The equation for the bob's horizontal location is x(t) = -A sin(ωt) and the bob is 3.47cm after 0.9 seconds
Equilibrium in a pendulum explanationSince the distance a from the equilibrium position can be described by a cosine function, we have:
a(t) = Acos(ωt + φ)
where A is the amplitude of the motion, ω is the angular frequency, and φ is the phase constant. We are given that the amplitude A = 7.5/2 = 3.75 cm (half the width of the swing) and the period T = 1.1 seconds. The angular frequency is related to the period by:
ω = 2π/T
so we have:
ω = 2π/1.1 ≈ 5.72 rad/s
To find the phase constant φ, we need to use the initial condition that the pendulum bob is released from its farthest right position. This means that at t = 0, a = A, so we have:
A = Acos(φ)
which implies:
cos(φ) = 1
Since we want a positive value of a when the bob is to the right of the equilibrium position, we choose φ = 0. Therefore, the equation for the bob's horizontal location is:
x(t) = -A sin(ωt)
where we have used the fact that the bob's motion is in a vertical plane and the angle between the vertical and the string of the pendulum is a right angle.
To find where the bob is after 0.9 seconds, we substitute t = 0.9 into the equation for x(t) and get:
x(0.9) = -3.75 sin(5.72 × 0.9) ≈ -3.47 cm
So the pendulum bob is about 3.47 cm to the left of the equilibrium position after 0.9 seconds.
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A survey is taken at a movie theater in Wayside. The first 200 people who entered the theater were asked about their favorite type of movie. What is true about this situation?
The population is the first 200 people at the theater, and the sample is the total number of people who go to the movie theater.
The population is the number of people who go to the movie theater, and the sample is the number of people in the town of Wayside.
The population is the total number of people who go to the movie theater, and the sample is the first 200 people at the theater.
The population is the number of people in the town of Wayside, and the sample is the number of people who go to the movie theater.
A survey is taken at a movie theater in Wayside. The first 200 people who entered the theater were asked about their favorite type of movie. The true about this situation is: The population is the total number of people who go to the movie theater, and the sample is the first 200 people at the theater.
In this situation, the population refers to the entire group of people who go to the movie theater in Wayside. The population includes all individuals who have the potential to be surveyed about their favorite type of movie.
The sample, on the other hand, is a subset of the population and represents the first 200 people who entered the theater. These 200 individuals are selected to provide information about the preferences of the larger population.
It is important to note that the sample is not the entire population but rather a smaller representative group. By surveying the sample, we aim to gather insights and make inferences about the preferences of the larger population of moviegoers in Wayside.
The correct answer is: The population is the total number of people who go to the movie theater, and the sample is the first 200 people at the theater.
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1.12x - 2.24y= 4.96 -3.56- 2.48y= -7.32
The hour marks on a clock face are 30° apart. What is the angle a line from the four o'clock mark to the twelve o'clock mark makes with a horizontal line?
mason asked some classmates if they play video games or not. the ratio of friends who play video games to everyone he asked is . how many of his friends do not play video games?
Mason's friends do not play video games are 4.
Mason asked some classmates whether they play video games.
The ratio of friends who play video games to everyone he asked is given as some fraction or decimal value.
Let's assume that the ratio is in the form of "x:y",
"x" represents the number of friends who play video games, and "y" represents the total number of friends that Mason asked.
To find out how many of his friends do not play video games,
To subtract the number of friends who play video games from the total number of friends that Mason asked.
This is because the remaining friends who were not counted in the "x" value of the ratio must be those who do not play video games.
So, the number of friends who do not play video games can be calculated as:
Total number of friends - Number of friends who play video games = y - x
The ratio of friends who play video games to everyone he asked is 3:7,
It means that out of 7 friends, 3 play video games, and 4 do not play video games.
