For problems 1, 2, and 3, use the function g(x) = sin(6x) .
1. Find the amplitude of the function. State the range of the function.
2. Find the period of the function. Find the key points of the function [intercept(s), maximum(s), and minimum(s)] for 1 period. Show all work.
3. Sketch the graph of g (one period), alongside the graph of f(x) = sinx on the interval [0,2/pi]. Label the axes.
For problems 4, 5, and 6, use the function g(x)=cos((x)/(4)).
4. Find the amplitude of the function. State the range of the function.
5. Find the period of the function. Find the key points of the function [intercept(s), maximum(s), and minimum(s)] for 1 period. Show all work.
6. Sketch the graph of g, alongside the graph of f(x) = cosx on the interval [0,2/pi] . Label the axes.
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Step-by-step explanation:
1. Amplitude = 1. g(x) = 1 sin(6x). The coefficient 1 is the amplitude. The range of the function is [tex]-1 \le g(x) \le 1[/tex] or, in interval notation, [-1, 1]
2. The period is [tex]\frac{2\pi}{6}=\frac{\pi}{3}[/tex].
x-intercepts (at the beginning, middle, and end of the period) [tex]0,\,\frac{\pi}{6},\,\frac{\pi}{3}[/tex]
Maximum (1/4 of way through period) [tex]\left(\frac{\pi}{12},\,1 \right)[/tex]
Minimum (3/4 of way through period) [tex]\left( \frac{\pi}{4}, \, -1 \right)[/tex]
Related Questions
In the pet supply area of the warehouse is a crate of flea shampoo for cats. Each crate holds 55 boxes. Each box holds 7 bottles of shampoo. Each bottle contains 7 mL of the chemical that gets rid of the fleas. How many liters of the chemical is in the crate of shampoo?
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Answer:
2.695 Liters of shampoo
Step-by-step explanation:
Step 1
We find the number of bottles in the crates
1 box = 7 bottles
55 boxes = x
Cross Multiply
x = 55 boxes × 7 bottle/1 box
x = 385 bottles
Step 2
Calculate the total number mL
1 bottle = 7 mL
385 bottles = x
Cross Multiply
x = 385 bottle × 7 mL/1 bottle
x = 2695 mL
Therefore the total number of mL of shampoo in the crates = 2695mL
Step 3
How many liters of the chemical is in the crate of shampoo?
We convert mL to Liters
1 mL =0.001 liter
2695mL = x
Cross Multiply
x = 2695mL × 0.001 liter/1 mL
x = 2.695 Liters of shampoo
Therefore, 2.695 liters of the chemical is in the crate of shampoo
Please help with this I need to pass this test or I fail I really appreciate it thank you:(
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Answer:
a because 75 plus 15 equal 90
Fill in the blanks to make the following statements true. Also named the property used.
a. (-5) + (-4) = ___ + (-5),
b. 4 + __ = 4,
c. - 53 + ___ = - 53,
d. 4 + [(-5) + (7)] = [4 + (7)] + ___,
e. 25 + [(-50) + 5 ] = (25 + 5) + ___,
f. (-4) + ___ = -4,
g. 4 + (-4) = ___,
h. 5 + ___ = 0 ,
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Answer:
a. (-4)
b. 0
c. 0
d. (-5)
e. (-50)
f. 0
g. 0
h. (-5)
question in photo! no need to explain answer,
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Answer:
i its 3 or 4
Step-by-step explanation:
Find the area of a rectangle that has a width of 4.25 inches and a length that is twice the width.
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Pls I need answer it’s due today!!!!!!!!!
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Step-by-step explanation:
in probability,or means addition.
14/28+19/28
1/2+19/28
you then find the LCM of the denominator.
14+19/28
33/28
you then divide 33 by 28.
Which ordered pair is a solution to the system of inequalities?
y< 3x
y<5
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In the figure, ∠6 and ∠3 are ...
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Answer:
They're supplementary angles AND same-side interior angles.
