A contestant on a game show spins a wheel that is located on a plane perpendicular to the floor. He grabs the only red peg on the circumference of the wheel, which is 1.5 m above the floor (the peg is) and pushes it downward. The peg reaches a min height of 0.25 m and a max height of 2.75 m above the floor. Sketch two cycles of the graph representing the height above the ground as a function of the total distance moved. Then determine the equation of the sine function
Answers
The spin of the wheel by the contestant is an illustration of a sine function whose equation is [tex]\mathbf{y =-1.25 sin(0.8x) + 0.25}[/tex]
The wheel is 1.5 m above the floor, and the peg reaches a maximum height of 2.75 m.
So, the amplitude is:
[tex]\mathbf{A = 1.5 - 2.75}[/tex]
[tex]\mathbf{A = -1.25}[/tex]
The vertical shift is the minimum height of the peg.
So, we have:
[tex]\mathbf{D = 0.25}[/tex]
The period (T) equals one circumference.
So, we have:
[tex]\mathbf{T = (max-min)\pi}[/tex]
This gives
[tex]\mathbf{T = (2.75-0.25)\pi}[/tex]
[tex]\mathbf{T = 2.5\pi}[/tex]
The frequency (B) is then calculated as:
[tex]\mathbf{B = \frac{2\pi}{T}}[/tex]
This gives
[tex]\mathbf{B = \frac{2\pi}{2.5\pi}}[/tex]
Divide
[tex]\mathbf{B = 0.8}[/tex]
A sine function is represented as:
[tex]\mathbf{y =A sin(B(x + C)) + D}[/tex]
Substitute the calculated values
[tex]\mathbf{y =-1.25 sin(0.8(x + C)) + 0.25}[/tex]
The horizontal shift (C) is 0.
So, the function becomes
[tex]\mathbf{y =-1.25 sin(0.8x) + 0.25}[/tex]
See attachment for the graph of the equation
Read more sine function at:
https://brainly.com/question/11904902
Related Questions
A pool company is creating an image for a client that has the look of a 3-D image for a family pool and a similar dog pool. Find the value of a in the drawing below:
Answers
Answer:
a = 21
Step-by-step explanation:
Based on the information given, we can calculate that
WZ x 3 = a
so...
7 x 3 = 21
Hope that helped!! :)
Answer:
I think it is 21 since the relationship between 4 and 12 4 * 3 is equal to 12 so I did the same for each side but angles don't change so 7*3=21
3х – 2y = 27
=
3х -
у = 24
Answers
Rearrange the equation by subtracting what is to the right of the equal sign from both sides of the equation :
3*x-2*y-(27)=0
STEP1:
Equation of a Straight Line
1.1 Solve 3x-2y-27 = 0
Tiger recognizes that we have here an equation of a straight line. Such an equation is usually written y=mx+b ("y=mx+c" in the UK).
"y=mx+b" is the formula of a straight line drawn on Cartesian coordinate system in which "y" is the vertical axis and "x" the horizontal axis.
In this formula :
y tells us how far up the line goes
x tells us how far along
m is the Slope or Gradient i.e. how steep the line is
b is the Y-intercept i.e. where the line crosses the Y axis
The X and Y intercepts and the Slope are called the line properties. We shall now graph the line 3x-2y-27 = 0 and calculate its properties
Calculate the Y-Intercept :
Notice that when x = 0 the value of y is 27/-2 so this line "cuts" the y axis at y=-13.50000
y-intercept = 27/-2 = -13.50000
Calculate the X-Intercept :
When y = 0 the value of x is 9/1 Our line therefore "cuts" the x axis at x= 9.00000
x-intercept = 27/3 = 9
Calculate the Slope :
Slope is defined as the change in y divided by the change in x. We note that for x=0, the value of y is -13.500 and for x=2.000, the value of y is -10.500. So, for a change of 2.000 in x (The change in x is sometimes referred to as "RUN") we get a change of -10.500 - (-13.500) = 3.000 in y. (The change in y is sometimes referred to as "RISE" and the Slope is m = RISE / RUN)
Slope = 3.000/2.000 = 1.500
Geometric figure: Straight Line
Slope = 3.000/2.000 = 1.500 x-intercept = 27/3 = 9 y-intercept = 27/-2 = -13.50000PLZ ANSWER QUICK. WILL GIVE BRAINLY. NO EXPLANATION NEEDED.