The number of friends who do not play video games can be calculated as:
y - x = 7 - 3 = 4
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In circle A, marc BC is 61° and marc EF is 76°: Points B, C, E, and F lie on Circle A. Lines BE and CF pass through point D, creating angle EDF. The measure of arc BC is 61 degrees, and the measure of arc EF is 76 degrees. What is m∠FDE? 30.5° 38° 76° 68.5°
The measure of angle FDE is 68.5°
the correct answer is an option (d)
Consider the following figure.
We know that whenever two chords cut across a circle, the resulting angle is equivalent to half of the sum of the measurements of the arc the angle intersects and that which the angle vertical to the first angle intercepts.
Here, chords BE and FC cuts across the circle forming ∠FDE.
According to above statement, the measure of ∠FDE would be equal to the sum of the measurements of the arc BC and FE
⇒ m∠FDE = 1/2( Arc BC + Arc FE)
⇒ m∠FDE = 1/2 (61° + 76°)
⇒ m∠FDE = 137/2
⇒ m∠FDE = 68.5°
Therefore, the correct answer is an option (d)
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Answer:
The measure of angle FDE is 68.5° (D)
Step-by-step explanation:
I TOOK THE TEST
Circle I and circle L are shown. Sector HIJ and sector KLM have the same area.
BLANK 1: Which formula should be used to solve this problem?
BLANK 2: What is the area of sector HIJ? Use 3.14 for pi.
BLANK 3: What is the measure of angle KLM?
1. Formula for the area of a sector of a circle, which is A = (θ/360)π[tex]r^2[/tex] 2. The area of sector HIJ is 2.51 square units. 3. The measure of angle KLM is approximately 0.29 degrees
What is circle?A circle is a geometric shape consisting of all the points in a plane that are a fixed distance (called the radius) away from a given point (called the center).
According to given information:BLANK 1: To solve this problem, we can use the formula for the area of a sector of a circle, which is A = (θ/360)π[tex]r^2[/tex], where θ is the central angle of the sector, r is the radius of the circle, and π is pi (approximately 3.14).
BLANK 2: To find the area of sector HIJ, we need to know the radius of circle I and the measure of angle HIJ. From the given information, we know that circle I has a radius of 8, and angle HIJ is 45 degrees. Therefore, the area of sector HIJ is:
A = (45/360) x 3.14 x [tex]8^2[/tex]
A = 3.14 x 8 x (45/360)
A = 3.14 x 8 x 0.125
A = 2.51 square units (rounded to two decimal places)
Therefore, the area of sector HIJ is 2.51 square units.
BLANK 3: We know that sector KLM has the same area as sector HIJ, and circle L has a radius of 10. Therefore, we can use the formula for the area of a sector of a circle again to find the measure of angle KLM. Let x be the measure of angle KLM in degrees. Then:
A = (x/360) x 3.14 x [tex]10^2[/tex] = 2.51
Simplifying this equation gives:
(x/360) = 2.51/(3.14 x [tex]10^2[/tex])
(x/360) = 0.0008
x = 360 x 0.0008
x = 0.288
Therefore, the measure of angle KLM is approximately 0.29 degrees (rounded to two decimal places).
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A surveyor interviews a random sample of 85,349 adults in Florida and finds that 72% state that they have visited a doctor within the past year. Records from the state board of health indicate that of the 21 million Florida residents, 12 million visit a doctor annually. Identify the population, parameter, sample, and statistic. Population: 57%; parameter: 21 million; sample: 72%; statistic: 85,249
Population: 21 million; parameter: 57%; sample: 85,249; statistic: 72%
Population: 21 million; parameter: 72%; sample: 85,249; statistic: 57%
Population: 85,249; parameter: 72%; sample: 21 million; statistic: 57%
Answer:
Population: 21 million; parameter: 57%; sample: 85,349; statistic: 72%.
Explanation:
The population is the entire group being studied, which in this case is all the residents of Florida, with a total population of 21 million.
The parameter is a numerical summary of the population, which in this case is the proportion of residents who visit a doctor annually and is stated as 57% in the problem.
The sample is a subset of the population that is selected for study, which in this case is the 85,349 adults surveyed by the surveyor.
