Create an equation in the form y = asin(x - d) + c given the transformations below.
The function has a maximum value of 8 and a minimum value of 2. The function has also been vertically translated 1 unit up, and horizontally translated 10 degrees to the right.

Answers

Answer 1

The equation representing the given transformations is y = 3sin(x - 10°) + 3.

To create an equation in the form y = asin(x - d) + c given the transformations, we can start with the standard sine function and apply the given transformations step by step:

Vertical translation 1 unit up:

The standard sine function has a maximum value of 1 and a minimum value of -1.

To vertically translate it 1 unit up, we add 1 to the function.

This gives us a maximum value of 1 + 1 = 2 and a minimum value of -1 + 1 = 0.

Horizontal translation 10 degrees to the right:

The standard sine function completes one full period (i.e., goes from 0 to 2π) in 360 degrees.

To shift it 10 degrees to the right, we subtract 10 degrees from the angle inside the sine function.

This accounts for the horizontal translation.

Adjusting the amplitude:

To achieve a maximum value of 8, we need to adjust the amplitude of the function.

The amplitude represents the vertical stretch or compression of the graph.

In this case, the amplitude needs to be 8/2 = 4 since the original sine function has an amplitude of 1.

Putting it all together, the equation for the given transformations is:

y = 4sin(x - 10°) + 2

This equation represents a sine function that has been vertically translated 1 unit up, horizontally translated 10 degrees to the right, and has a maximum value of 8 and a minimum value of 2.

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Related Questions

Simplify the expression: *
5(-2n + 4) + 2(n + 3)

Answers

Answer:

26- 8n

Step-by-step explanation:

-10n + 20 + 2n + 6

-10n+2n +6 +20

-8n + 26

Best regards

Answer:

-8n+26

Step-by-step explanation:


Given parallelogram ABCD with
m B = 5x and mC = 3x+4.
Find the number of degrees in mD

Answers

Answer: X=22

Step-by-step explanation:

Find the LCM of the following.
A. 28,42,35
B. 48,72,96
C. 36, 44

Answers

A. 28,42,35

28/2= 14 42/2= 21 35/7= 5

14/ 2= 7 21/3= 7

28= 2^2 × 7

42= 2 × 3 × 7

35= 7 × 5

LCM= 420

B. 48,72,96

48/2= 24. 72/2= 36. 96/3= 32

24/2= 12. 36/3= 12. 32/2= 16

12/3= 4. 12/3= 4. 16/2= 8

4/2= 2. 4/2= 2. 8/2= 4

4/2= 2

48= 2^4 × 3

72= 2^3 × 3^2

96= 2^5 × 3

LCM= 288

C. 36, 44

36/3= 12. 44/2= 22

12/3= 4. 22/2= 11

4/2= 2

36= 3^2 × 2^2

44= 2^2 × 11

LCM= 396

Answer:

The answer is in the attachment

Step-by-step explanation:

!!PLEASE PLEASE PLEASE PLEASE MARK ME THE BRAINLIEST!!

Find the LCM of the following.A. 28,42,35B. 48,72,96C. 36, 44

Why is it called a square 1?

Answers

Square 1 is so named because of the shape of the puzzle: it is a cube with four sides, each with nine squares, creating a square shape

The puzzle is also sometimes referred to as a "magic cube" because it can be rearranged into different shapes and configurations.Square 1 is a 3-dimensional puzzle that consists of nine squares on each side of a cube. The puzzle is made up of four layers of nine colored squares that can be rotated around the center axis. This creates a square-like shape, hence the name “Square 1”. The object of the game is to arrange the nine squares on each side so that all of the colors match up. This requires the player to manipulate and rotate the pieces in order to achieve the desired outcome.

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pleaseeee help!!!!!!

pleaseeee help!!!!!!

Answers

Answer: 5. x=110 degrees

y=70 degrees

6. c=8

Step-by-step explanation:

5. x=110 degrees  ==> x and 110 are congruent angles.

