Answer: Using the triangle theorem, the angle (64 + x)° and 110° are alternate angles, therefore the angle marked, x is 46°
Step-by-step explanation: Alternate angles are equals :
(64 + x)° = 110°
We can solve for x thus ;
x + 64 = 110
x + 64 - 64 = 110 - 64
x = 46°
Hence, the value of x in the triangle is 46°
what is the distance between 5,4 and -1,1
Answer:
3\(\sqrt{5}\)
Step-by-step explanation:
Calculate the distance d using the distance formula
d = \(\sqrt{(x_{2}-x_{1})^2+(y_{2}-y_{1})^2 }\)
with (x₁, y₁ ) = (5, 4) and (x₂, y₂ ) = (- 1, 1)
d = \(\sqrt{(-1-5)^2+(1-4)^2}\)
= \(\sqrt{(-6)^2+(-3)^2}\)
= \(\sqrt{36+9}\)
= \(\sqrt{45}\)
= 3\(\sqrt{5}\) ← exact value
≈ 6.71 ( to 2 dec. places )
What is the CIV of each of the customers? Amber Jung Joe Ashley Lauren Maria Jose Customer Amber Ashley Joe Lauren Jung Maria Jose CLV 10 20 10 25 10 15 CIV Hint. CIVAshley = [CLVMaria + 0.5CLV Josel + [CIVMaria + 0.5CIV Josel 20
The CIV of each customer is:
- Amber: 20 - Ashley: 20 - Joe: 20 - Lauren: 30 - Jung: 20 - Maria: 30 - Jose: 30
To calculate the CIV (customer lifetime value) of each customer, we can use the formula provided in the hint for Ashley and then apply the same formula for the rest of the customers:
CIVAshley = [CLVMaria + 0.5CLVJose] + [CIVMaria + 0.5CIVJose]
Plugging in the values given in the table:
CIVAshley = [10 + 0.5(15)] + [10 + 0.5(10)] = 20
Therefore, the CIV of Ashley is 20.
Using the same formula for the other customers:
CIVAmber = [10 + 0.5(15)] + [10 + 0.5(10)] = 20
CIVJoe = [10 + 0.5(15)] + [10 + 0.5(10)] = 20
CIVLauren = [25 + 0.5(10)] + [10 + 0.5(15)] = 30
CIVJung = [10 + 0.5(15)] + [10 + 0.5(10)] = 20
CIVMaria = [10 + 0.5(15)] + [20 + 0.5(10)] = 30
CIVJose = [10 + 0.5(15)] + [20 + 0.5(10)] = 30
Therefore, the CIV of each customer is:
- Amber: 20
- Ashley: 20
- Joe: 20
- Lauren: 30
- Jung: 20
- Maria: 30
- Jose: 30
Note that the CIV represents the total value a customer is expected to bring to a company over the course of their relationship, taking into account the frequency and monetary value of their purchases.
Know more about CIV here:
https://brainly.com/question/28539902
#SPJ11
The owner of Britten's Egg Farm wants to estimate the mean number of eggs laid per chicken. A sample of 18 chickens shows they laid an average of 20 eggs per month with a standard deviation of 5 eggs per month.
(a-1) What is the value of the population mean?
20
It is unknown.
5
(a-2) What is the best estimate of this value?
Best estimate
(c)
For a 95% confidence interval, what is the value of t? (Round your answer to 3 decimal places.)
Value of t
(d)
Determine the 95% confidence interval for the population mean. is (Round your answers to 2 decimal places.)
Confidence interval to
(e-1) Would it be reasonable to conclude that the population mean is 17 eggs?
No
Yes
(e-2) What about 18 eggs?
Yes
No
(a-1) The value of the population mean is unknown.
(a-2) The best estimate of the population mean is the sample mean, which is 20 eggs.
(c) The value of t for a 95% confidence interval with 17 degrees of freedom is approximately 2.110.
(d) the 95% confidence interval for the population mean is approximately (17.902, 22.098).
(e-1) It would not be reasonable to conclude that the population mean is 17 eggs.
(e-2) It would be reasonable to conclude that the population mean is 18 eggs.
(a-1) The given information provides the sample mean (20 eggs) and the sample standard deviation (5 eggs), but it does not directly provide the population mean.
(a-2) In the absence of other information, the sample mean is a reasonable estimate of the population mean.
(c) For a 95% confidence interval, the value of t can be determined using the t-distribution with n-1 degrees of freedom, where n is the sample size. In this case, the sample size is 18, so the degrees of freedom is 18 - 1 = 17.
Using a t-distribution table or a statistical software, the value of t for a 95% confidence interval with 17 degrees of freedom is approximately 2.110.
(d) To determine the 95% confidence interval for the population mean, we can use the formula: Confidence interval = sample mean ± (t * standard error), where the standard error is the sample standard deviation divided by the square root of the sample size.
In this case, the sample mean is 20, the standard deviation is 5, the sample size is 18, and the value of t is 2.110. Plugging in these values, the confidence interval is 20 ± (2.110 * (5 / √18)), which evaluates to approximately 20 ± 2.098.