Here is your questions
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Answer:
Step-by-step explanation:
strategy: find the distance of the two points, take half of that, b/c that will be the radius, Then use the area of a circle formula to find the answer
P1 = (1,-1) in the form (x1,y1)
P2= ((3,3) in the form (x2,y2)
dist = sqrt [ (x2-x1)^2 + (y2-y1)^2 ]
dist = sqrt [ 3 -1 )^2 + 3-(-1)^2 ]
dist = sqrt [ 2^2 + 4^2 ]
dist = sqrt [ 4 + 16 ]
dist = sqrt [20]
r = [tex]\sqrt{20}[/tex] /2
area of circle = [tex]\pi[/tex][tex]r^{2}[/tex]
area of circle = [tex]\pi[/tex]([tex]\sqrt{20}[/tex] /2)^2
area of circle = [tex]\pi[/tex]([tex]\sqrt{20}[/tex] /2)([tex]\sqrt{20}[/tex] /2)
area of circle = [tex]\pi[/tex](20 / 4)
area of circle = [tex]\pi[/tex]5
area of circle = 5[tex]\pi[/tex]
Please help me please I really need help.
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Answer:
B. 113°Step-by-step explanation:
Tc = R + (Th - R)e^(-0.036t)Substitute values and solve for Tc:
Tc = 68° + (146° - 68°)e^(-0.036*15)Tc = 113.45° ≈ 113°Correct choice is B
A butterfly has a wingspan of 66 mm and a height of 6 cm.
Which is greater, its wingspan or its height?
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Answer:
wingspan
Step-by-step explanation:
there's 10 mm in every cm
!!!!!!!!!!!!!!!!!!!!!!!!!!
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Answer:
x=49
Step-by-step explanation:
right on edge.......Faxtuu
Your answer is
49
Stefan sells Jin a bicycle for $125 and a helmet for $18. The total cost for Jin is 130% of what Stefan spent originally to buy the bike and helmet. How much did Stefan spend originally? How much money did he make by selling the bicycle and helmet to Jin?
Answers
Answer:
Stefan originally spent $ 110 on the bike and helmet, with which he is making a profit of $ 33.
Step-by-step explanation:
Since Stefan sells Jin a bicycle for $ 125 and a helmet for $ 18, and the total cost for Jin is 130% of what Stefan spent originally to buy the bike and helmet, to determine how much did Stefan spend originally and how much money did he make by selling the bicycle and helmet to Jin, the following calculations must be performed:
130 = 125 + 18
100 = X
100 x (125 + 18) / 130 = X
100 x 143/130 = X
14,300 / 130 = X
110 = X
143 - 110 = 33
Therefore, Stefan originally spent $ 110 on the bike and helmet, with which he is making a profit of $ 33.
Can someone pls help me!!! NO LINKS... I will mark brainiest to.
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ILL MARK BRAINLIEST.
Which One Doesn't Belong? Determine which equation fromthe four below doesn't belong and justify your answer. Could there be a different answer?
A. solve for x: 2x + 6 + 1x = 3x + 6
B. solve for x: 5x + 6 + -2x = 3x + 6
C. solve for x: 3x + 7 = 3(x +2)
D. solve for x: 2x + 6 = 3x + 7
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Answer:
c
Step-by-step explanation:
c because you would get fals as the answer because to solve you first distribute so you would get 3x+7=3x+6 and both 3 x's would cancel out so you would get 7=6 so that would be false
I’LL MARK AS BRAINLIEST!!! Plz no links
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Answer:
6 people
Step-by-step explanation:
75% of 8 is 6
multiply 8 by the decimal .75
Solve 3-²I need work shown
Answers
Answer:
1/9
Step-by-step explanation:
Answer:
its 987556467724
Step-by-step explanation:
I took quiz and got it right thid my proof
Find the slope of the line that passes through the points (-4.2) and (6.6).
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Step-by-step explanation:
(6-2)/(6+4)= 4/10= 2/5 is the slope
answer is D
A train travels 120km to the nearest kilometer for 3.5 hours correct to the 2 significant figures.
Calculate the least speed of the train to 2 decimal places.
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Answer:
Least speed = 33.66 km/h
Step-by-step explanation:
The least distance is 119.5 km, and the most time it took was 3.55 hours.
Therefore the least speed = least distance/most time
= 119.5/3.55 km/h
= 33.66 km/h
will name brainliest
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Answer:
14.1 =x
Step-by-step explanation:
Since this is right triangle, we can use trig functions
sin theta = opp/ hypotenuse
sin 42 = x /21
21 sin 42 = x
14.05174273 =x
Rounding to the nearest tenth
14.1 =x
Answer:
x = 14.1 (Rounded to the nearest tenths)
Step-by-step explanation:
Since the opposite side of the angle given needs to be found out and hypotenuse, Sin ratio would be used;
Sin(42) = [tex]\frac{x}{21}[/tex]
=> Now multiply 21 on both sides of =, in order to isolate x;
Sin(42) * 21 = x
14.1 = x
Hope this helps!