The statistic is a numerical summary of the sample, which in this case is the proportion of adults in the sample who stated that they have visited a doctor within the past year and is stated as 72% in the problem.
What is the difference of the fractions? 4/7 - 10/7
Answer:
-6/7
Step-by-step explanation:
consider a dataset of towers in every state which is normally distributed. consider a sample of 40 towers. the sample data has a mean of 68 with a standard deviation of 15. how many degrees of freedom we use to find the t-critical statistic value?
39 degrees of freedom will be used to find the t-critical statistic value.
We need to find degrees of freedom for the t-critical statistic value with 40 sample towers and a normally distributed population. According to the given dataset we can assume that we have the 95% confidence interval which is taken as default if nothing is mentioned about it.
The degrees of freedom (df) for a t-distribution are calculated as given below:
df = n - 1
where n is the sample size of the problem.
In this case, the sample size is 40, so the degrees of freedom would be:
df = 40 - 1 = 39
Therefore, we would use 39 degrees of freedom to find the t-critical statistic value for a 95% confidence interval.
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The diameter of a circle is 3.6 m. Find the radius, circumference and area. Show your working.
Step-by-step explanation:
Given :
d = 3.6m
r = d/2
r = 3.6/2
r = 1.8 m
We know that,
C = 2πr
C = 2 * 22/7 * 1.8
C = 11.3 m
Now,
A = π r²
A = 22/7 × (1.8)²
A = 22/7 × 3.24
A = 10.1 m²
Answer:
The Radius is 1.8, The circumference is 11.3 ,The area is 10.2
Step-by-step explanation:
The radius of a circle from diameter: if you know the diameter d , the radius is r = d / 2 .
To calculate the circumference, you need the radius of the circle: Multiply the radius by 2 to get the diameter. Multiply the result by π, or 3.14 for an estimation.That's it; you found the circumference of the circle.Or you can use the circle's diameter:Multiply the diameter by π, or 3.14.The result is the circle's circumference.
Diameter of circle= 3.6cm So, radius of circle=3.6/2Radius of circle = 1.8 Now ,Area of circle =πr². [r=radius] so 3.14 times 1.8 times 1.8 and you get 10.17 then round it to the nearest tenth and it is 10.2
liv and hassan graphed the transformation shown below in 5-10 record which graph meets the given criteria by writing liv hassan both or neither
Considering the attached figure, the transformation questions are answered as follows
5. Hassan
6. Liv
7. Both
8. Liv
9. Neither
What is reflection in transformationReflection is a type of transformation in geometry that involves flipping a shape over a line of reflection, such that the image is a mirror image of the original shape. The line of reflection is a fixed line that acts as the axis of symmetry for the transformation.
Liv was a translation, that moved the preimage from the second quadrant to an image in quadrant 1. But Hassan image was a reflection that flipped the preimage from the first quadrant to an image in quadrant 2
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how to find the scale factor of 10 cm=5m
The scale factor of 10cm to 5m is 50.
What is scale factor?The scale factor is a measure for similar figures, who look the same but have different scales or measures.
For example ,if a length of 5cm is doubled and it gives a length 10cm, the scale factor is 10/5 = 2. This means that we can express scale factor with a formula;
scale factor = new dimension / old dimension
Here, the old dimension is 10cm and the new dimension is 5m. We need to convert the 5m into cm
therefore 5m = 5× 100 = 500cm
therefore scale factor = 500/10 = 50
This means the scale factor of 10cm = 5m is 50
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Find B in degrees. 4 B 3 round to the nearest hundredth
Step-by-step explanation:
For right triangles tan B = opposite leg / adjacent leg
tan B = 3/4
arctan (3/4) = B = 36.87 degrees
Himpunan penyelesaian dari :
18 - 2x < 3.(2x - 1) - 3
adalah ….
