identify the image of xyz for a composition of a 90 degree rotation and a 180 degree rotation, both about point x.
Answers
Answer: 90° option a
180° option b
Step-by-step explanation: If we do a rotation of 90° about the X point, this means that the angle between the lines XZ and X'Z must be equal to 90°.
The options that have a 90° angle between these two lines are a and c.
And here you can see that, if the rotation is counterclockwise, the option a is a rotation of 90° and option c is a rotation of 270°, while if the rotation is defined clockwise, the option c is 90° and option a is 270°.
Usually, the rotations are defined as counterclockwise, so under this viewpoint, the right answer is option a.
For a 180° rotation the angle between XZ and X'Z' must be equal to 180°, the only option that has a 180° angle is option b, so here b is the answer.
To find the image of triangle XYZ after a 90 degree rotation followed by a 180 degree rotation about point X, we perform the rotations successively, leading to a total rotation of 270 degrees counterclockwise about point X.
Explanation:To identify the image of the triangle XYZ after a composition of a 90 degree rotation and a 180 degree rotation, both about point X, we must perform the transformations step by step.
Firstly, we will apply a 90 degree rotation around point X. Imagine triangle XYZ in a coordinate plane where X is the origin. A 90 degree rotation would result in each point (x,y) of the triangle moving to (-y, x). The identity of triangle XYZ changes as each point follows this rule.
Next, we will apply a 180 degree rotation around point X. A 180 degree rotation is the same as an inversion of a point at (x,y) to (-x,-y). Again, each point of the already transformed triangle will follow this rule.
Overall, the composition of these two rotations is effectively a single rotation by 90 + 180 = 270 degrees. Triangle XYZ will thus have been rotated 270 degrees counterclockwise around point X to its final image position.
Related Questions
PLEASE HELP ME
If strictly practiced, which of the following methods of birth control is 100 percent effective?
abstinence
condoms
withdrawal
diaphragm with spermicide
Answers
Find the hypotenuse of a right triangle if the legs are: 5 and 12
Answers
In this case a would be 5 and b would be 12. If you add these into the equation and then square root your answer, that should be the hypotenuse of the triangle. Hope I helped, have a nice day :)
Quadrilateral RSTU is a rectangle with diagonal RT. If 8x + 4 and = 3x – 2, find x
Answers
Answer:
did u ever find the asnwer? cuz I need it rn
Step-by-step explanation:
A television production company charges a basic fee of $4000 and then $2000 per hour when filming a commercial.
A. Write an equation in slope-intercept form relating the basic fee and per-hour charge.
B. Graph your equation
C. Use your graph to find the production costs if 4 hours of filming were needed.
Please help me! I don't understand anything that i am learning right now and its all just confusing
Answers
b. graphing
c. $12,000
Hope this helped☺☺
The equation in slope - intercept form is as - y[h] = 2000h + 4000 and for 4 hours of filming, the production cost would be $12000.
What is Equation Modelling?
Equation modelling is the process of writing a mathematical verbal expression in the form of a mathematical expression for correct analysis, observations and results of the given problem.
Given is a television production company charges a basic fee of $4000 and then $2000 per hour when filming a commercial.
Assume that the number of hours required for filming the commercial be [h]. Then, we can write, the equation as follows -
y[h] = 2000h + 4000
The graph of the equation is attached with the answer.
For 4 hours of filming, the production cost would be -
y[4] = 2000 x 4 + 4000 = 8000 + 4000 = 12000
Therefore, the equation in slope - intercept form is as - y[h] = 2000h + 4000 and for 4 hours of filming, the production cost would be $12000.
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Tickets to a movie cost $7.25 for adults and $5.50 for students. a group of friends purchased 8 tickets for $52.75. how many adult tickets did they purchase?
Answers
ABC is an isosceles right triangle in which AB has a slope of -1 and angle ABC = 90 degrees. Triangle ABC is dilated by a scale factor of 1.8 with the origin as the center of dilation, resulting in the image A'B'C'. What is the slope of B'C'?
