What are the amplitude, period, and midline of f(x) = −4 cos(2x − π) + 3?

Answers

Answer 1

[tex]\bf \qquad \qquad \qquad \qquad \textit{function transformations} \\ \quad \\ % function transformations for trigonometric functions \begin{array}{rllll} % left side templates f(x)=&{{ A}}sin({{ B}}x+{{ C}})+{{ D}} \\\\ f(x)=&{{ A}}cos({{ B}}x+{{ C}})+{{ D}}\\\\ f(x)=&{{ A}}tan({{ B}}x+{{ C}})+{{ D}} \end{array} \\\\ -------------------\\\\[/tex]

[tex]\bf \bullet \textit{ stretches or shrinks}\\ \left. \qquad \right. \textit{horizontally by amplitude } |{{ A}}|\\\\ \bullet \textit{ flips it upside-down if }{{ A}}\textit{ is negative}\\ \left. \qquad \right. \textit{reflection over the x-axis} \\\\ \bullet \textit{ flips it sideways if }{{ B}}\textit{ is negative}\\ \left. \qquad \right. \textit{reflection over the y-axis}[/tex]

[tex]\bf \bullet \textit{ horizontal shift by }\frac{{{ C}}}{{{ B}}}\\ \left. \qquad \right. if\ \frac{{{ C}}}{{{ B}}}\textit{ is negative, to the right}\\\\ \left. \qquad \right. if\ \frac{{{ C}}}{{{ B}}}\textit{ is positive, to the left}\\\\ \bullet \textit{vertical shift by }{{ D}}\\ \left. \qquad \right. if\ {{ D}}\textit{ is negative, downwards}\\\\ \left. \qquad \right. if\ {{ D}}\textit{ is positive, upwards}[/tex]

[tex]\bf \bullet \textit{function period or frequency}\\ \left. \qquad \right. \frac{2\pi }{{{ B}}}\ for\ cos(\theta),\ sin(\theta),\ sec(\theta),\ csc(\theta)\\\\ \left. \qquad \right. \frac{\pi }{{{ B}}}\ for\ tan(\theta),\ cot(\theta)[/tex]

with that template in mind, let's check

[tex]\bf f(x)=-\stackrel{A}{4}(\stackrel{B}{2}x\stackrel{C}{-\pi } )\stackrel{D}{+3}\\\\ -------------------------------\\\\ Amplitude\implies 4\\\\ Period\implies \cfrac{2\pi }{B}\implies \cfrac{2\pi }{2}\implies \pi [/tex]

now, the function is just the parent cos(x), shrunk some, -4, and shifted about, now D = +3, that means it has a vertical shift of 3 units up.

the parent function cos(x), has a midline of y = 0, now, if we shift it upwards by 3 units, the new midline will then be y = 3.

Related Questions

A 1950 kg car moves with a velocity of 11 m/s. What is its kinetic energy? Joules

Answers

The formula for Kinetic Energy is given by

KE = 0.5 × mv²

We have:
m, the mass = 1950 kg
v, the velocity = 11 m/s

KE = 0.5 × 1950 × 11²
KE = 117975 joules

rewrite 8/9 with a denominator of 63

Answers

To write 9 as 63, you need to multiply it by a number. 63/9 = 7.
So you need to multiply 9 by 7 to get 63.

But since it's a fraction, you can't multiply the denominator without multiply the numerator. So you need to multiply the denominator, 9, by 7 and the numerator, 8, by 7.

8/9 = (8*7) / (9*7) = 56/63

So 8/9 = 56/63

Hope this helps! :)

Final answer:

To rewrite the fraction 8/9 with a denominator of 63, multiply both the numerator and denominator by 7 to get 56/63.

Explanation:

To rewrite 8/9 with a denominator of 63, you need to find a number that you can multiply both the numerator (8) and the denominator (9) of the original fraction by, so that the denominator becomes 63. To do this, divide 63 by the original denominator, 9, which gives you 7. Thus, the number you need to multiply by is 7.

Multiply both the numerator and the denominator by 7:

Numerator: 8 times 7 = 56

Denominator: 9 times 7 = 63

Therefore, the fraction 8/9 with a denominator of 63 is 56/63.