Step-by-step explanation:
18-2x<3(2x-1)-3
21-2x<6x-3
24<8x
3<x
Interval notation
(3, ∞)
In trapezoid ABCD, O is the point of intersection from the diagonals. The area of AOD is 15 ft^2. The altitudes from B and O to the longer base are in a 5:3 ratio. Find the area of ABD and the area of MOC if M is the midpoint of the leg CG
If M is the midpoint of the leg CG, then the
a) Area of ABD = 18.75 ft^2
b) Area of MOC = 15 ft^2
To solve this problem, we need to use the properties of trapezoids and their diagonals. Let's start with finding the area of ABD.
First, notice that ABD and COD are similar triangles because they share angle O. Thus, we can write
AB/CD = AD/CO
Since AD = BC (opposite sides of a trapezoid are parallel), we can simplify to:
AB/CD = BC/CO
We also know that the area of AOD is 15 ft^2
Area of ABD/ Area of COD = AB/CD
We can substitute the ratio AB/CD from the similarity relation above to get
Area of ABD/ Area of COD = BC/CO
Since the bases of the trapezoids are parallel
Area of ABD/ Area of COD = BD/CO
Finally, we can use the fact that the altitudes from B and O to the longer base are in a 5:3 ratio to write
Area of ABD/ Area of COD = 5/3
Area of ABD = 5/8 × Area of COD
We know that the area of AOD is 15 ft^2, so the area of COD is twice that, or 30 ft^2. Therefore
Area of ABD = 5/8 × 30 = 18.75 ft^2
Next, we need to find the area of MOC. To do this, we can use the fact that the diagonals of a trapezoid divide it into four triangles, and the areas of these triangles are proportional to the lengths of the diagonals.
Let x be the length of OC, and let y be the length of OG. Then we have
Area of MOC/ Area of MOG = x/y
Also, since M is the midpoint of CG, we have
x = 2y
Substituting this into the first equation, we get
Area of MOC/ Area of MOG = 2
We know that the area of MOG is half the area of AOD, so
Area of MOG = 15/2 ft^2
Therefore, we have
Area of MOC = 2 × Area of MOG = 15 ft^2
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The box plot represents the scores on quizzes in a history class.
A box plot uses a number line from 69 to 87 with tick marks every one-half unit. The box extends from 75 to 82 on the number line. A line in the box is at 79. The lines outside the box end at 70 and 84. The graph is titled History Quizzes, and the line is labeled Scores on Quizzes.
What value does 75% of the data lie below? Find the value.
75% of the data lies below 81.5.
What value does 75% of the data lie below? Find the value.In a box plot, the box represents the middle 50% of the data, with the lower edge of the box (the "whisker") representing the 25th percentile and the upper edge of the box (the other "whisker") representing the 75th percentile.
Since the lower edge of the box is at 75, we know that at least 25% of the data lies below 75. Similarly, since the upper edge of the box is at 82, we know that at least 25% of the data lies above 82. Therefore, the middle 50% of the data lies between 75 and 82.
To find the value that 75% of the data lies below, we need to find the 75th percentile. Since the line in the box is at 79, we know that 50% of the data lies below 79. Therefore, we need to find the value that is greater than 79 and such that 75% of the data lies below it.
We can use the length of the box (82 - 75 = 7) to find the size of each quartile. Since the middle 50% of the data lies in the box, each quartile contains 25/2 = 12.5% of the data.
To find the value that 75% of the data lies below, we need to add 12.5% to 50% (which is the location of the line in the box). Therefore, we need to find the value that is greater than 79 and such that 62.5% of the data lies below it.
Since the length of the number line is 87 - 69 = 18, each tick mark represents 0.5 units. Therefore, to find the tick mark that corresponds to the 62.5th percentile, we can add 0.5 units for every 12.5% increase. Starting from 79, we need to add 0.5 x 5 = 2.5 units to reach the tick mark that corresponds to the 62.5th percentile. Therefore, the value that 75% of the data lies below is:
79 + 2.5 = 81.5
So, 75% of the data lies below 81.5.