Answers
This kind of transformation results in a similar figure.
So the triangle A'B'C' will be similar to triangle ABC: which means that all the angles are preserved (thy are congruent).
Being the angles congruent the slope of B'C' will be the same angle of BC.
Since, the slope of AB is - 1, the other two sopes are one 0 and the other undefined (∞). The horizontal side has slope 0 and the vertical side has slope ∞.
Since you did not attache any figure I do not know whether B'C' is the horizontal or the vertical side.
The answer is that the slope of B'C' is zero if it is the horizontal side, and the slope is ∞ if B'C' is the vertical side.
Answer:
Slope of 1
Step-by-step explanation:
C. 1
A student solved this problem and said the answer was hour 3/4. Cindy rode her bike for 1/2 hour and ran for 1/4 hour. What was the total length of time that Cindy exercised? Is the student's answer reasonable?
A. Yes, the answer is reasonable.
B. No, the answer is not reasonable. It should be about 2 hours.
C. No, the answer is not reasonable. It should be about 1/4 hour.
D. No, the answer is not reasonable. It should be about 6 hours.
Answers
1/2=2/4 - equivalent fractions
2/4+1/4=3/4
choice A
Cindy rode her bike for 1/2 of an hour,
She ran 1/4 of an hour.
1/2 + 1/4 = 3/4
The answer is A
Hope this helps :)
A line that is parallel to y=12 has slope m=
Answers
any parallel line to y = 12, like the red one and the green one there, will have the same slope as y = 12, what is the that slope anyway?
well, let's pick any two points y = 12 passes by, hmmmmm say 2, 12 and 4, 12
[tex]\bf \begin{array}{ccccccccc} &&x_1&&y_1&&x_2&&y_2\\ % (a,b) &&(~ 2 &,& 12~) % (c,d) &&(~ 4 &,& 12~) \end{array} \\\\\\ % slope = m slope = m\implies \cfrac{\stackrel{rise}{ y_2- y_1}}{\stackrel{run}{ x_2- x_1}}\implies \cfrac{12-12}{4-2}\implies \cfrac{0}{2}\implies 0[/tex]
A patient needs 0.024grams of a sulfa drug. There are 8-mg tablets in stock. how many tablet should be given?,
Answers
Sean has 3 times as many vegetable plants as Liz and Sejuan combined. Liz has 3 vegetable plants, and Sejuan has 2 vegetable plants. How many vegetable plants does Sean have?
Which statements about this word problem are true? Check all that apply.
This is an example of a part-whole problem.
This is an example of a comparison problem.
Addition then multiplication can be used to solve the problem.
Subtraction then division can be used to solve the problem.
Division then multiplication can be used to solve the problem.
Answers
This is a comparison problem in mathematics where addition and multiplication are used. Liz and Sejuan together have 5 vegetable plants and since Sean has 3 times what both of them have combined, Sean has 15 vegetable plants.
Explanation:The problem at hand is about a comparison of the number of vegetable plants between Sean, Liz and Sejuan. It's an example of a comparison problem where addition and multiplication are used to find the solution. First, you need to find the total number of plants that Liz and Sejuan have by adding their plants together (3 + 2). We get a result of 5. Then, we know that Sean has 3 times as many plants as Liz and Sejuan together, so you multiply the combined total by 3 (5 * 3). The result is 15, so Sean has 15 vegetable plants.
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How many triangles are formed by dawing all the diagonals from a single vertex of a convex polygon
Answers
(n-2) triangles can be formed by drawing all the diagonals from a single vertex.
What is Polygon?a polygon is a plane figure that is described by a finite number of straight line segments connected to form a closed polygonal chain.
Given a convex polygon with n vertices, the number of triangles that can be formed by drawing all the diagonals from a single vertex can be calculated.
a diagonal is a line segment joining two vertices of a polygon or polyhedron, when those vertices are not on the same edge
Let's consider a convex polygon with 4 vertices.
