The function f(t) = 25 sin (pi over 2t) + 10 models the temperature of a periodic chemical reaction where t represents time in hours. What are the maximum and minimum temperatures of the reaction, and how long does the entire cycle take? Maximum: 35°; minimum: −15°; period: 4 hours<--- my answer Maximum: 25°; minimum: 10°; period: pi over 2 hours Maximum: 100°; minimum: −15°; period: pi over 2 hours Maximum: 35°; minimum: 35°; period: 8 hours

QUESTION POSTED AT 18/01/2020 - 07:03 AM

Answered by admin AT 18/01/2020 - 07:03 AM

Answer:

The correct answer is:

                   Maximum: 35°; minimum: −15°; period: 4 hours

Step-by-step explanation:

We are given a function f(t) which represent the temperature of a periodic chemical equation as:

      f(t)=25\sin (\dfrac{\pi}{2}t)+10

Hence, the maximum value of the function is attained when Sine function is maximum and the minimum value is attained when the sine function attains the minimum value.

We know that the Maximum value of sine function=1

and Minimum value of Sine function is: -1

when Sine function=1

we have: f(t)=25+10=35°

Hence, Maximum value of function= 35°

Also when Sine function= -1

We have: f(t)= -25+10= -15°

Minimum value of function= -15°

Also, we know that period of sine function of the type:

a\sin (bt)+c is given by:

Period=\dfrac{2\pi}{b}

Here we have:

b=\dfrac{\pi}{2}

Hence,  Period=\dfrac{2\pi}{\dfrac{\pi}{2}}\\\\\\Period=4

Hence,  Period=4

Post your answer

Related questions

Which scenario is represented by this equation? 1200 =3×+120

G. is your answer have a nice evening

ANSWERED AT 19/02/2020 - 06:08 PM


QUESTION POSTED AT 19/02/2020 - 06:08 PM

Lilana takes 4 breaths per 10 seconds during yoga.At this rate about how many breaths would Lilana takes in 2 minuets of yoga?

60 seconds in 1 minute.....so there is 120 seconds in 2 minutes

4 / 10 = x / 120.....4 breaths to 10 seconds = x breaths to 120 seconds
cross multiply
10x = 480
x = 480/10
x = 48 breaths <==

ANSWERED AT 19/02/2020 - 05:28 PM


QUESTION POSTED AT 19/02/2020 - 05:28 PM

(3y^0 x^2)^6 times y^-3 zx8

Ok so some basic rules

(x^m)(x^n)=x^{m+n}
(ab)^c=(a^c)(b^c)
(x^m)^n=x^{mn}
x^0=1
x^{-m}= \frac{1}{x^m}

so
[(3y^0x^2)^6][y^{-3}zx^8]
[(3(1)x^2)^6][y^{-3}zx^8]
[(3x^2)^6][y^{-3}zx^8]
[(3^6)((x^2)^6)][y^{-3}zx^8]
[(3^6)(x^{12})][y^{-3}zx^8]
(3^6)(x^{12})(y^{-3})(z)(x^8)
(3^6)(x^{12})(x^8)(y^{-3})(z)
(3^6)(x^{20})(\frac{1}{y^3})(z)
\frac{3^6x^{20}z}{y^3}
\frac{729x^{20}z}{y^3}

ANSWERED AT 19/02/2020 - 05:17 PM


QUESTION POSTED AT 19/02/2020 - 05:17 PM

What is the area of a rectangle which is 57 cm long and its breadth is 34 cm? One weird question for you to answer, what's my name?

Area of a rectangle is length*width.
If length is is 57 cm and width is 34 cm, then area is 
(57 cm)(34 cm) = 1938 cm^2

ANSWERED AT 19/02/2020 - 05:01 PM


QUESTION POSTED AT 19/02/2020 - 05:01 PM

Seth is trying to find the unit price for a package of blank compact discs on sale at 10 for $5.49. Find his mistake and correct it. Here's his math problem - 10/$5.49 =$1.82 each

He needs to flip the equation. So the real answer is 5.49/10=0.549

ANSWERED AT 19/02/2020 - 04:38 PM


QUESTION POSTED AT 19/02/2020 - 04:38 PM

If it takes 5 hours for felicias phone to get on 1% how many hours will it take to get 100%

If it takes 5 hours for Felicia's phone to get to 1%, it will take x hours to get to 100%.

We need to find x.

So we can simply just say 5 • 100.

X = 500

So it would (unfortunately) take Felicia's phone 500 hours to get to 100%.

Hope this helped!