A single 6-sided die is rolled twice. find the probability of getting a 55 the first time and a 11 the second time. express the probability as a simplified fraction.

Answers

They are independent events therefore they will not affect each other so rolling a certain number will always be 1/6.

1/6 x 1/6 x 1/6 x 1/6 = 1/1296

If the circumference of a circle is 201 centimeters what is the radius of the circle (to the nearest whole number)? Use 3.14 for pi

A) 32 centimeters
B) 128 centimeters
C) none
D) 16 centimeters
E) 64 centimeters

Answers

Final answer:

The radius of a circle with a circumference of 201 centimeters is approximately 32 centimeters, found by dividing the circumference by 2 times pi (π), using 3.14 as the value of pi. The correct answer is A) 32 centimeters.

Explanation:

The question asks us to find the radius of a circle when its circumference is given to be 201 centimeters. We use the circumference formula of a circle, which is C = 2πr, where C stands for circumference, π (pi) is a constant approximately equal to 3.14, and r represents the radius of the circle.

To find the radius, we rearrange this formula to solve for r:

Divide both sides of the equation by 2π to isolate r.

Plug in the given circumference value, C = 201 cm, and the approximate value of pi, π = 3.14, into the rearranged formula.

So the calculation would be r = C / (2π) = 201 / (2 * 3.14) = 201 / 6.28. When we compute this, we get r ≈ 32 centimeters to the nearest whole number.

Therefore, the correct answer is A) 32 centimeters.

On a town map, each unit of the coordinate plane represents 1 mile. Three branches of a bank are located at A(−3, 1), B(4, 3), and C(2, −1). A bank employee drives from Branch A to Branch B and then drives halfway to Branch C before getting stuck in traffic. What is the minimum total distance the employee may have driven before getting stuck in traffic? Round to the nearest tenth of a mile if necessary.

Answers

distance formula : sqrt ((x2 - x1)^2 + (y2 - y1)^2)
(-3,1)...x1 = -3 and y1 = 1
(4,3)...x2 = 4 and y2 = 3
now we sub
d = sqrt ((4 - (-3)^2 + (3 - 1)^2)
d = sqrt ((4 + 3)^2 + (2^2))
d = sqrt (7^2 + 2^2)
d = sqrt (49 + 4)
d = sqrt 53
d = 7.28 ...so its 7.28 miles from A to B

d = sqrt ((x2 - x1)^2 + (y2 - y1)^2)
(4,3)...x1 = 4 and y1 = 3
(2,-1)...x2 = 2 and y2 = -1
now we sub
d = sqrt ((2 - 4)^2 + (-1 - 3)^2)
d = sqrt (-2^2) + (-4^2)
d = sqrt (4 + 16)
d = sqrt 20
d = 4.47....but the employee only drives halfway....so this trip was 4.47/2 = 2.235

so the minimum total distance is : 7.28 + 2.235 = 9.515 rounds to 9.5 miles

which is the smallest number? 3/4,1/5,10/23,2/31

Answers

A quick and easy way to do this particular question is to think all of these numbers are close to 1/2 except 2/31. So, the lowest is 2/31.

H O P E T H I S H E L P S!

3333333333333333333333

How are the variables on the graph related?

Answer choices:

A. As speed decreases, height stays constant.

B. As speed decreases, height increases.

C. As speed increases, height decreases.

D. As speed increases, height increases.

Answers

Having a look at the graph, we will find that:
For speed: it is increasing along the x-axis
For height: it is increasing along the y-axis

This means that the function is linearly increasing.

Based on this, the correct choice would be:
D. As speed increases, height increases

a construction company charges $500 for the plans plus $600 per square foot to build a new home. Write an equation that shows this relationship

Answers

x = square feet

total cost = 500 + 600x

Let c be the curve of intersection of the parabolic cylinder x2 = 2y, and the surface 3z = xy. find the exact length of c from the origin to the point 2, 2, 4 3 . step 1

Answers

Parameterize the curve [tex]C[/tex] by [tex]\mathbf r(t)=\left\langle t,\dfrac{t^2}2,\dfrac{t^3}6\right\rangle[/tex] (essentially replacing [tex]x=t[/tex] and finding equivalent expressions for [tex]y,z[/tex] in terms of [tex]t[/tex].

