as:

[tex]b = \sin(45)[/tex]

In radical form:

[tex]\sin(45) =\frac{\sqrt 2}{2}[/tex]

So:

[tex]b=\frac{\sqrt 2}{2}[/tex]

A. 93
B. 57
C. 132
D. 123

Answers

Answer:

B

Step-by-step explanation:

The interior angles of a triangle always add up to 180 degrees.

We have two angles already and they add up to 60+63=123 degrees

180-123=57

so the remaining angle is 57 degrees

9514 1404 393

Answer:

  D.  123°

Step-by-step explanation:

The external angle is equal to the sum of the remote internal angles.

  m∠1 = 60° +63°

  m∠1 = 123°

What type of units are used to describe volume?

Answers

units used to describe volume are cubic

Answer:

The most basic common unit is Liters (L), but people also commonly use milliliters (mL) and cubic centimeter (cm^3).

Explain the difference between parallel and perpendicular slope in fewer than twenty words.

Answers

Answer:

parallel refers to two equidistant lines, Because the lines are equally distant, they have the same slope and the angle between them is zero. On the other hand, when two lines intersect at a right angle, they are called perpendicular.

Step-by-step explanation:

how to deal with never being loved after your bf told u he never actually loved you

Answers

Answer:

don't lose your hope

think positive

You find self love. Focus on yourself he ain’t deserve you queen!

Which is the volume of the Sphere with a diameter of 6 inches?
Volume
Sphere
=
A
288 Tt in
B
48 Tt in
C 36 Tt in
D 108 Tt in

Answers

Answer:

C

Step-by-step explanation:

because 6×6 is 36 so yeahh

Find the area of this parallelogram. Be sure to include the correct unit in the answer! (cm) , (cm2) , (cm3)

HELP PLEASE ! asap. i have a 30% in geometry & really tryna pass before summer .

Answers

Answer:

100cm^2 is what it means

Answer:

156 cm²

Step-by-step explanation:

The area of a parallelogram is found by finding the product of its base and perpendicular height. Here, the base is 12cm and the perpendicular height is 13cm.

12cm x 13cm = 156 cm²

please Help.
Ahmed And Ebrahim are recording how far a ball rolls down a ramp during each second. the table below shows the data the have collected.​

Answers

Answer:

Read below for the answer :)

Step-by-step explanation:

So, when you read it at first, it doesn't seem to match in any way. Well look at it from left to right. If you take notice of the bottom numbers, 1 to 9 is a difference of 8. And 2 to 13 = a difference of 11. 8-11 = a plus 3 system. Likewise, 3 to 17 = 14, or, 11 +3.

The answer is yes, and that is the reason above :)


I need help please !!!!!!!!

Answers

I don’t understand what this question is asking

Answer:

line and point

hope it's correct..

If x-5 = 8, which equation below would also be true?

Answers

Answer:

A

Step-by-step explanation:

because

[tex]x - 5 = 8 \\ x = 8 + 5 \\ x = 13 \\ x - 5 + 2 = 8 + 2 \\ x - 3 = 10 \\ x = 10 + 3 \\ x = 13[/tex]

help me i really need the help

Answers

Answer:

G: 1 3/4

Step-by-step explanation:

you have to divide, 8 3/4 cups by 5 and you get 1 3/4!

Answer:

G. 1 3/4

Step-by-step explanation:

There are multiple ways you can do this, but there's one easy way.

You can convert 8 3/4 to a decimal, which is 8.75.

From there, divide 8.75 by 5 and you get 1.75, which is 1 3/4/

What is the value of the expression
6t - 2
+4(t + 1) when t = 5?
4.

Answers

Answer:

(6 x 5) - 2 + 4(5 + 4)

30 - 2 +20 +16

A = 64

Step-by-step explanation:

i need help with this pls

Answers

Answer:

Angles B & C both = 157 degrees .

Step-by-step explanation:

Angle A is adjacent to Angle B, which means they are the same size. 23 degrees for A & B.

23+23 = 46.

We have two straight lines, one line = 180. 180*2 = 360.

Take 46 from 360 because we already figured out two angles.

360 - 46 = 314

Divide 314 by 2 because we have two unknown angles...

314 / 2 = 157 .

Angle B & C = 157.

A pet store has
10 hamsters for every 8 cats.

What is the ratio of hamsters to cats?
8:18
8:10
10:8

Answers

Answer: 10:8

Step-by-step explanation:

There are 10 hamsters and 8 cats

Since hamsters is first in the ratio, you put the 10 and then the 8

10:8

Hope this helps!

Answer:

the last option 10:8....

HELP WILL MARK BRAINLIEST IF GOTTEN RIGHT

Answers

Answer:

10π (after use calculator)

Step-by-step explanation:

A = 2πr

so,

A = 2(π)(5)

A = 10π

then use your calculator

and u will get the answer

I think the answer is 78.5

Area of a circle formula is : A=πr2

identify an equation in point slope form for the line perpendicular to y=-2x+8 that passes through (-3,9)

Answers

Answer:

y - 9 = 1/2(x + 3)

Step-by-step explanation:

find the slope that is perpendicular to line y = -2x + 8, which is the negative reciprocal slope: 1/2

substitute the new slope 1/2 and the given/known point (-3, 9) into the point-slope form:

=> y - 9 = 1/2(x - (-3)) => y - 9 = 1/2(x + 3)

point-slope form:

1. Find the Surface Area of the Rectangular
Prism.
5 ft
4 Ft
3 ft

Answers

Answer:

The total surface area is 94ftsq

lateral surface area is 70ftsq

top surface area is 12ftsq

bottom surface area is 12 ft sq

Jaysen flips a coin and selects a letter tile at random from those shown.

What is the probability of flipping heads and selecting a vowel? Express your answer as a fraction in simplest form.

Answers

Answer:

The probability of flipping heads is 1/2 and the probability of picking a vowel is 4/10 or 2/5

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