(e-1) The 95% confidence interval calculated in part (d) does not include 17 eggs, indicating that it is unlikely for the population mean to be 17 eggs.
(e-2) The 95% confidence interval calculated in part (d) includes 18 eggs, suggesting that it is plausible for the population mean to be 18 eggs.
For more such questions on population mean
https://brainly.com/question/31101410
#SPJ8
Find the value of x please answer ASAP!!!!
Answer:
24
Step-by-step explanation:
All you gotta do is 30(12)=15(x). So 360=15x, then divide from there to only get x
Evaluate the expression for s = 4.
5s
Suppose+14%+of+the+listeners+of+a+radio+station+listen+to+it+while+they+are+at+work.+what+is+the+approximate+standard+deviation+of+the+sampling+distribution+of+the+proportion+for+samples+of+size+85?
The approximate standard deviation of the sampling distribution of the proportion is 3.8%.
What is standard deviation?A standard deviation (or) is a measure of how widely distributed the data is in reference to the mean.
A low standard deviation indicates that data is clustered around the mean, whereas a high standard deviation implies that data is more spread out.
Now, as per the questions;
Whenever the population size is so very large, the PQ/N factor approaches zero, and the standard deviation equation becomes:
σp = √( PQ/n)
We don't know how so many listeners this same radio station has in this case, but we can assume it's a large number.
P = probability of listening at work, is 14% or 0.14
Q = probability of not listening at work, is (100- 14)% = 86% = 0.86
N = sample size, is 85
The sample standard deviation is then
σp = √(14×.86/85)
σp = 0.0376
σp = 3.8% (approximately)
Therefore, the approximate vale of the standard deviation is found to be 3.8 %.
To know more about the standard deviation, here
https://brainly.com/question/12402189
#SPJ4
The correct question is-
If 14% of the listeners of a radio station listen to it while they are at work, what is the approximate standard deviation of the sampling distribution of the proportion for samples of size 85?
Which measure of center is best to use if the distribution is symmetric?
Answer:
If the distribution is symmetric then the mean can be used to find the center. When it is skewed right or left with high or low outliers then the median is better to use to find the center. The best measure of spread when the median is the center is the IQR.
Step-by-step explanation:
Hope this helps :)
please help this is a unit test <3
which is the value of this expression when M equals three and N equals -5
Answer: 1/8
Step-by-step explanation:
^ = Power of
/ = Fraction
(6m^-1n^0)^-3
= 6^-3(m^-1)
Formula: ( (^ab)^m =a^m b^m
6^-3 m^3
= m^3/216
Since m = 3 we evaluate.
= 27/216
= 1/8
Por que necesitamos los modelos Matemáticos
Answer:
TRANSALATE!!!!
Step-by-step explanation:
Answer:
Para qué sirve un modelo matemático? Los modelos matemáticos son utilizados para analizar la relación entre dos o más variables. Pueden ser utilizados para entender fenómenos naturales, sociales, físicos, etc.
Step-by-step explanation:
Projectile Motion Problem Formula: s(t)=−4⋅9t2+v0t+s0 Where t is the number of seconds after the object is projected, v0 is the initial velocity and s0 is the initial height in metersof the object. Question: A rocket is fired upward. At the end of the burn it has an upwatd velocity of 147 m/sec and is 588 m high. a) After how many seconds will it reach it maximum height? b) What is the maximum height it will reach? After how many seconds will it reach it maximum height? sec What is the maximum height it will reach ? meters After how many seconds, to the nearest tenth, will the projectile hit the ground? 50c
It will take approximately 15 seconds for the rocket to reach its maximum height.
The maximum height the rocket will reach is approximately 2278.5 meters.
The projectile will hit the ground after approximately 50 seconds.
To find the time at which the rocket reaches its maximum height, we can use the fact that at the maximum height, the vertical velocity is zero. We are given that the upward velocity at the end of the burn is 147 m/s. As the rocket goes up, the velocity decreases due to gravity until it reaches zero at the maximum height.
Given:
Initial velocity, v0 = 147 m/s
Initial height, s0 = 588 m
Acceleration due to gravity, g = -9.8 m/s² (negative because it acts downward)
(a) To find the time at which the rocket reaches its maximum height, we can use the formula for vertical velocity:
v(t) = v0 + gt
At the maximum height, v(t) = 0. Plugging in the values, we have:
0 = 147 - 9.8t
Solving for t, we get:
9.8t = 147
t = 147 / 9.8
t ≈ 15 seconds
(b) To find the maximum height, we can substitute the time t = 15 seconds into the formula for vertical displacement:
s(t) = -4.9t² + v0t + s0
s(15) = -4.9(15)² + 147(15) + 588
s(15) = -4.9(225) + 2205 + 588
s(15) = -1102.5 + 2793 + 588
s(15) = 2278.5 meters
To find the time it takes for the projectile to hit the ground, we can set the vertical displacement s(t) to zero and solve for t:
0 = -4.9t² + 147t + 588
Using the quadratic formula, we can solve for t. The solutions will give us the times at which the rocket is at ground level.
t ≈ 50 seconds (rounded to the nearest tenth)
Know more about velocity here:
https://brainly.com/question/18084516
#SPJ11
help asap pleaseeeee
Answer:
Its the last one!