The length of [tex]C[/tex] is given by the line integral

[tex]\displaystyle\int_C\mathrm dS=\int_{t=0}^{t=2}\|\mathbf r'(t)\|\,\mathrm dt[/tex]
[tex]=\displaystyle\int_0^2\left\|\left\langle1,t,\dfrac{t^2}2\right\rangle\right\|\,\mathrm dt[/tex]
[tex]=\displaystyle\int_0^2\sqrt{1+t^2+\dfrac{t^4}4}\,\mathrm dt[/tex]
[tex]=\displaystyle\frac12\int_0^2\sqrt{4+4t^2+t^4}\,\mathrm dt[/tex]
[tex]=\displaystyle\frac12\int_0^2\sqrt{(t^2+2)^2}\,\mathrm dt[/tex]
[tex]=\displaystyle\frac12\int_0^2(t^2+2)\,\mathrm dt[/tex]
[tex]=\dfrac12\left(\dfrac{t^3}3+2t\right)\bigg|_{t=0}^{t=2}[/tex]
[tex]=\dfrac12\left(\dfrac83+4\right)[/tex]
[tex]=\dfrac{10}3[/tex]

Given the equation D =m/v if D=2/3 and v=m+1., then m=
-3
2
1

Answers

D = m/v D = 2/3 v = m + 1

2/3 = m/m + 1

2/3(m + 1) = m

2(m + 1)/ 3 = m

2(m + 1) = 3m

2m + 2 = 3m

2 = 3m - 2m

2 = m

m = 2

hope that helps, God bless!

-3 1/2 * 0.5 help please

Answers

Convert -3 1/2 into an improper fraction. That fraction is -7/2. Mult. this by 1/2.
Result is -7/4 (answer)

Let -3 1/2 = -7/2.

Let 0.5 = 1/2.

(-7/2)(1/2) = -7/4

Done.

Write ratio in simplest form

6:3/5

Answers

you cdan simplify the ratio 6:3 by dividing both terms GCF ( greatest common factor) divide both terms by three 6 divided by 3 is 2 . 3 divided by 3 is 1. so 6:3 is 2:1

The value V of a square glass varies directly as the square of its length X cm. If the value of a square glass with length 3 cm is $243, find the value of a glass with length 5 cm

Answers

Given that the value V of a square glass varies directly as the square of its length X cm.

Then, the variation equation is given by

[tex]V\propto X^2 \\ \\ \Rightarrow V=kX^2[/tex]

Given that value of a square glass with length 3 cm is $243, we have:

[tex]243=k(3)^2=9k \\ \\ \Rightarrow k= \frac{243}{9} =27 \\ \\ \Rightarrow V=27X^2[/tex]

Thus, the value of a glass with length 5 cm is

[tex]V=27(5)^2=27\times25=\bold{\$675} [/tex]

The value V of a square glass varies directly as the square of its length X cm. This means that V is proportional to [tex]X^2[/tex], which can be expressed as:

[tex]\[ V = kX^2 \][/tex]

where k is the constant of proportionality.

Given that the value of a square glass with length 3 cm is $243, we can use this information to find the constant k:

[tex]\[ 243 = k(3)^2 \][/tex]

[tex]\[ 243 = 9k \][/tex]

[tex]\[ k = \frac{243}{9} \][/tex]

[tex]\[ k = 27 \][/tex]

Now that we have the value of k, we can find the value of a glass with length 5 cm by substituting X = 5 into the original equation:

[tex]\[ V = 27(5)^2 \][/tex]

[tex]\[ V = 27 \times 25 \][/tex]

[tex]\[ V = 675 \][/tex]

Therefore, the value of a glass with length 5 cm is $675.

The answer is: 675.

