Answers
The general formula of such functions is:
f(x) = A sin (bx + c) + d, where:
A= period
b = coefficient of x
c= phase shift (horizontal shift)
d= vertical shift
Since there is no vertical shift nor horizontal shift, our function becomes:
f(x) = A. sin(b.x)
In the graph we notice that A=2
Let's calculate b. Remember that the PERIOD = 2π/b, but the period given on the graph is 8π, then:
:
8π = 2π/b → and b= 2π/8π → b= 1/4
Finally the equation is : f(x) = 2.sin(x/4)
The given graph is scaled form of trigonometric function graph.
The formula for the graph function f(x) is given by:
[tex]f(x) = -2sin(\dfrac{x}{4})[/tex]
How to find the formula for f(x) for given graph?Note down the properties one by one.
Firstly its a periodic function.
Secondly, the maximum value of the function is 2 and minimum value is -2
Thirdly the function assumes maximum or minimum value when it reaches to [tex]2 \pi n; n \in \mathbb Z[/tex]
Fourthly, the graph from the center to right side goes down then up then down then up and so on.
If you've seen graph of sine function, then you'd know that the graph is periodic(repeating same values after some interval), the maximum and minimum values being 1 and -1 and maximum or minimum values are achieved when input is [tex]\dfrac{n\pi}{2}; \: n \in \mathbb{Z}[/tex]
Plus, the graph from center to right goes up then down then up then down and so on.
Transforming sine graph to make the given graph:First we need down then up instead of up and down. Since down is negative output in its graph and up is positive, thus we will negate the value of sine function.
[tex]-sin(x)[/tex] will have flipped mountains and valley's in comparison to that of sin(x).
Now since the maximum and minimum values are needed to be 2 and -2 instead of 1 and -1, thus we will scale the output with factor of 2.
[tex]-2sin(x)[/tex] will have maximum and minimum as 2 and -2 respectively.
We need the graph to be maximum or minimum at x = [tex]2 \pi n; n \in \mathbb Z[/tex] and not at x = [tex]\dfrac{n\pi}{2}; \: n \in \mathbb{Z}[/tex]. Thus, we will scale down the input of -2sin(x) so that it treats [tex]2 \pi n; n \in \mathbb Z[/tex] as if it was given [tex]\dfrac{n\pi}{2}; \: n \in \mathbb{Z}[/tex].
The scaling needs to be by 1/4 since [tex]\dfrac{1}{4} \times 2\pi n = \dfrac{n\pi}{2}[/tex]
Thus, the resultant function is [tex]-2sin(\dfrac{x}{4})[/tex]
The below plotted graph shows graph of sin(x) (in red) and that of [tex]-2sin(\dfrac{x}{4})[/tex] (in blue).
Learn more about graph of sine function here:
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Related Questions
What is the slope of the line that passes through th epoints (26, 7) and (-39, 12)?
Answers
Use the slope formula: m = ------------ = -------- = -1/13
-39 - 26 -65
A linear function has a slope of -7/9 and a y-intercept of 3. How does this function compare to the linear function that is represented by the equation y+11=-7/9(x-18)
Answers
Answer:
A
Step-by-step explanation:
it has the same slope and the same y-intercept
(b) if the length, width, and height are increasing at a rate of 0.1 ft/sec, 0.2 ft/sec, and 0.5 ft/sec respectively, find the rate at which the surface area of the box is changing when x = 20 ft, y = 15 ft, and z = 25 ft.
Answers
Final answer:
By applying the derivative of the surface area of a rectangular prism formula with respect to time, it is found that the surface area of the box is increasing at a rate of 61 ft^2/sec when the dimensions are 20 ft by 15 ft by 25 ft.
Explanation:
The question involves calculating the rate of change of the surface area of a box with respect to time using derivatives, a concept from calculus. Given the rates at which the length (x), width (y), and height (z) are increasing, we can find the rate at which the surface area S is changing by using the surface area formula for a rectangular prism, S = 2(xy + xz + yz), and differentiating with respect to time.
At the given dimensions (x = 20 ft, y = 15 ft, z = 25 ft), and rate of increase (dx/dt = 0.1 ft/sec, dy/dt = 0.2 ft/sec, dz/dt = 0.5 ft/sec), the rate of change of surface area dS/dt is calculated by:
dS/dt = 2( (dy/dt)z + y(dz/dt) + (dx/dt)z + x(dz/dt) + (dx/dt)y + x(dy/dt) )
dS/dt = 2( (0.2)(25) + (15)(0.5) + (0.1)(25) + (20)(0.5) + (0.1)(15) + (20)(0.2) )
dS/dt = 2(5 + 7.5 + 2.5 + 10 + 1.5 + 4)
dS/dt = 2(30.5)
dS/dt = 61 ft2/sec
Therefore, the surface area of the box is increasing at a rate of 61 ft2/sec when the dimensions x, y, and z are 20 ft, 15 ft, and 25 ft respectively.