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Answer:
The lower quatile (Q1), and it is 79
Step-by-step explanation:
If you were to pick 84 that would be 100%
See image. If you can show work please do so otherwise thank u in advanced
From the figures, AB is a tangent to the C because they make a right angles (90⁰)
What is a tangent to a circle?Recall that in n Euclidean plane geometry, a tangent line to a circle is a line that touches the circle at exactly one point, never entering the circle's interior. Tangent lines to circles form the subject of several theorems, and play an important role in many geometrical constructions and proofs.
We shall be determining the angle at C to see if it gives 90⁰
Using trigonometrical ratios of tangent
TanB = Opposite/Adjacent
Tan B. = 4.8/7.2
Tan B = 0.6667
B = Tan⁻¹0.6667
<B = 33.69⁰
Also in the same manner,
TanS = opp/Adj
Tan S = 7.2/4.8
Tan S = 1.5
S = Tan⁺¹1.5
< S = 56.31⁰
Npw <S + <B = 56.32 + 33.69 = 89.9999247 = 90⁰
Therefore AB makes tangent at C
20.
Tan C = Opp/Adj
Tan C = 15/11.2
Tan C = 1.3393
C = Tan⁺¹1.3393
< C = 53.25
Also, Tan B = 11.2/15
Tan B = 0.7467
B = 36.75
<B + <C = 36.75 + 53.25 = 89.9986 = 90⁰
Therefore AB makes a tangent at C
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AB and CD are parallel lines. AD and BC meet at X. 3 (a) Show that triangles ABX and DCX are similar. 3 (b) Work out the length of XD.
A. We can see here that triangles ABX and DCX are similar because using the Angle-Angle Similarity:
∠BXA = ∠DXC (Vertically opposite angles)∠ABX = ∠DCX (Alternate angles)∠XAB = ∠XDC (Alternate angles)B. Length XD = 12.5cm.
What are similar triangles?Similar triangles are triangles that have the same shape but not necessarily the same size. In other words, corresponding angles of similar triangles are equal, and corresponding sides are in proportion.
More formally, two triangles ABC and DEF are similar if and only if:
The three corresponding angles are equal: ∠A = ∠D, ∠B = ∠E, ∠C = ∠F.The corresponding sides are in proportion: AB/DE = BC/EF = AC/DF.The length of XD:
CD/AB = XD/AX
10/4 = XD/5
XD = 50/4 = 12.5cm.
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Which proportion is equivalent to 15/60 = 8/32?
Answer:
To determine which proportion is equivalent to 15/60 = 8/32, we can simplify both fractions to their lowest terms and compare them:
15/60 = 1/4 (by dividing both numerator and denominator by 15)
8/32 = 1/4 (by dividing both numerator and denominator by 8)
We can see that both simplified fractions are equal to 1/4. Therefore, the proportion that is equivalent to 15/60 = 8/32 is:
15/60 = 8/32 = 1/4
Answer:
480
Step-by-step explanation:
To find which proportion is equivalent to 15/60 = 8/32, we can cross-multiply and simplify:
15/60 = 8/32
(15)(32) = (60)(8)
480 = 480
Therefore, the two proportions are equivalent.
I hope this helps! Let me know if you have any other questions.
Find the difference in the place value of the two seven in the number 872574
The difference in the place value of the two seven in the number 872574 is 69,930.
In the given value we have to find the place value of two 7. To find the place value of the two seven we need to find the occurrence of seven in the value.
In the given value of 8,72,574,
the first 7 occur at ten thousand place
Its place value = 7 × 10000 = 70000
The second 7 occurs at ten’s place
Its place value = 7 × 10 = 70
The difference between the two place values of 7
= 70000 - 70
= 69930
Therefore, the difference in the place value of two 7 is 69,930
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how many ways are there to seat n couples around a circular table so that no couple sits together? (note: rotated seatings are considered to be the same, but reflected seatings are considered to be different.)
Each couple can sit in two different seats (either clockwise or counterclockwise from their partner), and we multiply by (n-1)! to account for the number of ways to arrange the couples around the table.
Let's consider the number of ways to seat n couples around a circular table without any restrictions first.