Answers
Answer:
None of these are correct
Step-by-step explanation:
XZ = XY + YZ = 48 + 50 = 98
a fair coin is flipped 10 times. what is the probability of getting the same number of heads and tails
Answers
If you flip a coin one time, the probability to get a Head is
p = 1/2
The probability of not getting a head in a single toss is :
q = 1 - 1/2 = 1/2
Thus there is only one unique situation to get the same number of heads and tails : in 10 toss you need to get exactly five heads, it will means that the rest is the tails.
Now using Binomial theorem of probability, the probability of getting exactly x = 5 heads in a total of n = 10 tosses is :
P(X = 5) = [tex]\frac{10!}{5!*5!} *(\frac{1}{2})^{5} *(\frac{1}{2})^{5}[/tex]≈ 0.246
So the probability of that is 24,6 %
Good Luck
The tables of ordered pairs represent some points on the graphs of two lines. What is the solution to the system of equations represented by the two lines?
Answers
Answer:
(-9, 5)
Step-by-step explanation:
1. Find the equations of both lines (y = mx +b).
For the table on the left, we can see that the y-intercept is 23 (at x=0, y=23). Hence, b = 23. We can also see that the y-value for the left table increases by increments of 2, meaning that the slope (m) will be 2. Thus:
f1(x) = 2x + 23
For the right table, do the same thing. The table tells us that when x = 0, y = -58 (so b = -58). We also see that the y-value DECREASES in increments of 7, meaning that the slope, m = -7. Thus,
f2(x) = -7x - 58
2. Set the equations equal to each other to find the x-value at which the two equations will intersect.
2x + 23 = -7x - 58
9x = -81
x = -9
3. Plug your newfound x-value into any of the two equations to find the y-value at which both equations will intersect.
y = 2x + 23
y = 2(-9) + 23
y = 5
OR
y = -7x - 58
y = -7(-9) - 58
y = 5
ANSWER: At the point (-9, 5), the two lines intersect. Hence, the solution to the equation is (-9, 5).
Answer:
x = -9 and y =. 5
Step-by-step explanation:
(-2, 19) and (-1, 21)
Slope: (21-19)/(-1- -2) = 2
y-intercept = 21 - (2)(-1) = 23
a) y =2x + 23
(-2,-44) and (-1,-51)
Slope: (-51- - 44)/(-1- -2) = -7/1 = -7
y-intercept: -44-(-7)(-2)=-58
b) y = -7x - 58
Substitute y in equation a.
-7x-58 = 2x + 23
-9x = 81
x = -9
Substitute X by -9 in equation b: y = -7(-9) - 58= 5
y = 5
Dave created a video that was originally 64 minutes long, but he ended up cutting it by 13%. How long was his video after he cut it?
Answers
Answer:
70 minute
it was help full
Now subtract that from 64 minutes:
64-8.32= 55.68 minutes
Victor borrowed $18.50 from his mother to go to the theater. A week later, he paid her $18.50 back. How much does he still owe her? He owes her $
Answers
Answer:
0
Step-by-step explanation:
brainlyyyyyyyy just helppppppppppppppppppppppppppppppppppppppppppp
Answers
50
If 10 is 20% of a number, we can multiply it by 5 to get the original number.
So 10 * 5 = 50, and 20% of 50 is 10.
I hope this helps! :)
pLS HELP ME 15 points in total
Answers
Answer:
Its 53 because 1=1 and 2=2
Step-by-step explanation:
please help me with this question!!
Answers
Answer:
\(x = 1\)
Step-by-step explanation:
Based on the given conditions, formulate: \(x = 12 \div 12\)
Cross out the common factor:\(x = 1\)
Answer: \(x = 1\)
what is the slope of the line that passes through the points (-3, 1) and (1, -5)
A) 1/2
B) -1/2
C) -3/2
Answers
Answer:
[tex]\boxed {\boxed {\sf C. \ - \frac {3}{2}}}[/tex]
Step-by-step explanation:
We are asked to find the slope of the line.