(n-2) triangles can be formed by drawing all the diagonals from a single vertex.
Hence, (n-2) triangles can be formed by drawing all the diagonals from a single vertex.
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You have a balance of $15,300 on your credit card with an 18% interest rate (1.5% per month). You pay $200 this month. Did your balance go up or down?
Will fan and medal
Answers
If balance is negative you charged $229.5 and you will add $200. So total balance will go down.
First, calculate the interest that will accumulate for 1 month on your current balance.
15300 * 0.015 = 229.5
Right now, we can stop since it's obvious that $229.50 of interest is greater than the $200.00 you're paying for that month. The new balance on your card will be:
$15,300 + $229.50 - $200 = $15,329.50
Vesna vulovic survived the longest fall on record without a parachute when her plane exploded and she fell 6 miles and 551 yards. how many feet is this?
Answers
1 yard = 3 feet
so 3 times 11,111 = 33,333 feet
4400 dollars is placed ina an account with an annual interest rate of %8.25. How much will be in the account after 29 years
Answers
Answer: 43839.13
Step-by-step explanation:
Final answer:
To calculate the amount in the account after 29 years, use the formula for compound interest. The amount in the account will be approximately $40,882.53.
Explanation:
To calculate the amount in the account after 29 years, we can use the formula for compound interest: A = P(1 + r/n)^(nt), where A is the final amount, P is the principal (initial amount), r is the annual interest rate (as a decimal), n is the number of times interest is compounded per year, and t is the number of years. In this case, the principal is $4400, the annual interest rate is 8.25%, and since it is not specified, we'll assume interest is compounded annually. So, the formula becomes:
A = 4400(1 + 0.0825/1)^(1*29)
To calculate this, we can enter the expression into a calculator or spreadsheet:
A = 4400(1 + 0.0825)^(29)
After evaluating this expression, we find that the amount in the account after 29 years will be approximately $40,882.53.
help, please show how to find x, thank you
Answers
now, notice the angle at the very top, the large triangle is really sharing it with smaller-inscribed triangle, and therefore is equal on both triangles.
therefore, the larger triangle, is similar with smaller-inscribed triangle by AA.
what the dickens does that mean?
[tex]\bf \cfrac{large}{small}\qquad \cfrac{4+5}{4}=\cfrac{5+x}{5}\implies \cfrac{9}{4}=\cfrac{5+x}{5}\implies 45=20+4x \\\\\\ 25=4x\implies \cfrac{25}{4}=x\implies 6\frac{1}{4}=x[/tex]
Paige bought 34 yards of yarn at the store and 2⁄9 of the yarn was blue. How many yards of blue yarn did Paige buy?
Answers
(2/9) * (100) = 22.22222222%
Making the following rule of three we have:
34 ----> 100%
x ------> 22.22222222%
Clearing x we have:
x = ((22.22222222) / (100)) * (34)
x = 7.555555555
x = 7.6
Answer:
Paige did buy 7.6 yards of blue yarn
Answer:
the right answer is 7 5/9 yards.
Step-by-step explanation:
Help me
Show all your work
Answers
3x +10x -2=11
3x+10x=13
13x=13
X=1
y = 5x-1
For this case, the first thing you should do is replace the value of y in the first equation.
We have then:
3x + 2 (5x-1) = 11
We rewrite:
3x + 10x-2 = 11
3x + 10x = 11 + 2
3x + 10x = 13
We clear x:
13x = 13
x = 13/13
x = 1
We now substitute the value of x in expression 2:
y = 5 (1) -1
y = 5-1
y = 4
Answer:
The solution to the system of equations is:
x = 1
y = 4
The difference of two numbers is 44 1 /2 . If the smaller of the two numbers increases 7 times then the difference will be 10 3/14 . Find the numbers.
Answers
The difference of two numbers is 44 1/2.
If the smaller of the two numbers increases 7 times
the difference will be 10 3/14.