A box is a right rectangular prism with the dimensions 8 inches by 8 inches by 14 inches. What is the surface area of this box?
fyi, question, answer choices, and prism are shown the the photo :) please answer ASAP and explain how you did it. I'm having alot of trouble with surface area.
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Answer:
Option C. 576 in^2
Step-by-step explanation:
Given ,
Length = 8 inches
Breadth = 8 inches
Height = 14 inches
Now ,
using surface area of box (Cuboid)
= 2(l×b + b×h + l×h )
= 2(8×8 + 8×14 + 14×8)
= 2 ( 64 + 112 + 112 )
= 2 ( 288)
= 576 inches^2.
The parabola y=[tex]x^{2}[/tex] is shifted up by 7 units and to the left by 1 unit. What is the equation of the new parabola?
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So, equation of new parabola is:
y=(x+1)^2+7
1. Find the value of the power. (1/2)4"
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Answer:
2
Step-by-step explanation:
You would use PEMDAS( parentheses exponents multiply adding subtracting) (1/2)4.
^
o.5×4
^
2
Janice is 7 years older than Tam. Complete the table, and then graph this situation.
Tam
x(years)
2 9
4 ?
6 ?
8 ?
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Answer:
The table in the exercise can be completed with the next results:
x y 2 9 4 11 6 13 8 15Step-by-step explanation:
As in the exercise Janice is 7 years older than Tam, to obtain the result in the table, you must add 7 to each age in the column x, with this we can make the next formula:
y = x + 7Remember that x is Tam's age, and y is Janice's age, so, you must replace the x variable in each case to obtain the result to y:
When x is 2:
y = 2 + 7y = 9When x is 4:
y = 4 + 7y = 11When x is 6:
y = 6 + 7y = 13When x is 8:
y = 8 + 7y = 15At last, to obtain the graph you can use the formula made: y = x + 7, and you'll obtain a graph like the attached picture, where each time x obtain a unit, the y variable obtain a unit too maintaining the diference of 7.
Meara orders three drinks at Starbucks for a total of $18.45. Sales tax in her state is 6%. How much will she pay, for just the tax, on her order at Starbucks?
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Answer:1.107 is how much tax she will pay
Step-by-step explanation:you needed to find 6 percent of 18.45.
A crab walk 1/12 of a mile an hour. The crab 1/5 of a mile away from the beach . How long will it take the crab to reach the beach
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Answer:
2.4 hours
Step-by-step explanation:
[tex]\frac{1}{5} /\frac{1}{12}[/tex]
2.4 hours
x^2+4*x-9
Give answer in surfs please
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Madison earned $80 last month pet sitting in her
neighborhood. She spent $54 and put the remainder of the
money in her piggy bank. What percent of her allowance
Madison put in her piggy bank?
A local movie theater was showing them
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Answer:
26
Step-by-step explanation:
Subtract
Answer: 32.5%
Step-by-step explanation:
80 - 54 = 2626/80 × 100 = 32.5%Maddie made 4 of her 6 shots on goal at soccer practice. If she continues to make goals at the same rate as in practice, use a tape diagram to determine how many shots she would make out of 72. Type your answer as a single number.
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Answer:
48
Step-by-step explanation: because 4/6 = a .66666666666667. and that times 72 is 48
Airport Auto Leasing has a ratio of cars to trucks that is 5 to 3. If each leasing center has 24 trucks, which auto leasing company has more cars? Main Street Auto Leasing has more cars since it has cars while Airport Auto Leasing has cars only.
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Complete question :
Main street Auto Leasing has a ratio of cars to trucks that is 9:4.
Airport Auto Leasing has a ratio of cars to trucks that is 5 to 3.
If each leasing center has 24 trucks, which auto leasing company has more cars?
Main Street Auto Leasing has more cars since it has ______ cars while Airport Auto Leasing has ____ cars only.
Answer:
Mainstreet has more cars
Mainstreet has 54 cars
Airport has 47
Step-by-step explanation:
Ratio of cars to trucks :
Mainstreet ; 9 : 4
Airport Auto Leasing ; 5 : 3
If each has 24 trucks :
Number of cars in Mainstreet ;
9 / 4 = 2.25 times more cars than trucks ;
Number of trucks * 2.25 = (24 * 2.25) = 54 cars
Airport Auto leasing :
5 / 3 = 1.666666 times more cars than trucks ;
Number of trucks * 1.666666 = (24 * 1.666666) = 40 cars
Hence, Mainstreet Auto leasing has more cars.