Slope is a number that tells us the steepness and direction of a line. It is the change in y over the change in x.
[tex]m= \frac{y_2-y_1}{x_2-x_1}[/tex]
In this formula, (x₁, y₁) and (x₂, y₂) are the points the line passes through.
We are given the points (-3, 1) and (1, -5). If we match the value with its corresponding variable, we see that:
x₁ = -3 y₁ = 1x₂ = 1 y₂ = -5Substitute the values into the formula.
[tex]m= \frac{-5 -1}{1 - -3}[/tex]
Solve the numerator.
-5-1= -6[tex]m= \frac{ -6}{1--3}[/tex]
Solve the denominator. Two back-to-back negative signs become a positive sign.
1 - -3 = 1+3 =4[tex]m=\frac{-6}{4}[/tex]
Simplify the fraction. Both the numerator and denominator can be divided by 2.
[tex]m= \frac{-6/2}{4/2}[/tex]
[tex]m= -\frac{3}{2}[/tex]
The slope of the line is -3/2, so the correct choice is C.
dude these qts are due in 10 mins pls help!
Answers
Answer:
I can't see the last answer choice.
9/LM = 6/4.5
Step-by-step explanation:
9cm is to 6cm as LM is to 4.5cm
9/6 = LM/4.5
Rewriting: 9/LM = 6/4.5
2m+m=24
[tex]2m + m = 24[/tex]
I don't know
Answers
Answer:
m = 8
Step-by-step explanation:
2m + m = 24 ( collect like terms on left side )
3m = 24 ( divide both sides by 3 )
m = 8
Answer:
m = 8
Step-by-step explanation:
2m + m = 24
3m = 24
(3m)/3 = (24/3)
m = 8
Check:
2*8 + 8 = 24
16 + 8 = 24
SnackTime Foods produced 3,181,990 grams of popcorn last year, which was placed in 7- gram bags. How many bags did the company fill? bags Submit
Answers
Answer:
The company filled 454570 bags.
Step-by-step explanation:
A pie was cut into 8 equal pieces. If Malena ate 18 of the pie, and Lupe ate 58 of the pie, how many whole pieces of the pie are left?
Answers
Answer:
2/8ths are left
Step-by-step explanation:
8 equal.pieces means 8/8
she ate 1/8 and he ate 5/8
thats 6/8
8/8 - 6/8 = 2/8
Answer:
1
Step-by-step explanation:
i dunno maybe not sure
If you treat 2 friends to lunch, the 1st lunch is $12. 35, the 2nd lunch is $14. 22, and your lunch is $11. 47. You want to add a 20% tip. How much will you pay in total?.
Answers
Explanation;
$12.35+$14.22+$11.47=$38.04
20% of $38.04=$7.70
=$45.74
The solution is
The total amount for the lunch is given by the equation A = $ 45.648
What is an Equation?Equations are mathematical statements with two algebraic expressions flanking the equals (=) sign on either side.
It demonstrates the equality of the relationship between the expressions printed on the left and right sides.
Coefficients, variables, operators, constants, terms, expressions, and the equal to sign are some of the components of an equation. The "=" sign and terms on both sides must always be present when writing an equation.
Given data ,
Let the total amount for the lunch be represented as A
Now , the equation will be
The amount for the first lunch = $ 12.35
The amount for the second lunch = $ 14.22
The amount for the third lunch = $ 11.47
The percentage of tip = 20 %
So , the total amount for the lunch without tip = $ 12.35 + $ 11.47 + $ 11.47
On simplifying the equation , we get
The total amount for the lunch without tip = $ 38.04
The amount of tip = total amount for the lunch without tip x percentage of tip
Substituting the values in the equation , we get
The amount of tip = 38.04 x ( 20/100 )
The amount of tip = 38.04 x 0.20
The amount of tip = $ 7.608
So ,
The total amount for the lunch A = total amount for the lunch without tip + amount of tip
Substituting the values in the equation , we get
The total amount for the lunch A = $ 38.04 + $ 7.608
The total amount for the lunch A = $ 45.648
Therefore , the value of A is $ 45.648
Hence , the total amount is $ 45.648
To learn more about equations click :
https://brainly.com/question/19297665
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To make 100g of jam you need 57g of strawberries, 17g of blackberries and the rest should be sugar.