Find the numbers?
x - y = 44 1/2
x - 7y = 10 3/14
6y = 34 2/7
y = 40/7
x = 703/14
Have a nice day
Required numbers as per the given condition are [tex]50\frac{3}{14}[/tex] and [tex]5\frac{5}{7}[/tex].
What is a number?" A number is defined as the count of any given quantity."
According to the question,
[tex]'x'[/tex] represents the greater number
[tex]'y'[/tex] represents the smaller number
As per the given condition equation we have,
[tex]x- y = 44\frac{1}{2} \\\\\implies x-y = \frac{89}{2}[/tex] ______[tex](1)[/tex]
[tex]x-7y =10 \frac{3}{14} \\\\\implies x-7y = \frac{143}{14}[/tex] ______[tex](2)[/tex]
Subtract equation [tex](2)[/tex] from [tex](1)[/tex] to get the required numbers,
[tex]6y = \frac{89}{2} -\frac{143}{14} \\\\\implies 6y = \frac{623-143}{14}\\ \\\implies 6y = \frac{480}{14}\\ \\\implies y = \frac{40}{7}\\ \\\implies y = 5\frac{5}{7}[/tex]
Substitute the value of [tex]'y'[/tex] in [tex](1)[/tex] we get,
[tex]x= \frac{89}{2}+ \frac{40}{7} \\\\\implies x = \frac{623+80}{14} \\\\\implies x= \frac{703}{14}\\ \\\implies x= 50\frac{3}{14}[/tex]
Hence, required numbers as per the given condition are [tex]50\frac{3}{14}[/tex] and [tex]5\frac{5}{7}[/tex].
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Jake forgot to replace the cap on a bottle of deodorant. The deodorant began to evaporate at the rate of 12% per day. If the original amount of deodorant in the bottle was 30 grams, which of the following graphs best represents the amount of deodorant f(x) that would remain in the bottle after x days?
graph of function f of x equals 30 multiplied by 0.88 to the power of x
graph of exponential function going down from left to right in quadrant 1 through the point 0, 40 and approaching the x axis
graph of function f of x equals 50 multiplied by 0.82 to the power of x
graph of exponential function going down from left to right in quadrant 1 through the point 0, 4 and approaching the x axis
Answers
f(x) = 30(0.88)^x
Answer:
1. Graph of function f of x equals 30 multiplied by 0.88 to the power of x
Step-by-step explanation:
We are given that,
Original amount of deodorant in the bottle = 30 grams
The rate of evaporation = 12% = 0.12
That is, we see that the deodorant is decreasing as the number of days increases.
So, the function form of the decrease in the amount of deodorant is given by,
[tex]f(x)=30(1-0.12)^x[/tex], where x is the number of days.
i.e. [tex]f(x)=30(0.88)^x[/tex], where x is the number of days.
Hence, the graph representing the amount of deodorant after x number of days is,
1. Graph of function f of x equals 30 multiplied by 0.88 to the power of x
A statement Sn about the positive integers is given. Write statements S1, S2, and S3, and show that each of these statements is true. Show your work. Sn: 12 + 42 + 72 + . . . + (3n - 2)2 = n(6n^2-3n-1)/2
Answers
[tex]S_1 = 12 \\ S_2 = 54 \\ S_3 = 126 \\ S_n = 15n^2 - 3n [/tex]
Explanation:
[tex]S_1 = 12 \\ S_2 = 12 +42 = 54 \\ S_3 = 12 + 42 + 72 = 126[/tex]
To calculate for [tex]S_n[/tex], note that the series is an arithmetic series because each term is equal to the preceding term plus a constant, which is 30 (called common difference).