Train “A” leaves Westtown and travels at 50 mph toward Smithville, 330 miles away. At the same time, Train “B” leaves Smithville and travels at 60 mph. After how many hours do the two trains meet?
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train A travels at 50 mph
train B travels at 60 mph
60 +50 = 110
330/110 = 3
they will meet in 3 hours
The length of the hypotenuse of a right triangle is 157 units. The length of one leg of the triangle is 132. Lara wrote the following step to find the length of the unknown leg: Length of the unknown leg = 1572 – 1322 = 24,649 – 17,424 = 7,225 units Which statement best explains whether Lara's step is correct or incorrect? It is correct because the length of the unknown side is the difference of the lengths of the sides. It is correct because the length of the unknown side is the difference of the squares of the sides. It is incorrect because the length of the unknown side is the square root of 42,073. It is incorrect because the length of the unknown side is the square root of 7,225.
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the correct answer for this is the last choice:
It is incorrect because the length of the unknown side is the square root of 7,225.
Answer:
It is incorrect because the length of the unknown side is the square root of 7,225.
Step-by-step explanation:
If u is a square matrix such that u^tu = i what can we say about det(u)
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[tex]\det(\mathbf{AB})=\det\mathbf A\det\mathbf B[/tex]
[tex]\det\mathbf A=\det\mathbf A^\top[/tex]
for any square matrices [tex]\mathbf A,\mathbf B[/tex]. So if
[tex]\mathbf U^\top\mathbf U=\mathbf I[/tex], and [tex]\det\mathbf I=1[/tex], we have
[tex]\det(\mathbf U^\top\mathbf U)=(\det\mathbf U)^2=1\implies\det\mathbf U=\pm1[/tex]
True or false: the population proportion and sample proportion always have the same value.
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The sample is a randomly selected representation of the population, therefore it cannot represent the true data with 100% accuracy.
As the sample size increases, the sample proportion approaches the population proportion.
- Flase
If l is a line whose equation is y=5x-3, find the equation of the image of l under each of the following translations a. (x,y) --> (x, y-6) b. (x,y) --> (x+2,y)
Answers
For example, let x=0, then y=-3. So (0, -3) is a point on the line.
If x=1, then y=5*1-3=5-3=2, so (1, 2) is a point on the line.
a)
Consider the transformations of these two points under (x,y) --> (x, y-6):
(0,-3) --> (0, -3-6)=(0, -9),
(1, 2) --> (1, 2-6)=(1, -4).
So (0, -3) and (1, 2) are translated to respectively (0, -9) and (1, -4).
The whole line is translated to the line containing (0, -9) and (1, -4).
The slope of the new line is [tex]m= \frac{-9-(-4)}{0-1}= \frac{-5}{-1}=5 [/tex]. The equation of the line is:
[tex]y-(-9)=5(x-0)[/tex],
that is, y=5x-9.
b)
Consider the transformations of these two points under (x,y) --> (x+2, y):
(0,-3) --> (0+2, -3)=(2, -3),
(1, 2) --> (1+2, 2)=(3, 2).
The slope of the new line is [tex]m= \frac{-3-2}{2-3}= \frac{-5}{-1}=5 [/tex].
The equation of the line is
[tex]y-2=5(x-3)[/tex],
which can be written as
y=5x-13.
Answer:
a) y=5x-9
b) y=5x-13
PLEASE ANSWER THIS QUICKLY! THANK YOU!
Answers
= 1/2 x 4/3
= 4/6
= 2/3
a = 2
b = 4
c = 3
d = 2
e = 3
In a scale diagram, 0.125 inch represents 125 feet. How many inches represents 1 foot?