What is the ratio of blackberries to sugar?
Give your answer in its simplest form.
Answers
2. Now, we can write the ratio of blackberries to sugar as 17:26. This can’t be simplified
Answer = 17:26
Hope this helps
3.) What would 9 gallons of gas cost at $2.12 per gallon? *
$18.80
O $17.56
$19.08
$11.12
Answers
Answer:
19.08
Step-by-step explanation:
each gal = $2.12
gals filled = 9
9 x 2.12 = 19.08
I would really like help
Answers
3 -25.875
4 -144
5 24
Answer:
[tex] \\ • \: \frac{1}{8} + (2 - 4 \times 7)[/tex]
[tex] \\ = \frac{1}{8} + (2 - 28)[/tex]
[tex] \\ = \frac{1}{8} + ( - 26)[/tex]
[tex] \\ = \frac{1}{8} - 26[/tex]
[tex] \\ = \frac{1 - 208}{8} [/tex]
[tex] \\ = \frac{ - 207}{8} [/tex]
[tex] \\ = - 25 \frac{7}{8} \: \: or \: \: - 25.875[/tex]
[tex] \\• \: 20 \times 3 - 7(8 \times 9)[/tex]
[tex] \\ = 20 \times 3 - 7 \times 72[/tex]
[tex] \\ = 60 - 504[/tex]
[tex] \\ = - 444[/tex]
[tex] \\ • \: 23 - ( \frac{4}{2} ) + 7 - 4[/tex]
[tex] \\ = 23 - 2 + 7 - 4[/tex]
[tex] \\ = 23 + 7 - 2 - 4[/tex]
[tex] \\ = 30 - 6[/tex]
[tex] \\ = 24[/tex]
[tex] \frak {\overbrace{\underbrace{{{hope \: it \: helps}}}}}[/tex]
8. Write an equation for the line in slope- intercept form.
Answers
Answer:
y equals 3x plus 4 is the answer
Step-by-step explanation:
hope it helps
The equation y=0.2x models a proportional relationship. Complete the table and graph the data.
Answers
y=0.2x
#0
[tex]\\ \sf\longmapsto y=0.2(0)=0[/tex]
(x,y)=(0,0)#5
[tex]\\ \sf\longmapsto y=0.2(5)=1[/tex]
(x,y)=(5,1)#10
[tex]\\ \sf\longmapsto y=0.2(10)=2[/tex]
(x,y)=(10,2)#15
[tex]\\ \sf\longmapsto y=15(0.2)=3[/tex]
(x,y)=(15,3)#20
[tex]\\ \sf\longmapsto y=0.2(20)=4[/tex]
(x,y)=(20,4)Step-by-step explanation:
The given Eqⁿ is, [tex]{ \purple{ \sf{y = 0.2x}}}[/tex]
[tex]{ \star}[/tex]Put x = 0, then
[tex]{ \purple{ \sf{y = 0.2(0) = 0}}}[/tex]
[tex]{ \boxed{ \red{ \sf{(x, \: y )\: = (0,0)}}}}[/tex]
[tex]{ \star}[/tex]Put x = 5, then
[tex]{ \purple{ \sf{y = 0.2(5) = 1}}}[/tex]
[tex]{ \boxed{ \red{ \sf{(x, \: y) \: = (5,1)}}}}[/tex]
[tex]{ \star}[/tex]Put x = 10, then
[tex]{ \purple{ \sf{y = 0.2(10) = 2}}}[/tex]
[tex]{ \boxed{ \red{ \sf{(x ,\: y) \: = (10,2)}}}}[/tex]
[tex]{ \star}[/tex]Put x = 15, then
[tex]{ \purple{ \sf{y = 0.2(15) = 3}}}[/tex]
[tex]{ \boxed{ \red{ \sf{(x, \: y) \: = (15,3)}}}}[/tex]
[tex]{ \star}[/tex]Put x = 20, then
[tex]{ \purple{ \sf{y = 0.2(20) = 4}}}[/tex]
[tex]{ \boxed{ \red{ \sf{(x, \: y) \: = (20,4)}}}}[/tex]
A group of friends is sharing 2 ½ pounds of berries
If each friend received 5/4 of a pound how many friends are sharing the berries
Answers
Answer:
2 friends
Step-by-step explanation:
Answer:
3 1/2
Step-by-step explanation:
Plzzz help meeeeeplzzz
Answers
Answer:
1 1 0 0 1 1 (base 2)
Step-by-step explanation:
Do it as a common sum operation, remember that when you have 2 or more you need to carry over.