We let
[tex]a_1 = \text{ first term} = 12 \\ a_2 = \text{ second term} = 42 \\ a_3 = \text{ third term} = 72\\. \\. \\. \\a_n = n\text{th term}[/tex]
Since [tex]S_n[/tex] is an arithmetic series, [tex]a_1, a_2, a_3, ... , a_n[/tex] is an arithmetic sequence and so the formula for the nth term is given by
[tex]a_n = a_1 + d(n - 1) \\ a_n = 12 + 30(n - 1) \\ \boxed{a_n = 30n - 18}[/tex]
Where d = common difference = 30
Now, since [tex]S_n[/tex] is an arithmetic series, we can use the formula for the sum of the arithmetic series, which is given by
[tex]S_n = \frac{n}{2} (a_1 + a_n) \\ \\ = \frac{n}{2} (12 + 30n - 18) \\ \\= \frac{n}{2} (30n - 6) \\ \\ = \frac{30n^2 - 6n}{2} \\ \\ \boxed{S_n = 15n^2 - 3n}[/tex]
Heron’s formula: Area = Triangle PQR has sides measuring 9 feet and 10 feet and a perimeter of 24 feet. What is the area of triangle PQR? Round to the nearest square foot.
Answers
Let's assume a,b,c the 3 sides of the triangle.
a=9
b=10
c=24-a-b=5
[tex]p= \dfrac{a+b+c}{2} =12\\ S= \sqrt{p(p-a)(p-b)(p-c)} = \sqrt{12*3*2*7} = \sqrt{504} =22,4499...\approx{22}[/tex]
helpppppppppppppppppppppppppppppp
Answers
first option: Harulo is correct because the angle is coterminal with 3π / 4 and the reference angle is π / 4.
Explanation:
1) 19 π/4 = 4π + 3 π/4, which is 4 complete turns and 3/4 of turn.
2) 3 π/4 is in the third quadrant, so the reference angle is π - 3 π/4 = π/4
3) sin (π/4) = sin (3π/4) = (√2) / 2
4) csc (π/4) = 1 / [ sin (3π/4) ] = 1 / [ (√2) / 2 ] = 2 / (√2) = √2, which shows the validity of the statement and csc(19π/4) = √2.
Jason's current yearly income is $13,000...If Jason’s training will allow him to get a job making $34,000 a year, how long will it take him to recover his initial investment of $35,200?
Answers
First, find the amount of extra money that he will make.
34,000 - 13,000 = 21,000
He will be making an extra 21,000 per year.
Now, divide the cost of his training by the amount of his increase.
35200 / 21000 = 1.68
That gives you the amount of years it will take him to pay off his investment.
The sculpture consists of five identical prisms. JD says the surface area of the sculpture is 44 times the surface area of one prism. Which statement about JD's method is true?
Answers
we know that
(see the attached figure n 2 to understand the problem)
[the surface area of one prism]=2*[x*x]+2*[x*y]+2*[x*y]----> 2x²+4xy
[the surface area of the sculpture]=2*[5*x*y]+2*[3*x*x]+2*[3*x*y]--> 6x²+16xy
now
JD says the surface area of the sculpture is 4 times the surface area of one prism
[the surface area of the sculpture]=4*(2x²+4xy)---> 8x²+16xy
we compare the value that JD says with the real value
(8x²+16xy) > (6x²+16xy)
the value that JD says is greater in comparison with the real value
This is because JD should also subtract the areas of eight hidden surfaces.
the answer is
JD should also subtract the areas of eight hidden surfaces
Jon is launching rockets in an open field. The path of the rocket can be modeled by the quadratic function h(t) = -16t^2 + 96t, where h(t) is the height in feet any time t in seconds. After how many seconds will the rocket reach a height of 80 feet for the second time
Answers
We set the equation equal to 80 feet:
80= -16t² + 96t
When solving quadratics, we want it equal to 0, so we subtract 80 from both sides:
80-80= -16t² + 96t - 80
0= -16t² + 96t - 80
We use the quadratic formula to solve:
[tex]t=\frac{-96\pm \sqrt{96^2-4(-16)(-80)}}{2(-16)} \\ \\t=\frac{-96\pm \sqrt{9216-5120}}{-32} \\ \\t=\frac{-96\pm \sqrt{4096}}{-32} \\ \\t=\frac{-96\pm 64}{-32} \\ \\t=\frac{-96+64}{-32} \text{ or } 0=\frac{-96-64}{-32} \\ \\t=1 \text{ or } t=5[/tex]
Simplify each expression. Use positive exponents.