Answers
Its pretty obvious:
0.125=125 feet
So 0.001=1 feet
Your answer is 0.001 feet
0.001=1 feet
answer is: 0.001 feet
i hoped this helped and have a wonderful day!! :)
Tan (pi/5) - tan (pi/30) / 1+tan (pi/5)tan (pi/30)
Answers
[tex]\bf tan({{ \alpha}} + {{ \beta}}) = \cfrac{tan({{ \alpha}})+ tan({{ \beta}})}{1- tan({{ \alpha}})tan({{ \beta}})}\qquad tan({{ \alpha}} - {{ \beta}}) = \cfrac{tan({{ \alpha}})- tan({{ \beta}})}{1+ tan({{ \alpha}})tan({{ \beta}})}\\\\ -------------------------------\\\\[/tex]
[tex]\bf \cfrac{tan\left( \frac{\pi }{5} \right)-tan\left( \frac{\pi }{30} \right)}{1+tan\left( \frac{\pi }{5} \right)tan\left( \frac{\pi }{30} \right)}\implies tan\left( \frac{\pi }{5} -\frac{\pi }{30} \right)\implies tan\left( \frac{6\pi -\pi }{30} \right)[/tex]
[tex]\bf tan\left( \frac{5\pi }{30} \right)\implies tan\left( \frac{\pi }{6} \right)\implies \cfrac{sin\left( \frac{\pi }{6} \right)}{cos\left( \frac{\pi }{6} \right)}\implies \cfrac{\quad \frac{1}{2}\quad }{\frac{\sqrt{3}}{2}} \\\\\\ \cfrac{1}{2}\cdot \cfrac{2}{\sqrt{3}}\implies \cfrac{1}{\sqrt{3}}\implies \cfrac{\sqrt{3}}{3}[/tex]
A rectangular flower box holds 1232 in3 of soil. Find the height of the box if it is 22 in. long and 7 in. wide
Answers
The image shows a portion of a bridge supported by two vertical pillars built from the points B and C on the slope below. The length of the bridge between pillar B and pillar C is BLANK feet.
Answers
The cosin of Angle A is Adjacent / Hypotenuse, or 40 / 50. Using this Info:
cos (A) = 40/50
cos (A) = .8
With this crucial piece of info, we can find the Total length of A-D (Point D being the point above C), by finding its relation to side AC (length of 50 + 70 =120 ft)
Cos (A) = adjacent / hypotenuse
Cos (A) = AD / (120) We know that cos (A) = .8
.8 = AD / (120) Multiply both sides by 120
96 = AD
We're almost there! Remember that we're trying the find x (?? in the diagram).
x + 40 = 96
x = 56 ft
Answer:
The length of the bridge between pillar B and pillar C is 56 feet.
Here's the answer from the plato.
I need help please ❓❓
Answers
(its too little characters so im putting this at the bottom disregard haha)
-18.4*0.45=-8.28
Middle school has 450 students vanlue school has 600 students which school has a greater percent of girls explain
Answers
0.006 is greater than 0.1
Is this true?
Answers
Please Help....Which statements include two quantities in the real world that are additive inverses? Select each correct answer. A plane ascends 500 yards and descends 100 yards. Twenty gallons of water leak from a pool and 20 gallons are put back into the pool. A driver drives 40 miles north and 30 miles south. A person deposits $100 in to her bank account and then withdraws $100 from the same account.
Answers
Answer: Second and Fourth options are correct.
Step-by-step explanation:
Since we know that
Additive inverse means
[tex]a+(-a)=0[/tex]
so, -a is the additive inverse of a.
So, according to options, we get that
A plane ascends 500 yards and descends 100 yards.
Ascends = (+)500 yards
Descends = (-) 100 yards
So, -100 is not an additive inverse of +500.
Twenty gallons of water leak from a pool and 20 gallons are put back into the pool.
Number of gallons are leaked out = (-)20
Number of gallons are put back = (+)20
So, we can write
+20-20=0
So, -20 is the additive inverse of +20.
A driver drives 40 miles north and 30 miles south.
Number of miles towards north = +40
Number of miles towards south = -30
So, -30 is not additive inverse of +40.
A person deposits $100 in to her bank account and then withdraws $100 from the same account.
Amount he deposited into her bank = $100
Amount he withdraws from bank = -100
So, we can write as
+100-100=0
So, -100 is an additive inverse of 100.
Hence, Second and Fourth options are correct.