Since there are 2 people in each couple, there are a total of 2n people. The number of ways to seat 2n people around a circular table is (2n-1)!/2n,
where we divide by 2n to account for rotations of the same seating arrangement.
Now, let's consider the restriction that no couple can sit together.
We can start by fixing one person in a couple, and then there are (2n-2) ways to seat the other person in that couple so that they don't sit together.
After that, we can fix another person and their partner, and there are (2n-4) ways to seat the remaining two people in their couple so that they don't sit together.
We can continue this process until all couples are seated.
Therefore, the total number of ways to seat n couples around a circular table so that no couple sits together is:
[tex](2n-2)(2n-4)(2n-6)...2 = 2^{n-1} * (n-1)![/tex]
We multiply by[tex]2^{n-1}[/tex] to account for the fact that each couple can sit in two different seats (either clockwise or counterclockwise from their partner), and we multiply by (n-1)! to account for the number of ways to arrange the couples around the table.
Note that reflected seatings are considered to be different, so we don't need to worry about dividing by 2 as we did in the unrestricted case.
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The point-slope form ofthe equation of the line that passes through ( 4, -3) and (12, 1) is y - 1 = 4(x - 12). What
the standard form of the equation for this line?
O x- 4y = 8
О x-4y = 2
О 4x-y=8
• 4x-y = 2
Answer:
4x - y = 2,
Step-by-step explanation:
The point-slope form of the equation of a line is y - y1 = m(x - x1), where (x1, y1) is a point on the line and m is the slope of the line. In this case, we are given that the line passes through the points (4, -3) and (12, 1). The slope of the line is then m = (1 - (-3)) / (12 - 4) = 1/4.
Substituting the slope and the point (4, -3) into the point-slope form of the equation, we get y - (-3) = 1/4(x - 4). Simplifying, we get y + 3 = 1/4x - 1.
To convert the equation to standard form, we multiply both sides of the equation by 4. This gives 4y + 12 = x - 4. Simplifying, we get 4x - y = 8.
Therefore, the standard form of the equation of the line is 4x - y = 8.
PLS HELP SOLVE W STEPS!!!! THANK YOU
Answer:
see what you got to do is you have to find n
Please help me!
see attached item for more info
Answer:
csc θ + cot θ
Step-by-step explanation:
(z + y)/x = z/x + y/x
sin θ = x/z
csc θ = 1/sin θ
csc θ = z/x
tan θ = x/y
cot θ = 1/tan θ
cot θ = y/x
z/x + y/x = csc θ + cot θ
What is the surface area of this right rectangular prism?
Enter your answer as a mixed number in simplest form by filling in the boxes.
Answer:
[tex]2((1 \frac{1}{3} )(1 \frac{1}{2} ) + (1 \frac{1}{2} )(5) + (1 \frac{1}{3}) (5))[/tex]
[tex]2(( \frac{4}{3} )( \frac{3}{2} ) + ( \frac{3}{2} )(5) + ( \frac{4}{3} )(5))[/tex]
[tex]2(2 + \frac{15}{2} + \frac{20}{3} )[/tex]
[tex]2( \frac{12 + 45 + 40}{6} )[/tex]
[tex] \frac{97}{3} = 32 \frac{1}{3} [/tex]
The surface area of this rectangular prism is 32 1/3 square feet.
AD BE
DC EC
Given:
Prove: AB || DE
A
MN
2
E
3 C
B
Complete the steps of the proof.
1.
2
3.
4.
DC
Statements
BE
EC
+1= 8+1
-DC =BE+EC
BE+EC
EC
=
AD + DC
DC
5. AC=AD+DC;
BC=BE+EC
6. ACB
EC
7.23 23
8. AABC-ADEC
9.21 22
1. given
2. addition property
3. property of proportion
4. addition of fractions
5. segment addition
postulate
Reasons
6. substitution property
7. reflexive property
8.
9.+
The two statements that completes the above proof are:
ΔABC ~ ΔDEC - Side - Angle - Side Postulate
∠1≅∠2 - Corresponding angles.