110+y=180      ==> y is the supplement of an angle which is congruent to 110.

110-110+y=180-110

y=180-110

y=70 degrees

6. c/4 = 6/3

c/4 =2

c=8

Hanson is doing an obstacle course in gym class. First, he runs 500 meters and jumps over a hurdle. Then, he crawls through a 20-meter tunnel. Finally, he dribbles a soccer ball 100 meters to the finish line. How many kilometers long is the obstacle course?

Answers

Answer:

0.620 km

Step-by-step explanation:

0.500 + 0.020 + 0.100 = 0.620, or 0.62 km long

Multiple Choice: The volume of the square-based pyramid with base edge 9 units and height 48 units is: a. 324 units³ b. 1296 units³ c. 3888 units³ d. not enough information 9 ↑ ¹48 68​

Multiple Choice: The volume of the square-based pyramid with base edge 9 units and height 48 units is:

Answers

The volume of the square-based pyramid is 3888 units³. Your answer is option B. 3888 units³.

The formula to calculate the volume of a pyramid is V = (1/3)Bh,

Where B is the area of the base and h is the height.

In this case, the base is a square with edge length 9 units, so the area is B = 9² = 81 units².

The height is given as 48 units.
Plugging these values into the formula, we get:
To find the volume of a square-based pyramid, you can use the following formula:

V = (1/3) * base area * height.

In this case, the base edge is 9 units and the height is 48 units.

First, find the base area:

A = side * side = 9 * 9

= 81 square units.

Next, calculate the volume:

V = (1/3) * 81 * 48 = 3888 cubic units.
V = (1/3)(81)(48)
V = 1296 units³
Therefore, the volume of the pyramid is 1296 units³, which is option b.

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A poll was taken to determine which candidate students were voting for in an upcoming class president election. Of the students who participated in the poll, 40% voted for Iverson and 50% voted for Vicky. There were 30 votes for Vicky.

There were
(blank) people who participated in the poll.

Answers

Answer:

Step-by-step explanation:

the way to find how many participanted in the class voted, you need to look at the percentages and the number of students that voted for Vicky.

50% of students voted for Vicky and the question later explained that the total of the 50% was 30 students. This mean we know half of the student that participated. To find the total amount of students to make 100%, you need to multiple 30 by 2. which is 60.

Now that we know there were 60 students in total, we can find how many participated by using Iverson's percentage.

this is the formula that can help with any percentage math problem:

The percentage of something ÷ 100% = the number you are looking for ÷ the total

in our case:

40÷100 = x (because it is the unknown term)÷60

from here you cross multiple getting

2400÷100x

which equals

24

now we have to add Vicky's and Iverson's voter

24 + 30= 54

60-54=6

6 students did not participate

the counselors at ekhs hypothesize that the online vs. classroom results could be greatly affected by the grade level of students that were put into each treatment group. they know that seniors generally score better on the sat than juniors. how could we adjust our experiment to ensure that there is even split of seniors and juniors in each class? draw an outline of the experiment with your modifications

Answers

The outline of this experiment has been drawn using the concept of = Randomized Block Design

The outline of the experiment has been drawn and attached below.

According to the information given in the question,

⇒ Each treatment groups are to be analyzed according to the grade levels of the students of the online and offline classes.

Refer to the attached file below to see the outline of the experiment of an even split.

Randomized Block Design can be explained as -

The units used in the experiment are categorized into groups.The samples should be divided into equal homogenous groups and blocks.This block diagram follows the concept of Stratified random sampling.Even split of any two events.Differentiates natural variability from the differences created by blocking variables.

The schematic diagram of this formation could have the following components,

Blocking ⇒ Grouping ⇒ Treatment of numbers ⇒ Finialzed product.

Let us consider the total number of students = 50

Number of juniors = 20

Number of seniors = 30

In the grouping section,

The number of students is divided into an equal number of subgroups,

According to the attached table, we can see that the adjacent groups are treated together ( one group online with one group in the classroom ).