ANSWERED AT 19/02/2020 - 04:30 PM


QUESTION POSTED AT 19/02/2020 - 04:30 PM

A picture frame is 5 inches on 2 sides and x inches on the other 2. If its perimeter is 50 inches, how long is each of the other sides? 20 22 45 48

The answer is 20 because 5+5=10. 50-10=40. 40 divided by 2 = 20!
The answer is 20!

ANSWERED AT 19/02/2020 - 04:28 PM


QUESTION POSTED AT 19/02/2020 - 04:28 PM

A school sells boxes of cookies each year for a charity fund. The data set shows the number of boxes the 10 families living on Willow Avenue buy, on average, every year. {2, 3, 2, 2, 0, 5, 2, 1, 1, 3} Does this data have negative, positive, or zero skew?

Answer:

This data set has zero skew as it is symmetric.

Step-by-step explanation:

We know that the symmetry exist in a data when the mean, median and mode of the data is same.

i.e. we are given a set of data as:

              {2, 3, 2, 2, 0, 5, 2, 1, 1, 3}

  • On arranging the data in increasing order we get :

    0  1   1   2   2   2   2   3   3   5

Hence, the value that occur in the middle is: 2

Hence, we have Median=2

  • Also, the mean is calculated as follows:

Mean=\dfrac{2+3+2+2+0+5+2+1+1+3}{10}\\\\\\Mean=\dfrac{21}{10}\\\\\\i.e.\\\\\\Mean=2.1

              Hence, Mean=2.1

  • Also, the mode of the data is the most frequently occurring data point in the set.

Here 2 occurs most number of times i.e. 4 times and hence we have:

                   Mode=2

Now, as the Mean, Median and Mode of the data are approximately same.

      Hence, we get the data is symmetric and hence has a zero skew.

ANSWERED AT 19/02/2020 - 04:25 PM


QUESTION POSTED AT 19/02/2020 - 04:25 PM

(15–7xy^2)–(y^3–y^2x–15)

15 - 7xy^2 - (y^3 - y^2x - 15)

Distribute negative sign
15 - 7xy^2 + -1(y^3 - y2x - 15)
15 + -7xy^2 + -1y^3 + -1(-xy^2) + (-1)(-15)
15 + -7xy^2 + -y^3 + x^2 + 15

Combine like terms
15 + - 7xy^2 + -y^3 +xy^2 + 15
( -7xy^2 + xy^2) + (-y^3) + (15 + 15)
-6xy^2 + -y^3+ 30

= -6xy^2 + -y^3+ 30

ANSWERED AT 19/02/2020 - 04:00 PM


QUESTION POSTED AT 19/02/2020 - 04:00 PM

15 is how many times more than 5? Write the expression not the answer.

Huh well, you can do 5 times x = 15 or 15/5 = x
x is the answer

ANSWERED AT 19/02/2020 - 03:57 PM


QUESTION POSTED AT 19/02/2020 - 03:57 PM

What kind of growth model (pattern) is shown in the table? x y 1 5 2 25 3 125 4 625 5 3,125 a. square root b. linear c. exponential d. quadratic

Answer:

Option C is correct.

The kind of growth model is shown in the table is exponential

Step-by-step explanation:

Exponential growth function is in the form of :  y = ab^x  ......[1];   where a is the initial value and b> 0.

Consider any two point from the table:

(1 , 5) and ( 2 , 25)

Substitute these in the equation [1] we get;

5 = ab^1         ......[2]

25 = ab^2      ......[3]

Divide equation [3] by [2] we have;

\frac{25}{5} = \frac{ab^2}{ab}

Simplify:

5 = b

Now substitute this value in equation [2] we get;

5 = a \times 5

Divide both sides by 5 we get;

\frac{5}{5} = \frac{5a}{5}

Simplify:

1=a or a = 1

Therefore, the table shown the  exponential growth function is, y = 5^x

ANSWERED AT 19/02/2020 - 03:44 PM


QUESTION POSTED AT 19/02/2020 - 03:44 PM

You have a bag of 10 marbles. three of them are red, five are blue, and two are green. what is the probability of randomly picking a green or blue marble out of the bag?

Probability when picking one is just number of "correct" anwsers devided by the total picking from

2 are green, 5 are blue, so 7 marbles are correct
the chance of picking one correct equals 7/10

ANSWERED AT 19/02/2020 - 03:37 PM


QUESTION POSTED AT 19/02/2020 - 03:37 PM

It is predicted that the population of a particular state will double every 25 years

I do not understand your question.