Find the quotient 4/6÷4/12

Answers

Keep Change Flip is the way to think about dividing fractions.
First- 4/6 divided by 4/12
Next- Change the division sign to multiplecation 4/6 time 4/12
Then- Flip the second number 4/6 times 12/4
Now multiply

48/24 this simplifies down to 2

The Red Sox have won 3 World Series titles in the last 11 years. At this rate, how long will it take them to win 20 World Series?

Answers

The answer is 74 years. do 11/3=3.67. Then 3.67x20 =73.4 and since that .4 is not a full year you would have to round up to 74

73 1/3 years
What I did was use a proportion:

11/3 and x/20
Then you cross multiply:

3x=220
Then solve.

please help me with this problem

Answers

129.95 * 0.55 = 71.4725

71.4725 * .06 = 4.28835

71.4725 + 4.28835 = $75.76

Answer = $75.76

will award 40 points if you answer correctly

Bottles of water sell for 1.50$ each.
Graph the relationship between the number of bottles sold and the total cost.

Answers

see picture for the graph

equation: y = 1.50x

Answer:

Step-by-step explanation:

took the test (k12) and its halfway to 50 if you see in the picture

The sum of the square of two consecutive whole number is 25. Find the numbers

Answers

Don't you mean "the sum of the squares ..."?
The sum of the squares of two consecutive whole numbers is 25. Find the numbers. Let the first be represented by x and the second by x+1.
Then x^2+(x+1)^2=25. Expanding, x^2+x^2+2x+1=25.
Rewriting this as a quadratic equation in standard form,

2x^2+2x+1=25, or 2x^2+2x-24=0. Simplifying, x^2+x-12=0.
Factoring, (x-3)(x+4)=0. Solving for x: x-3=0, so x=3; x+4=0, so x=-4.
Choose the positive x value: x=3. Then the next consecutive number is 2+1=3+1=4.

Check: Does 3^2 + 4^2 = 5^2 = 25? Yes.
The numbers are 3 and 4.

What is the unit rate 3 for $5 4 for$6

Answers

The unit rate for 3 for $5 is around $1.70 or $1.60

The unit rate for 4 for $6 is $1.50

You have two separate problems here.

a) 3 for $5 needs to be expressed as cost per unit. Write $5/(3 units), and then simplify. Here the unit rate is ($5/3) / unit, or $1.67 per unit.

b) 4 for $6: Write $6/(4 units), and then reduce to lowest terms:
(6/4) dollars per unit, or $1.50/unit

The answer because I don’t know it

Answers

What's the highest term that goes into 12x³, 8x², and 12x evenly? If it helps, you can break it up into two questions: what's the greatest common factor between 12 and 8, and what's the greatest common factor between x³, x², and x? Once you have those, multiply the two together, and you'll have the greatest common factor for all three monomials.

Also important to keep in mind: when we say we want to "factor" an expression with more than one term added together, what we really want to do is reverse the distributive property. In case you've forgotten, the distributive property is a property of multiplication that states that if you have three numbers a, b, and c, a(b+c) = ab + ac. You distribute the a to each of the terms in the parentheses. Here, you're given the ab + ac part, and you have to work your way back. To give an example, if we had the expression:

[tex]24x+36[/tex]

We can use the fact that 12 is the greatest common factor of 24x and 36 to rewrite it:

[tex]12(2x)+12(3)[/tex]

And, realizing that 12 has been distributed to the 2x and the 3, reverse the distributive property to get:

[tex]12(2x)+12(3)=12(2x+3)[/tex]

Tom received a coupon in the mail for 30%off one regular priced item for a local sporting goods store He wishes tp purchase a soccer ball for 22.50 and shin guards for 17.00 which item would he use his coupon justify your answer by comparing the discount taken for each item

Answers

it should be used on the higher priced item to get a bigger discount.

So it should be used on the soccer ball

soccer ball: 22.50 * 0.30 = 6.75 discount

shin guards: 17.00 * 0.30 = 5.10 discount

6.75 is greater than 5.10

Which is the solution to the equation 2.6a + 18.4 = 28.8 round the nearest tenth if necessary. 1.4, 4, 18.2, 27

Answers

You would subtract 18.4 from 28.8 then divide that answer by 2.6. The answer would therefor be 4.