Therefore,

The outline of this experiment has been drawn using the concept of = Randomized Block Design

The outline of the experiment has been drawn and attached below.

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the counselors at ekhs hypothesize that the online vs. classroom results could be greatly affected by

The maximum weight of a shipping container is 125 pounds. What is the maximum weight in kilograms?
a. 56.7 kg
b. 62.5 kg
c. 75 kg
d. 100 kg

Answers

The maximum weight in kilograms is approximately 56.7 kg. Hence, the correct option is (a) 56.7 kg.

The maximum weight of a shipping container is 125 pounds.

We need to find out what is the maximum weight in kilograms.

Step 1: Find out 1 pound weight in kilograms We know that 1 pound = 0.45359237 kilograms (we already know that)

Step 2: Convert the maximum weight in pounds to kilograms

Maximum weight in pounds = 125 Maximum weight in kilograms

= 125 x 0.45359237

= 56.69904625≈ 56.7 kg

Therefore, the maximum weight in kilograms is approximately 56.7 kg.

Hence, the correct option is (a) 56.7 kg.

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help you awesome people

help you awesome people

Answers

Answer:

9

Step-by-step explanation:

This is because it is the number being multiplied

Hope this helps!

Answer: 9^2 or can also be read as 9 squared.The base itself is worth 9 but when you include the exponent its 81.When your solving exponents your multiplying the base by itself as many times as the exponent reads.In this case its 9x9 (2 times). The value of the base is 9 (just wanted to explain the other stuff just in case you didn't know)

have a good day :)

What is the domain of the functions below:

y=5x / |x-1|+1
(The / symbol is a fraction)

Answers

Answer:

domain is all real numbers

Distancia entre los puntos: (6,-1) (3,4).

Answers

The distance between the points (6, -1) and (3, 4) is √34 or approximately 5.83 units.

To calculate the distance between two points on a Cartesian plane, you can use the Euclidean distance formula. The formula is the following:

d = √((x₂ - x₁)² + (y₂ - y₁)²)

Where (x₁, y₁) and (x₂, y₂) are the coordinates of the two points.

Applying the formula to the points (6, -1) and (3, 4), we have:

d = √((3 - 6)² + (4 - (-1))²)

= √((-3)² + (4 + 1)²)

=√(9 + 25)

= √34

Therefore, the distance between the points (6, -1) and (3, 4) is √34 or approximately 5.83 units.

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What does the number of times a number is to be multiplied by itself?

Answers

The number of times a number is multiplied by itself is known as the power or exponent. To calculate the power of a number, we use the exponent formula \(n^{p}\) = n × n × n × ... × n, where n is the base number and p is the exponent. For example,\(4^{2}\) = 16 and \(4^{3}\)= 64.

The number of times a number is multiplied by itself is known as the power or exponent. For example, let's say we have the number 4. If we want to calculate 4 to the power of 2 (\(4^{2}\)), we are essentially multiplying the number 4 by itself twice. This is written as 4 multiplied by 4, which is equal to 16. In mathematical notation, the calculation is written as \(4^{2}\)  = 16.To calculate the power of a number, we can use the exponent formula: \(n^{p}\) = n × n × n × ... × n

where n is the base number and p is the exponent. For example, if we want to calculate\(4^{3}\) (4 to the power of 3), we would write the formula as 4 × 4 × 4 = 64. The corresponding mathematical notation is \(4^{3}\) = 64.

In summary, the number of times a number is multiplied by itself is known as the power or exponent. To calculate the power of a number, we use the exponent formula \(n^{p}\) = n × n × n × ... × n, where n is the base number and p is the exponent. For example,\(4^{2}\) = 16 and \(4^{3}\)= 64.

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what is the slope y=5x-3

Answers

Answer:

The slope is 5.

Explanation:

In the slope-intercept form of an equation

\(y=mx+b\)

m is the slope, and b is the y-intercept of the equation.