The rectangle below has an area of 55x^6+22x^455x 6 +22x 4 55, x, start superscript, 6, end superscript, plus, 22, x, start superscript, 4, end superscript. The width of the rectangle is equal to the greatest common monomial factor of 55x^655x 6 55, x, start superscript, 6, end superscript and 22x^422x 4 22, x, start superscript, 4, end superscript. What is the length and width of the rectangle?
Answers
Answer: I had difficulty reading the problem, so please check my interpretation.
Width is 11x^4 and Length is 5x^2 + 2
Step-by-step explanation:
Area of rectangle is 55x^6+22x^4Width is equal to the GCF of 55x^6 and 22x^4The greatest common factor of 55x^6 and 22x^4 is 11x^4. So the width is 11x^4.
Length = (55x^6+22x^4)/(11x^4)
Length = 5x^2 + 2
If you are to
evaluate your life now using polynomial functions , how will you
look at it?
Answers
Help pls! This is timed
Answers
Answer:
c. is correct
Step-by-step explanation:
hipe its attachments
Solve the simultaneous equations
x + y = – 6
-x + 2y = 15
Answers
Answer:
x = -9, y = 3
Step-by-step explanation:
I hope it helps!
Lamar is a commercial real estate agent who earns a yearly salary of $82,500 plus a 2.5% commission on his total sales. If his total sales in one year are $3.75 million, what are Lamar’s earnings for that year?
Answers
Answer:
$176,250
Step-by-step explanation:
Multiply $3.75 million by Tomas commission on his total sales.
Since you can't multiply a percentage you have to turn the commission into a decimal by moving it two spaces to the left. (Note: if it doesn't have a decimal add one add the end of the number then move it two spaces to the left)
$3,750,000 x .025 or 0.025 = $93,750
Add $93,750 to Tomas yearly salary
$93,750 + $82,500 = $176,250
So
If Tomas sold properties that totaled $3.75 million in sales during one year, his earnings for that year would be $176,250
sir? sir? are u there? help me -_-
Answers
Answer:
a) The easiest way is to use a calculator such as a Casio brand or Sharp brand and key in 9C7 to get 36.
However, you can also use this formula: [tex]nCr=\frac{n!}{r!(n-r)!}[/tex] where n is the total number of items and r is how many you are selecting.
Plug in values:
[tex]\frac{9!}{7!(9-7)!} =\frac{9!}{7!*2!}=\frac{9*8}{2!}=36[/tex]
b) The easiest way is to use a calculator such as a Casio brand or Sharp brand and key in 9P7 to get 181440.
However, you can also use this formula: [tex]nPr=\frac{n!}{(n-r)!}[/tex] where n is the total number of items and r is how many you are selecting.
Plug in values:
[tex]\frac{9!}{(9-7)!} =\frac{9!}{2!}=9*8*7*6*5*4*3=181440[/tex]
Substance A has 2% alcohol mixture, and substance B has 6% alcohol mixture. To mix substance A and B for a capacity of 60 liters with 3.2% alcohol mixture, how many liters of substance A and B are used each?
Answers
Answer:
18 liters of 6% substance B
42 liters of 2% substance A
Step-by-step explanation:
let x be the liters of 6%, the balance of 60 - x liters is the 2% together they make 60 liters of 3.2%
6x + 2(60 - x) = 3.2(60)
distribute
6x + 120 - 2x = 192
Combine like terms
4x = 72
Divide bothsides by 4
x = 18 liters of 6%
60 - x = 42 liters of 2%