ANSWERED AT 19/02/2020 - 03:26 PM


QUESTION POSTED AT 19/02/2020 - 03:26 PM

20% of a number is x. What is 100% of the number? Assume x>0.

100% of a number would be 5 * 20.

5x

ANSWERED AT 19/02/2020 - 02:47 PM


QUESTION POSTED AT 19/02/2020 - 02:47 PM

Katle owes mathias $10 and cabin $5 katle has $3 in her pocket what's the meaning of 0 in this situation

In this situation, the only 0 that could be found is the one that attached to 10.
For this, the 0 only represent the real value of the money,and basically nothing else.
It also represent the amount of money Katle has left, after borrowing $12 and pay all of his debt.

ANSWERED AT 19/02/2020 - 02:39 PM


QUESTION POSTED AT 19/02/2020 - 02:39 PM

The tip for excellent service in a restaurant is 20 for every 100 of the meal what is the total bill (cost of meal plus tip) for a 60 meal?

I would think the tip would be 15 wich would make the meal all together 85.

ANSWERED AT 19/02/2020 - 02:34 PM


QUESTION POSTED AT 19/02/2020 - 02:34 PM

Hannah has 127 books in her collection. Her school is hosting a book donation. There are z students at her school, and they each plan to donate the same number of books and reach a total donation of 300 books! How many books will Hannah have in her collection after her donation? Write your answer as an expression.

Answer:

b/50

Step-by-step explanation:                                                                          There were 150 students who donated a total of b books.

The students donated an average of b/150 books each.

Hannah donated 3 times as many books as the average.

b/150 * 3 = b/50

Hannah donated b/50 books.

ANSWERED AT 19/02/2020 - 02:30 PM


QUESTION POSTED AT 19/02/2020 - 02:30 PM

Adam makes $25 per lawn he mows. How much does he make if he mows 4 lawns? Question 4 options: $29 $50 $75 $100

$25 x 4 = $100

edwbede

ANSWERED AT 19/02/2020 - 01:35 PM


QUESTION POSTED AT 19/02/2020 - 01:35 PM

A line has a slope of - 4/5. Which ordered pairs could be points on a line that is perpendicular to this line? Check all that apply. a. (-2,0) and (2,5) b. (-4,5) and (4,-5) c. (-3,4) and (2,0) d. (1,-1) and (6,-5) e. (2,-1) and (10,9)

we know that

if two lines are perpendicular

then the product of their slopes is equal to minus one

so

m1*m2=-1

in this problem we have

m1=-\frac{4}{5}

the value of m2 must be equal to

m2=-\frac{1}{m1} =-\frac{1}{(-4/5)}=\frac{5}{4}

we know that

The formula to calculate the slope between two points is equal to

m=\frac{(y2-y1)}{(x2-x1)}

Find the slopes of each of ordered pairs and compare with m2

case a) (-2,0)\ and\ (2,5)

Substitute in the formula

m=\frac{(5-0)}{(2+2)}

m=\frac{(5)}{(4)}

The slope is equal to m2

so

The ordered pair case a)  could be points on a line that is perpendicular to the given  line

case b) (-4,5)\ and\ (4,-5)

Substitute in the formula

m=\frac{(-5-5)}{(4+4)}

m=\frac{(-10)}{(8)}

m=-\frac{5}{4}

The slope is not equal to m2

so

The ordered pair case b)  could not be points on a line that is perpendicular to the given  line

case c) (-3,4)\ and\ (2,0)

Substitute in the formula

m=\frac{(0-4)}{(2+3)}

m=\frac{(-4)}{(5)}

The slope is not equal to m2

so

The ordered pair case c)  could not be points on a line that is perpendicular to the given  line

case d) (1,-1)\ and\ (6,-5)

Substitute in the formula

m=\frac{(-5+1)}{(6-1)}

m=\frac{(-4)}{(5)}

The slope is not equal to m2

so

The ordered pair case d)  could not be points on a line that is perpendicular to the given  line

case e) (2,-1)\ and\ (10,9)

Substitute in the formula

m=\frac{(9+1)}{(10-2)}

m=\frac{(10)}{(8)}

m=\frac{5}{4}

The slope is equal to m2

so

The ordered pair case e)  could be points on a line that is perpendicular to the given  line

therefore

the answer is

(-2,0)\ and\ (2,5)\\(2,-1)\ and\ (10,9)

ANSWERED AT 19/02/2020 - 01:33 PM


QUESTION POSTED AT 19/02/2020 - 01:33 PM

Thomas buys a cardboard sheet that is 12 by 8 inches. Create an equation for this situation, find the zeros, and sketch the function. What is the size of the cutout he needs to make so that he can fit the maximum amount of food in the box? If Thomas wants a volume of 12 cubic inches, what size does the cutout need to be? What would be the dimensions of this box? Using complete sentences, explain the connection between the cutout and the volume of the box. Design an equation that would work for any cardboard sheet length, q, and width, p.