Now in our case,

\(\begin{gathered} m=5 \\ b=-3 \end{gathered}\)

therefore, the slope is 5 and the y-intercept is -3.

What is the slope of the line in this graph?

What is the slope of the line in this graph?

Answers

Answer:

The slope is 5/6

Step-by-step explanation:

To calculate the slope here, there are two ways.

Count the rise over run with the boxes

Or

Find Any 2 points and use y2-y1/x2-x1 to find slope

Both ways work.

For this graph Since it looks pretty basic, I‘ll use the rise over run technique

Now we start from the origin side that is where one point is and just rise vertically until I reach a point and when I do, just run that many steps.

So I reached till 5 and ran to 6 which is a  point on the coordinate graph

So to put it in slope form, it’s rise over run

Heres a easy way to remember it

lets say you wake up, you have to rise first and then run

You can’t run and then rise, that makes no sense

So here its rise 5 and run 6

so 5/6 is the slope

Find the value of x.
helpppp pleaseee!!

Find the value of x.helpppp pleaseee!!

Answers

Answer:

x = 50

Step-by-step explanation:

Since this is a quadrilateral, the sum is 360 degrees

2x+x+10 + 3x+x = 360

Combine like terms

7x+10 =360

Subtract 10 from each side

7x+10-10 = 360-10

7x = 350

Divide by 7

7x/7 = 350/7

x = 50

Answer:

\(x = 50\)

Step-by-step explanation:

Sum of the interior angles in a quadrilateral

= 360°

Let's solve now

\(x + 10 + 3x + x + 2x = 360 \\ 7x + 10 = 360 \\ 7x = 360 - 10 \\ 7x = 350 \\ \frac{7x}{7} = \frac{350}{7} \\ x = 50\)

hope this helps you.

Suppose your​ friend's parents invest $25,000 in an account paying 6% compounded annually. What will the balance be after 9 ​years?

The account balance will be ​$_

Answers

Answer:  $42,236.97

Work Shown:

A = P*(1+r/n)^(n*t)

A = 25000*(1+0.06/1)^(1*9)

A = 42236.9739750673

A = 42236.97

please help!!!!!!!!!!!!!!!! 100pts,

please help!!!!!!!!!!!!!!!! 100pts,

Answers

Answer:

80,000

Step-by-step explanation:

To solve this, use the Fundamental Counting Principle.

Simply calculate how many options there are for each digit in the combination, then multiply them to find the total number of combinations.

First digit: 0 - 9  →  10 optionsSecond digit: 0 - 9  →  10 optionsThird digit: 0 - 9  →  10 optionsFourth digit: 0 - 9  →  10 optionsFifth digit: 2 - 9  →  8 options

Total number of different combinations (codes):

⇒ 10 · 10 · 10 · 10 · 8 = 80,000

First four digits have 10options

Last digit have

10-2=8options

So Total ways

10⁴×810000×880000ways

what is equivalent to 5/4?

Answers

Answer:

10/8      15/12   20/16,   25/20,   30/24,   35/28,   40/32, 45/36, 50/40, 55/44, 60/48, 65/52, 70/56, 75/60, 80/64, 85/68, 90/72, 95/76, 100/80

There are probably hundreds of fractions that are equivalent to 5/4 but i am going to list 3-

1. 10/8

2. 15/12

3. 20/16

4. Angel's bank allows them 3 free ATM withdrawals each month, then charges a $5 ATM fee.
a. Write an equation to model how much Angel will pay in fees (y) based on their number of ATM
withdrawals (x).

Answers

The equation that represents Angel's pay in fees based on their number of ATM withdrawals y = 3 + 5x

How to determine Angel's pay in fees will based on their number of ATM withdrawals

Information from the question are

Angel's bank allows them 3 free ATM withdrawals each month

then charges a $5 ATM fee

Angel will pay in fees = y

number of ATM withdrawals = x

The Angel's bank  ATM withdrawals can be modeled as a linear function

What is linear function ?