Answer:

Your answer is B=4

Step-by-step explanation:

hope it helps once again

Evaluate 4x-3 when x=_3

Answers

Final answer:

To evaluate the expression 4x-3 for x = -3, we substitute -3 into the expression and follow the order of operations, resulting in a value of -15.

Explanation:

To evaluate the expression 4x-3 when x is -3, we simply substitute -3 in place of x and calculate the result as follows:

Replace x with -3: 4(-3) - 3.Multiply 4 by -3: -12 - 3.Finally, subtract 3 from -12 to get: -15.

Therefore, evaluating 4x-3 when x is -3 gives us -15.

Write the equation of a vertical line containing (5,-8)

Answers

check the picture below.

Devin brought his snails collection to school. He has 10 snails. How could he put them into 2 tanks so two classes could see them?
Write equation for all the possible ways.
One of the ways is given.
Explain how you know you have found all the ways.

Answers

10 divided by 2 = 5 is one of the equations

which of the following shows a strategy to use to find 4x275 (4x300)+(4x25)
(4x300)-(4x25) (4x275)-100 (4x200)+75

Answers

[tex]4*275 (4x^3^0^0)+(4x^2^5) (4x^3^0^0)-(4x^2^5) (4x^2^7^5)-100 (4x^2^0^0)+75[/tex]

The correct strategy is (4x275) - 100. So option (3) is correct.

To find 4 multiplied by 275 using the given strategies, let's go through each one:

1. (4x300) + (4x25):

First, calculate (4x300) = 1200. Then, calculate (4x25) = 100. Finally, add these results together: 1200 + 100 = 1300.

2. (4x300) - (4x25):

Calculate (4x300) = 1200. Then, calculate (4x25) = 100. Now, subtract the second result from the first: 1200 - 100 = 1100.

3. (4x275) - 100:

Simply multiply 4 by 275 to get 1100. Then, subtract 100: 1100 - 100 = 1000.

4. (4x200) + 75:

Calculate (4x200) = 800. Then, add 75: 800 + 75 = 875.

The correct strategy is the third one: (4x275) - 100.

Detailed Calculation:

1. [tex]$4 \times 275 = 1100$[/tex]

2. [tex]$1100 - 100 = 1000$[/tex]

So, using the strategy of (4x275) - 100, the result is 1000.

Assume that the distance from Earth to the moon is exactly 238,855 miles and that it took astronauts 75 hours to reach the moon in 1969. How far did the astronauts travel each hour, on average, during their trip to the moon? 3,004.73 miles mc026-1.jpg miles 3,317.4305 miles mc026-2.jpg miles

Answers

you would do 238855 divided by 75 ===3184.73333 mph

On average during their trip, their speed was 3184.8 miles/hr.

What is a unitary method?

A unitary method is a mathematical way of obtaining the value of a single unit and then deriving any no. of given units by multiplying it with the single unit.

We know Distance = Speed×Time.

∴ Speed = Distance/Time.

Given, The distance from Earth to the moon is exactly 238,855 miles and it took astronauts 75 hours.

So, the average speed is (238855/75) miles/hr.

= 3184.8 miles/hr.

learn more about unitary method here :

https://brainly.com/question/22056199

#SPJ2

Find the volume of the solid whose base is the circle x^2+y^2=81 and the cross sections perpendicular to the x-axis are triangles whose height and base are equal.

Find the area of the vertical cross section A at the level x=6.

Answers

Sent a picture of the solution to the problem (s). Just rotate pic.

The volume of the cone will be 1526.8 cubic units. The area of the vertical cross-section A at level x = 6 will be 72 square units.

What is Geometry?

It deals with the size of geometry, region, and density of the different forms both 2D and 3D.