For the answer to the question above,

1. If we let x as the side of the square cut-out, the formula for the capacity (volume) of the food dish is:
V = (12 - 2x)(8 - 2x)(x)
V = 96x - 40x^2 + 4x^3
To find the zeros, we equate the equation to 0, so, the values of x that would result to zero would be:
x = 0, 6, 4

2. To get the value of x to obtain the maximum capacity, we differentiate the equation, equate it to zero, and solve for x.
dV/dx = 96 - 80x + 12x^2 = 0
x = 5.10, 1.57
The value of x that would give the maximum capacity is x = 1.57

3. If the volume of the box is 12, then the value of x can be solved using:
12 = 96x - 40x^2 + 4x^3
x = 0.13, 6.22, 3.65
The permissible value of x is 0.13 and 3.65

4. Increasing the cutout of the box increases the volume until its dimension reaches 1.57. After that, the value of the volume decreases it reaches 4.

5. V = (q -2x) (p - 2x) (x)

ANSWERED AT 19/02/2020 - 01:10 PM


QUESTION POSTED AT 19/02/2020 - 01:10 PM

What is the answer to 12 = 4/5w ?

12 =  \frac{4}{5} w
Multiply Crusader, we have:
4w = 12*5
4w = 60
w =  \frac{60}{4}
\boxed{w=15}

Confirm that the solution is correct:

12 = \frac{4}{5} w
12 = \frac{4}{5} *15
12 =  \frac{60}{5}
\boxed{12 = 12}(TRUE)

Answer:
\boxed{w=15}

ANSWERED AT 19/02/2020 - 01:09 PM


QUESTION POSTED AT 19/02/2020 - 01:09 PM

Find side b if a =10 inches and side c = 16 inches.

Then it would be 52inches or 160 inches depends of your looking for area or perimeter

ANSWERED AT 19/02/2020 - 12:49 PM


QUESTION POSTED AT 19/02/2020 - 12:49 PM

How many times does 4 go into 108

All you need to do is divide:

108/4=27

4 goes into 108, 27 times

Hope this helped!! :)

ANSWERED AT 19/02/2020 - 12:32 PM


QUESTION POSTED AT 19/02/2020 - 12:32 PM

In the figure below, CEF is an equilateral triangle. Points B, C and E are collinear; Points A, C and F are collinear; g = 40 degrees; and k = 45 degrees. Find angle l. Show all work.

There exists the same question with the figure as shown in the attachment.

The given are:
g = 40 degrees
k = 45 degrees

Ask:
angle of " l "

So this is how to solve this:

Step 1:
Since CEF is an equilateral triangle, then each has 60 degrees.
i is equal to l because they are opposite angles

Step 2:
angle l is inside CEF, then the value of angle l is 60

ANSWERED AT 19/02/2020 - 12:21 PM


QUESTION POSTED AT 19/02/2020 - 12:21 PM

If the original quantity is 10 and the new quantity is 7 what is the percent decrease?

7 divided by 10 then subtract 100% =30

ANSWERED AT 19/02/2020 - 12:01 PM


QUESTION POSTED AT 19/02/2020 - 12:01 PM

The population f(x), in millions, of State A of a country after x years is represented by the function shown below: f(x) = (1.08)x The graph shows the population g(x), in millions, of State B of the country after x years: Graph of function g of x equals 2 multiplied by 1.08 to the power of x Which conclusion is correct about the population of State A and State B? The original population of State B was half of the original population of State A. The original population of State A was half of the original population of State B. The original population of State B was one-fourth of the original population of State A. The original population of State A was one-fourth of the original population of State B.

-- State-A . . . Population = 1 · (1.08)ˣ

-- State-B . . . Population = 2 · (1.08)ˣ

' x ' = number of years after the original population
At the beginning, x=0.
Any quantity raised to the zero power = 1.
At the beginning, when x=0, the original populations were
       State-A  =  1 · 1  =  1
       State-B  =  2 · 1  =  2

The original population of State A was half of
the original population of State B.


ANSWERED AT 19/02/2020 - 11:53 AM


QUESTION POSTED AT 19/02/2020 - 11:53 AM