(x–2y–4x3) –2,
Answers
(x^-2y^-4x³)^-2
We can combine the x terms inside the brackets using the concept;
x ^a × x^b = x^(a+b)
Therefore,
(x^-2)(x^3) = x^(3-2) = x^!
Thus we get;
(xy^-4)^-2
Using the concept
(x^a)^b = x^(ab)
Therefore
= x ^(-2×1) y^(-2×-4)
=x^-2y^8
But using the concept; x^-a = 1/x^a
Thus, x^-2y^8 = y^8/x²
Hence the simplified equation is;
= y^8/x²
1 .
Factor 13x⋅(x−3)+10⋅(x−3)
2.
Factor 17t⋅(17t−9)−12⋅(17t−9)
Answers
The product of two consecutive even integers is 528. find the integers
Answers
4x^2 + 4x = 528
4x^2 + 4x -528 = 0
x^2 + x -132 = 0
Using quadratic formula
x = 11
Therefore, the integers are
22 and 24
A line has a slope of - 3/5. Which ordered pairs could be points on a parallel line? Check all that apply.
A). (–8, 8) and (2, 2)
B). (–5, –1) and (0, 2)
C). (–3, 6) and (6, –9)
D). (–2, 1) and (3, –2)
E). (0, 2) and (5, 5)
I think it's A, but I'm not sure. Please help, I'll pick Brainliest! :-P
Answers
The ordered pairs will be the points on the parallel line are
(-8, 8) and (2, 2)
(-2, 1) and (3, -2)
What is the slope of a line?A slope of a line is the change in y coordinate with respect to the change in x coordinate.
How to find the slope of line from the two points?If [tex](x_{1} ,y_{1} )[/tex] and [tex](x_{2} , y_{2} )[/tex] be the two points then the slope of the line is given by
[tex]slope = \frac{y_{2} -y_{1} }{x_{2}-x_{1} }[/tex]
According to the given question.
We have slope of a line is [tex]\frac{-3}{5}[/tex].
As, we know that the two parallel lines have the same slope.
Now according to the given ordered pairs
A). (-8, 8) and (2, 2)
[tex]slope = \frac{2-8}{2+8} = \frac{-6}{10} =\frac{-3}{5}[/tex]
Therefore, (-8, 8) and (2, 2) are the ordered pairs could be the points on the parallel line.
B) (-5, -1) and (0, 2)
[tex]slope = \frac{2+1}{0+5} =\frac{3}{5} \neq \frac{-3}{5}[/tex]
Hence, the ordered pair (-5, -1) and (0, 2) will never be the points on the parallel line.
C) (-3, 6) and (6, -9)
[tex]slope = \frac{-9-6}{6+3} =\frac{-15}{9} =\frac{-5}{3}\neq \frac{-3}{5}[/tex]
The ordered pair (-3, 6) and (6, -9) will never be the points on the parallel line.
D). (-2, 1) and (3, -2)
[tex]slope = \frac{-2-1}{3+2} =\frac{-3}{5}[/tex]
Therefore, (-2, 1) and (3, -2) are the ordered pairs could be the points on the parallel line.
E). (0, 2) and (5, 5)
[tex]slope = \frac{5-2}{5-0} =\frac{3}{5} \neq \frac{-3}{5}[/tex]
Therefore, (0, 2) and (5, 5) are the ordered pairs could not be the points on the parallel line.
Hence, the ordered pairs will be the points on the parallel line are
(-8, 8) and (2, 2)
(-2, 1) and (3, -2)
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To determine if the given ordered pairs could be points on a parallel line with a slope of -3/5, we can calculate the slope of each line and compare it to the original slope. The pairs (D) (-2, 1) and (3, -2) have a slope of -3/5, making them parallel.