The equation of the base circle is given below.

x² + y² = 81

x² + y² = 9²

Then the radius of the circle is 9 units. Then the height of the cone is the same as the diameter of the circle.

h = 2r

h = 2 x 9 = 18

The volume of the cone will be

V = (1/3)πr²h

V = (1/3) × π × 9² × 18

V = 1526.8 cubic units

The area of the vertical cross-section A at the level x = 6 will be

A = (1/2) x (18 - 6) x (18 - 6)

A = (1/2) x 12²

A = (1/2) x 144

A = 72 square units

More about the geometry link is given below.

https://brainly.com/question/7558603

#SPJ2

3. Find the scale factor using the given scale drawings and measurement below

Answers

Final answer:

The question asks to find the scale factor for given scale drawings and measurements. A scale factor is computed by creating a ratio comparing the measurement of the scale drawing to the actual measurement, simplifying that ratio to find the scale factor.

Explanation:

The subject of the question is concerned with finding the scale factor from a given scale drawing and measurements. In mathematics, particularly in geometry, a scale factor is used to transform the size of a figure without altering its shape.

Step-by-Step Explanation

To find the scale factor for each given scale drawing, you will need to create a ratio or a fraction that compares the scale measurement to the actual measurement. Here’s how you might solve one of the problems:

Example: What is the scale factor if 3 inches is equal to 12 feet?

Solution:

Convert all measurements to the same unit, for instance, turn feet into inches (1 foot = 12 inches).Write the ratio of the scale drawing to the actual measurement.Reduce the ratio to its simplest form to find the scale factor.

Write an explicit formula for the sequence (3,7,11,15,19,23,27,...)

Answers

Final answer:

The explicit formula for the given sequence is a_n = 3 + 4(n-1).

Explanation:

The given sequence is (3, 7, 11, 15, 19, 23, 27, ...).

To find the explicit formula for this sequence, we can observe that each term is obtained by adding 4 to the previous term. So, the formula can be written as:

an = 3 + 4(n-1)

where n represents the position of the term in the sequence.

Other Questions

Which answer identifies the participial phrase and the word it modifies in this sentence? The candle flickering on the table provides the only light in the room. The participial phrase flickering on the table modifies candle. The participial phrase provides the only modifies table. The participial phrase The candle modifies flickering. The participial phrase in the room modifies light. Hurry please!! Use any model you choose to solve the story problem. Zoey found that box of dog food was left in the pantry. She shared this food equally among her 4 dogs. What fraction of the full box of dog food did each dog get? Lawrence is watching a video in his psychology class that talks about how little albert was conditioned to fear a specific item. what was the source of albert's fear? The separate work of broca and of wernicke provided the first compelling clinical evidence that language and speech functions are performed primarily by the _____ cerebral hemisphere. How many kilojoules of energy are released when .1.60 kg of water cools from 80.0 C to 60.0 C? Which elements of the story suggest that it is an earth diver creation story What is one thing for which Scrooge is not prepared as he wakes up the second time If charlene brewster has times of 8.4, 8.6, 8.3, 8.5, 8.7 ans 8.5 and a performance rating of 110% percent, what is the normal time for this operation? is she faster or slower then normal? What does the exclamation mark mean on my 2013 honda odyssey? Sarah rode her bike 53 km in 4 hours.What was her average speed per hour?A.5.3 km/hB.12.5 km/hC.13.25 km/hD.21.2 km/h The cost of a ticket t to a concert with a 3% sales tax can be represented by the expression t + 0.03t. Simplify the expression. Then determine the total cost after the sales tax if the original price is $72. What disagreement led to legal conflicts between the mexican and european-american landowners in the 1880s? If you ask three strangers about their birthdays, what is the probability: Suppose candidate a for a town council seat receives 43% of the votes in an election. as voters leave the polls they are asked who they voted for. what is the probability that less than 40% of the 80 voters surveyed indicate they voted for candidate a? assume an infinite population. 35% of the students at Grandy High School are freshman. If there are 525 Freshman, how many students are not freshman? The features found only in plant cells, only in animal cells, or in both plant and animal cells: What types of countries/regions are likely to have more males than females? What American educator was partially responsible for the creation of the NAACP? W.E.B. Du Bois Booker T. Washington Frederick Douglass James Carter Help!Von wo ____ unser Flug (depart) _______?A) wird, abfliegenB) werden, abfliegenC) werden, ankommenD) wird, ankommen 14 is 8% of what number Steam Workshop Downloader