A linear function consists of functions where the variables has exponents of 1. The graph of linear functions is a straight line graph and the relationship is expressed in the form.

y = 3 + 5x

Definition of variables to suit Angel's bank  ATM withdrawals

y = Angel will pay in fees

$5 = charges per withdrawal

x = number of ATM withdrawals

3 = free ATM withdrawals each month

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Evaluate the following with each given number.

f(x)=7x−x2+2

Answers

This the answer. X=-2/5

please help me answer this

please help me answer this

Answers

Answer:

pie

Step-by-step explanation:

Aerin's friend Fritz gives her a riddle to solve about the ages of the people in his family. There are 5 people in Fritz's family: Mom, Dad, his sisters Adele and Erika, and Fritz. Here are the clues to the puzzle. 1) Mom is 8 years younger than Dad. 2) Dad is 2 times as old as Fritz. 3) Adele is 4 years old. 4) Fritz's age plus Adele's age equals Erika's age. 5) Mom was 24 when Erika was born. 6) In 9 years, Mom will be twice as old as Erika will be. All the ages are whole numbers. Aerin decides to use variable for the unknown ages and write equations to express the information. M

Answers

Answer:

Dad = 47, Mom = 39, Fritz = 11, Erika = 15 and Adele = 4

Step-by-step explanation:

Let M = Mom's age, D = Dad's age, F = Fritz's age, A = Adele's age and E = Erika's age.

Given that

1) Mom is 8 years younger than Dad, we have D = M + 8   (1)

2) Dad is 2 times as old as Fritz. D = 2F   (2)

3) Adele is 4 years old. A = 4     (3)

4) Fritz's age plus Adele's age equals Erika's age. F + A = E   (4)

5) Mom was 24 when Erika was born. M = E + 24    (5)

6) In 9 years, Mom will be twice as old as Erika will be. M + 9 = 2(E + 9)   (6)

Substituting (5) into (6), we have

E + 24 + 9 = 2(E + 9)

E + 33 = 2E + 18

subtracting E from both sides, we have

2E - E + 18 = 33 + E - E

E + 18 = 33

subtracting 18 from both sides, we have

E + 18 - 18 = 33 - 18

E = 15

M = 15 + 24 = 15 + 24 = 39

From (4) F = E - A = 15 - 4 = 11

From (1) D = M + 8 = 39 + 8 = 47

So, their ages are Dad = 47, Mom = 39, Fritz = 11, Erika = 15 and Adele = 4

Determine whether or not the vector field is conservative. If it is conservative, find a function f such that
F =∇.f
F(x, y, z) = eyzi + xzeyzj + xyeyzk

Answers

The vector field F(x, y, z) = eyzi + xzeyzj + xyeyzk is conservative, and a potential function f is f(x, y, z) = xeyzi + xy²ezj + xyzek + C

How to determine vector field?

To determine if a vector field is conservative, we need to check if its curl is zero. If the curl is zero, it implies that the vector field can be expressed as the gradient of a scalar function.

Taking the curl of F, we have:

curl(F) = (∂F₃/∂y - ∂F₂/∂z)i + (∂F₁/∂z - ∂F₃/∂x)j + (∂F₂/∂x - ∂F₁/∂y)k

Evaluating the partial derivatives, we get:

curl(F) = (z - z) i + (x - x) j + (y - y) k

= 0

Since the curl of F is zero, the vector field F is conservative. We can find a potential function f by integrating each component of F with respect to its respective variable:

f(x, y, z) = ∫eyzi dx = xeyzi + g₁(y, z)

∫xzeyzj dy = xy²ezj + g₂(x, z)

∫xyeyzk dz = xyzek + g₃(x, y)

Here, g₁, g₂, and g₃ are arbitrary functions of the remaining variables. Combining these results, we obtain the potential function:

f(x, y, z) = xeyzi + xy²ezj + xyzek + C

Where C is the constant of integration. Therefore, a potential function f exists for the given vector field F, and it is given by f(x, y, z) = xeyzi + xy²ezj + xyzek + C.