You want to buy an item that costs $100. Which of these is the most cost-effective choice for buying the item?
using a paid membership card to buy it at a 10 percent discount
buying it online at a 10 percent discount with a $5 shipping charge
buying it at a 10 percent discount without sales tax
Answers
Answer:
C.
buying it at a 10% discount without sales tax
Step-by-step explanation:
what is the slope of the line represented by the equation 2x+ 3y= -12
Answers
Answer:
Slope: -2/3
Step-by-step explanation:
In order to solve this we first have to clear the equation for Y:
[tex]2x+ 3y= -12\\3y=-12-2x\\y=\frac{-12-2x}{3}\\ y=-4-\frac{2}{3} x[/tex]
Remember that the equation in the form of Y is represented in this way:
y=mx+c
Where M is the slope and C is the constant, so the slope is the number that is multiplying x, in the equation, in this case -2/3 is the number that is multiplying x, sot eh slope of the equation is -2/3
Let z ∼ norm(0, 1). use the normal table and also r's "pnorm" function to find (a) p r(z ≤ 1.45) (b) p r(z > −1.28) (c) p r(−0.674 ≤ z < 1.036) (d) p r(z > 0.836)
Answers
(a) P(z<=1.45)=pnorm(1.45)=0.9264707
(b) P(z>-1.28)=pnorm(-1.28,lower.tail=FALSE)=0.8997274
(c) P(-0.674<=z<1.036)=pnorm(1.036)-pnorm(-0.674)=0.5997433
(d) P(z>0.836)=pnorm(0.836,lower.tail=FALSE)=0.2015775
Using normal probability tables (find one on the Internet if you don't have a book) use the normal table of left probabilities, i.e. the shaded part is on the left.
(a) Go to line 1.4, and column 0.5 to find the value 0.9265
(b) Go to line -1.2 and column 0.8 to find 0.1003, subtract from 1 to get the right tail (i.e. z>-1.28), or 1-0.1003=0.8997
(c) The probability between two values of z is found be the difference of the left tails
Here P(-0.674)=0.2502 (interpolate between P(-0.67) and P(-0.68).
P(1.036)=0.8499 (interpolate between P(1.03)=0.8485 and P(1.04)=0.8499
So P(-0.674<=z<1.036)=0.8499-0.2502=0.5997
(d) P(z<0.836)=interpolate between P(z<0.83)=0.7967 and P(z<0.84) =0.7995 to get 0.7894
P(z>0.836)=1-P(z<0.836)=1-0.7984=0.2016
To find the probabilities using the normal table and R's pnorm function, follow these steps: (a) p r(z ≤ 1.45) is 0.9265 or 92.65%. (b) p r(z > −1.28) is 0.8997 or 89.97%. (c) p r(−0.674 ≤ z < 1.036) is 0.6017 or 60.17%. (d) p r(z > 0.836) is 0.2013 or 20.13%.
Explanation:To find the probabilities using the normal table and r's pnorm function, we can follow these steps:
For (a) p r(z ≤ 1.45), we can use the normal table or the pnorm function in R to find the area to the left of 1.45. The area is 0.9265 or 92.65%.
For (b) p r(z > -1.28), we can find the area to the left of -1.28 using the normal table or the pnorm function in R, which is 0.1003 or 10.03%. To find the area to the right of -1.28, we subtract this value from 1. The area is 0.8997 or 89.97%.
For (c) p r(-0.674 ≤ z < 1.036), we can find the area to the left of -0.674 using the normal table or the pnorm function in R, which is 0.2514 or 25.14%. To find the area to the left of 1.036, we can use the normal table or the pnorm function in R, which is 0.8531 or 85.31%. The difference between these two values gives us the area between the z-scores, which is 0.8531 - 0.2514 = 0.6017 or 60.17%.
For (d) p r(z > 0.836), we can find the area to the left of 0.836 using the normal table or the pnorm function in R, which is 0.7987 or 79.87%. To find the area to the right of 0.836, we subtract this value from 1. The area is 0.2013 or 20.13%.
3.5 times (5.8 - 7.09)
Answers
We can use PEMDAS to solve this.
3.5(5.8-7.09)
Parentheses
3.5 x -1.29
Multiplication
-4.51500
The answer is -4.51500
Hope this helps! :)
The value of the expression simplified using PEMDAS rule is -4.515.
What is PEMDAS?"The order of operations is a rule that tells the correct sequence of steps for evaluating a math expression. We can remember the order using PEMDAS: Parentheses, Exponents, Multiplication and Division (from left to right), Addition and Subtraction (from left to right)".
For the given question,
The expression is 3.5 times (5.8 - 7.09).
PEMDAS rule is used to simplify this expression.
The expression is simplified as [tex]3.5[/tex] × [tex](5.8 - 7.09)[/tex]
⇒[tex]3.5[/tex] × [tex](-1.29)[/tex]
⇒[tex]-4.515[/tex]
Hence we can conclude that the value of the expression simplified using PEMDAS rule is -4.515.