Explanation:A line with a slope of -3/5 is a line that slopes downwards from left to right. In order for a line to be parallel to this line, it must have the same slope. To determine if the given ordered pairs could be points on a parallel line, we can calculate the slope of each line and compare it to the slope of the original line.
B) (-5, -1) and (0, 2): The slope of this line is (2 - (-1))/(0 - (-5)) = 3/5, which is different from the original slope of -3/5. Therefore, this line is not parallel.
D) (-2, 1) and (3, -2): The slope of this line is (-2-(-2))/(3-(-2)) = -3/5, which is equal to the original slope of -3/5. Therefore, this line is parallel.
E) (0, 2) and (5, 5): The slope of this line is (5 - 2)/(5 - 0) = 3/5, which is different from the original slope of -3/5. Therefore, this line is not parallel.
So, the parallel lines are (D) (-2, 1) and (3, -2).
1. picture
2.picture
3.which graph represents f(x)=4sin(2πx)?
4. A cosine function has a period of 3, a maximum value of 20, and a minimum value of 0. The function is a reflection of its parent function over the x-axis.
Which function could be the function described?
5. A sinusoidal function whose frequency is 3, maximum value is 15, minimum value is −3 has a y-intercept of 6.
Which function could be the function described?
f(x)=9sin(6πx)+3
f(x)=9sin(3x)+3
f(x)=9sin(x3)+6
f(x)=9sin(6πx)+6
Answers
See the attached image. Specifically see figure 1.
==============================================
Problem 2
See the attached image. Specifically see figure 2.
==============================================
Problem 3
Answer: bottom right corner
------------------------
f(x) = 4*sin(2pi*x)
f(x) = a*sin(b*x)
a = 4 is the amplitude
b = 2pi
T = 2pi/b = 2pi/2pi = 1 is the period
The graph that has a period of 1 and amplitude 4 is the bottom row of choices. We can rule out the graph on the left because sine starts off increasing as you move away from the origin and go from left to right.
==============================================
Problem 4
Answer: f(x) = -10cos(2pi*x/3)
------------------------
T = period = 3
b = 2pi/T = 2pi/3
amplitude = (max - min)/2
amplitude = (20-0)/2
amplitude = 10
y = 10 is the midline since d = (20+0)/2 = 10
f(x) = a*cos(bx)+d
f(x) = -10*cos(2pi*x/3)+10
Note: the value of 'a' is negative because of the reflection over the x axis
==============================================
Problem 5
Answer: Choice D
f(x) = 9*sin(6pi*x)+6
------------------------
min = -3
max = 15
midline: d = (max + min)/2 = (15-3)/2 = 6
amplitude: a = (max - min)/2 = (15+3)/2 = 9
f = frequency = 3
T = period = 1/f = 1/3
b = 2pi/T = 2pi/(1/3) = 6pi
f(x) = a*sin(bx)+d
f(x) = 9*sin(6pi*x)+6
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The graph is shown in the figures.
Sinusoidal functionIt is a function that repeats itself after a regular interval of time.
How to calculate?1. Graph of g(t) = 4sin(3t) + 2 is shown below.
2. Graph of f(x) = 3cos(2x) - 1 is shown below.
3. Graph D represents the f(x) = 4sin(2[tex]\rm \pi[/tex]x) because the value of sine maximum and the minimum are 1 and -1 so the value of f(x) is maximum and the minimum is 4 and -4.
4. The maximum and minimum value of f(x) 20 and 0. and period is 3. then our f(x) will be
[tex]f(x) = 10\ cos(\dfrac{2\pi }{3}x ) +10[/tex]
5. For this D is the correct option. because maximum and minimum values, as well as frequency, satisfy the equation.
Thus, the graph is shown in figures.
More about the sinusoidal function link is given below.
https://brainly.com/question/12078395