What is the Side - Angle - Side postulate?The Side-Angle-Side (SAS) postulate states that if two sides and the angle between them in one triangle are congruent to two sides and the angle between them in another triangle, then the triangles are congruent.
Corresponding angles are equal because of the congruence of the triangles. Two angles are corresponding if they occupy the same relative position in two distinct intersecting lines, such that they are on the same side of the transversal and are in the same position in relation to the intersection. Corresponding angles are equal if the two intersecting lines are parallel.
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What ordered pair is represented by the function g(4) = 22?
Ordered pair is represented by the function g(4) = 22 is (4,22)
Define ordered pairAn ordered pair is a pair of mathematical elements written in a specific order, typically represented by the notation (a, b). The first element in the pair is called the x-coordinate, while the second element is called the y-coordinate. The order of the elements is important, so (a, b) is not the same as (b, a) unless a = b.
Ordered pairs are commonly used in mathematics to represent points in the Cartesian plane, where the x-coordinate represents the horizontal distance from the origin and the y-coordinate represents the vertical distance from the origin. They can also be used to represent solutions to equations, inputs and outputs of functions, and many other mathematical concepts.
Given Function
g(4)=22
For the value of x=4
The output of function is y=22
So, the ordered pair is (4,22).
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(Repost because urgency)
Not sure how to go about tackling this question?
Should I try to get [tex]y=\frac{x(k+1)}{k-1}[/tex] into the form of the ratio by rationalizing first then simplify?
Answer:
y = [tex]\frac{x(k+1)}{k-1}[/tex]
Step-by-step explanation:
First, recall that in a proportion (a set of equivalent ratios), the product of means is equal to the product of extremes. For example,
if [tex]\frac{a}{b} = \frac{c}{d}[/tex] (or a:b = c:d) the product of means (b and c) is equal to the product of extremes (a and d), and we have ad = cb.
Using this knowledge, in the proportion (y+x):(y-x) = k:1, let us find the product of means and extremes and set them equal, like so:
(y+x):(y-x) = k:1 =
k(y-x) = y+x =
ky - kx = y+x
To solve for y, move all terms including y to one side, like so:
ky - kx = y+x =
ky - y = kx + x
Now, factor out y.
ky - y = kx + x =
y(k - 1) = kx + x
Then, factor out the common term x.
y(k - 1) = kx + x =
y(k - 1) = k(x + 1)
Now, finish isolating the variable by dividing by (k-1), and we have:
y = [tex]\frac{x(k+1)}{(k-1)}[/tex]
consider these functions f(x)=3x^3+8x-2 k(x)=4x what is the value of k(f(x)
The value of function k(f(x)) is 12x³ + 32x - 8.
What is Function composition:Function composition is a way to combine two or more functions to form a new function. In this case, we are given two functions f(x) and k(x), and we need to find the value of k(f(x)), which means we need to apply the function k(x) to the output of the function f(x).
Here we have
Functions f(x)= 3x³ +8x -2 and k(x) = 4x
To find k(f(x)), we need to substitute the expression for f(x) into k(x) wherever we see x. So, we have:
k(f(x)) = 4(f(x)) = 4(3x³ + 8x - 2)
We can simplify this expression by distributing the 4:
k(f(x)) = 12x³ + 32x - 8
Therefore,
The value of function k(f(x)) is 12x³ + 32x - 8.
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Algebraic expression for a number divided by 12
Answer:
hope this helps
Step-by-step explanation:
Let "x" be the number.
The algebraic expression for "a number divided by 12" can be written as:
x/12
Here, "x" is being divided by 12, which means that we are finding the quotient of "x" when it is divided by 12.
Answer:
The answer is *some variable* upon 12 or *some variable* ÷ 12
Examples:
x÷12 or x upon 12
y÷12 or y upon 12
m÷12 or m upon 12
Step-by-step explanation:
You must apply a variable, such as "x,y,m,... etc" to "some number." Your expression then changes to the examples I have given above.
Hope this helped you :)