Learn more about PEMDAS rule here
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An unknown number x is at most 30. Which graph best represents all the values of x?
Number line graph with closed circle on 30 and shading to the right.
Number line graph with closed circle on 30 and shading to the left.
Number line graph with open circle on 30 and shading to the left.
Number line graph with open circle on 30 and shading to the right
Answers
Answer:
b
Step-by-step explanation:
44 tens is the same as
Answers
Group a contains 157 students. of these, 51 students in group a have taken math 2a, 80 have taken math 2b, and 70 have taken math 2c. 15 have taken both math 2a and 2b, 20 have taken both math 2a and 2c, and 13 have taken both math 2b and 2c. how many students in group a have taken all three classes?
Answers
and this is the answer to you question
Answer:
86
Step-by-step explanation:
The stock market decreased by 135 points during a 5 day week.
What was the average daily change in the market for that week?
Answers
The table shows the annual profits (in thousands of dollars) of a county fair from 2008 to 2012.what must the 2012 profit be ( in hundreds of dollars ) to brake even over the five year period?
Answers
Suppose that a person rolls two balanced dice three times in succession. determine the probability that on each of the three rolls, the sum of the two numbers that appear will be 7.
Answers
The number of combinations that will result in a sum of 7 is:
1 + 6
6 + 1
2 + 5
5 + 2
3 + 4
4 + 3
For a total of 6 combinations per roll. While the total number of combinations per roll are:
6 * 6 = 36
Hence the probability that the sum is 7 would be:
Probability = 6 / 36 = 1 / 6
For a succession of three times, the overall probability that each three rolls will be a sum of 7 is:
Overall probability = (1/6) * (1/6) * (1/6)
Overall probability = 1/216 = 4.63 x 10^-3 = 0.463%
Final answer:
The probability of rolling a sum of 7 three times in succession using two balanced dice is 1/216.
Explanation:
To determine the probability that on each of the three rolls of two balanced dice, the sum of the two numbers that appear will be 7, we first need to identify the probability of rolling a sum of 7 with a single roll of two dice. There are six ways to roll a sum of 7: (1,6), (2,5), (3,4), (4,3), (5,2), and (6,1). The total number of possible outcomes when rolling two dice is 6*6 = 36. Therefore, the probability of rolling a sum of 7 on one roll is P(sum=7) = 6/36 = 1/6.
Since each roll is independent of the others, the probability of this event occurring three times in succession is the product of the individual probabilities. Thus:
P(First roll is 7) = 1/6P(Second roll is 7) = 1/6P(Third roll is 7) = 1/6Therefore, the probability of all three rolls resulting in a sum of 7 is:
P(Three 7's in a row) = P(First roll is 7) * P(Second roll is 7) * P(Third roll is 7) = (1/6) * (1/6) * (1/6) = 1/216.
Find the slope of the line that passes through (90, 93) and (-4, 49).
Answers
Norfolk va has a population of 242,628 people. Baltimore, Md has 376,865 more people than Norfolk. Charleston,SC has 496,804 less than Baltimore. What is the total population of all 3 cities?
Answers
The total population of Norfolk, VA, Baltimore, MD, and Charleston, SC is 984,810 people. This is calculated by adding the respective populations of the three cities together.
Explanation:The total population of the three cities can be found by adding their respective populations together. Given that Norfolk, VA has a population of 242,628 people, and Baltimore, MD has 376,865 more people than Norfolk, we calculate the population of Baltimore by adding these two figures together to get 619,493 people. Charleston, SC has 496,804 less than Baltimore, so its population is found by subtracting 496,804 from 619,493 to get 122,689 people. To find the total population of all 3 cities, we add the populations of Norfolk, Baltimore and Charleston together, giving us 984,810 people in total.
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Use the distributive property to simplify the following expression 4x(2x-6)
Answers
8x - 24x
= -16x
[tex]\textsf{Hi Brainy User, I'm Here to Help you!}[/tex]
- - - - - - - - - - - - - - - - - - -
[tex]\textsf{Using the distributive property, \textbf{a(b+c)=ab+ac}, expand the given expression:}[/tex]
[tex].\qquad\bullet\sf{4x(2x-6)=4x*2x-4x*6=8x^2-24x}[/tex]
[tex]\sf{\bf{$Answer: 8x^2-24x}}[/tex]
[tex]\Large\underbrace{\overbrace{\boldsymbol{Reflection - RoSe}}}^\star_\star[/tex]