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What is​3/5​written as a percent?

Answers

Answer:

60%

Step-by-step explanation:

5÷3=0.6

0.6×100=60

Turn it into a percent.

60%

Could I please have BRAINLIEST?

Answer:

60%

Step-by-step explanation:

a closed box is made of wood 2cm thick and its length breadth and height externally are 80cm 60cm and 50cm find the volume of the wood​

Answers

Answer:

Step-by-step explanation:

External length=80cm

External breadth=60 cm

External height=50 cm

External volume=l×b×h=80×60×50=240000cm^3

Internal length=80-2-2=76cm

Internal breadth=60-2-2=56 cm

Internal height=50-2-2=46cm

Internal volume=l×b×h=76×56×46=195776cm^3

Volume of wood= External volume-Internal volume=240000-195776=44224cm^3

Evaluate with help of distributive property :
i. 425 x 136 ii. 4005 x 67

Answers

Answer:

1 : 57,800.

2: 268,335

Step-by-step explanation:

hope it helps you

The expressions are evaluated using distributive property below -

We have -

i. 425 x 136

ii. 4005 x 67

We have to evaluate them with help of distributive property.

State the  property of distributivity of multiplication over addition.

Distributive property of multiplication over addition :  

a × (b + c) = a × b + a × c

According to question, we have -

i. 425 x 136

ii. 4005 x 67

Now -

425 x 136 = 425 x (6 + 30 + 100) = 425 x 6 + 425 x 30 x 425 x 100

and

4005 x 67 = 4005 x (60 + 7) = 4005 x 60 + 4005 x 7

Hence, the evaluation using distributive property is done.

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The table shows the ratio between the number of books ordered and their cost: Number of Books Cost (dollars) 7 14 8 16 9 18 Find equivalent ratios when the number of books ordered is 1, 2, and 3. Write them as ordered pairs in the form (x-coordinate, y-coordinate). Starting from the origin, explain how to plot the three equivalent ratios on a coordinate grid. (10 points)

Answers

14/7 = 2

16/8 = 2

18/9 = 2

This shows the cost of one book is $2

Multiply the number of books bought by 2 to get the cost:

1 x 2 = 2

2 x 2 = 4

3 x 2 = 6

Answer: (1,2) (2,4) (3,6)

Starting from the origin (0,0) for every 1 book bought ( x axis) move 2 more up than the previous total (y axis)

Using the 3 ordered pairs in the answer at x value 1 place a dot at y 2, then a dot at x2,y4 and again at x3,y6

Answer:

I'm doing the same test right now the ratios are 1 to 2 but the answers would be 1 to 2, 2 to 4, and 3 to 6 . you have to double the numbers that are shown

Step-by-step explanation:

I didn't copy the guy above it's litterallty simple multiplication hope my answer helped

Find the circumference of a circle when the area of the circle is 64πcm²​

Answers

Answer:

50.27 cm

Step-by-step explanation:

We Know

The area of the circle = r² · π

Area of circle = 64π cm²

r² · π = 64π

r² = 64

r = 8 cm

Circumference of circle = 2 · r · π

We Take

2 · 8 · (3.1415926) ≈ 50.27 cm

So, the circumference of the circle is 50.27 cm.

Answer: C=16π cm or 50.24 cm

Step-by-step explanation:

The formula for area and circumference are similar with slight differences.

\(C=2\pi r\)

\(A=\pi r^2\)

Notice that circumference and area both have \(\pi\) and radius.

\(64\pi=\pi r^2\)        [divide both sides by \(\pi\)]

\(64=r^2\)             [square root both sides]

\(r=8\)

Now that we have radius, we can plug that into the circumference formula to find the circumference.

\(C=2\pi r\)          [plug in radius]

\(C=2\pi 8\)          [combine like terms]

\(C=16\pi\)

The circumference Is C=16π cm. We can round π to 3.14.

The other way to write the answer is 50.24 cm.

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