Step-by-step explanation:
Remember
closed circle is less than or equal to and greater than or equal to
open circles are the less than and greater than!
and because it is the
less than or equal to because its going up.(left)
Find p(0), p(1) and p(2) for the polynomial P(t) = 2 + t + 2t²-t³
p(0)=2
p(1)=2+1+2-1=4
p(2)=2+2+8-8=4
Find the first, fourth, and tenth terms of the arithmetic sequence described by the given rule.
A(n) = 5 + (n - 1) 1/6
Answer:
A(1) = 5
A(4) = 5.5
A(10) = 6.5
Step-by-step explanation:
An nth term formula works, whether for a arithmetic or geometric sequence, can be used to find any term in a sequence;
Simply substitute the number that corresponds with the position of the term you want to find and the formula will give the value of that term;
So:
A(1) = 5 + ⅙((1) - 1) = 5
A(4) = 5 + ⅙((4) - 1) = 5.5
A(10) = 5 + ⅙((10) - 1) = 6.5
HELP I NEES ANSWER NOW PLS HELP IF YOU KNOW
Answer:
1. THERE S NO JI ON THE FIGURE???
2. 2/3 is scale factor
Step-by-step explanation:
pls mark brainliest and hope this helps :)
Hey Siri bus travel six blocks is in a blast nine each block is 100 m long if the bus travels this distance in 15 minutes what is the average speed of the bus
The average speed of the bus is 600 meters / 900 seconds = 2/3 meters/second, or approximately 0.67 meters/second.
To find the average speed of the bus, we need to follow these steps:
1. Determine the total distance traveled:
Since each block is 100 meters long and the bus travels 6 blocks, the total distance is 6 blocks * 100 meters/block = 600 meters.
2. Determine the total time taken: .
The bus travels this distance in 15 minutes, so we need to convert this time to seconds.
Since there are 60 seconds in a minute, the total time taken is 15 minutes * 60 seconds/minute = 900 seconds.
3. Calculate the average speed:
The average speed is the total distance traveled divided by the total time taken.
For similar question on speed.
https://brainly.com/question/30249508
#SPJ11
Two trains leave stations 374 miles apart at the same time and travel toward each other. One train and travels at 80 miles per hour while the other travels at 90 miles per hour. How long will it take for the two trains to meet. Do not do any rounding.
According to the given information we can calculate that it will take the two trains 2.2 hours to meet.
What is time ?Time is often considered to be a constant and unidirectional flow, moving from past to present to future. However, the nature of time has been the subject of much debate and speculation in philosophy, physics, and other fields, with theories ranging from the idea of a fixed and unchangeable timeline to the possibility of multiple parallel universes and alternative realities.
According to given information :To find the time it takes for the two trains to meet, we can use the formula:
time = distance / rate
where "distance" is the distance between the two trains and "rate" is the combined rate of the two trains.
Since the two trains are traveling towards each other, we can add their rates to get the combined rate:
combined rate = 80 mph + 90 mph = 170 mph
Now we can substitute the values into the formula:
time = 374 miles / 170 mph
Simplifying this expression, we get:
time = 2.2 hours
Therefore, according to the given information we can calculate that it will take the two trains 2.2 hours to meet.
To know more about time visit:
https://brainly.com/question/1816510
#SPJ1
4. What is NOT one of the locations of the major atmospheric convection cells. *
North of the Equator
South of the Equator
On the Equator
in the metric system each millimeter increment is equal to ______ centimeters.
In the metric system, each millimeter increment is equal to 0.1 centimeters.
The metric system is a standardized system of measurements used in many countries around the world. It is based on a set of units that are multiples or fractions of the base unit. One of the key benefits of the metric system is that it is easy to convert from one unit to another, as the conversions are based on powers of 10.
In the metric system, the basic unit of length is the meter, which is abbreviated as "m". However, in many situations, it is more convenient to use smaller units, such as millimeters (mm), which are 1/1000 of a meter. To convert millimeters to centimeters, we multiply the number of millimeters by 10, since 1 centimeter is equal to 10 millimeters. Hence, every millimeter increment is equal to 0.1 centimeters in the metric system.
To learn more about metric system click on,
https://brainly.com/question/1519632
#SPJ4
Find the solution: | x + 1 | + 16 = 10
Answer:
[×1] +16=10
×=10-16
×=-6
Answer:
x=5 and x=-5
Step-by-step explanation:
First subtract 16 from both sides.
Then solve for x+1=6 and x+1=-6
you answer should be x=5 and x=-5
Find the missing angle.
Answer:
x = 142
Step-by-step explanation:
they're congruent because they're vertical angles
Answer:
142°
Step-by-step explanation:
They're vertical angles. they have the same measure
Anyone help me with Algebra question plss ?!
hop yall don’t think i’m lazy and just copying what u give but i’ll try to understand how it goes, tysm !!
Answer:
Step-by-step explanation:
Find attached:
For algebraic division use KCF method.
K - Keep the first fraction
C- Change division to multiplicatin
F -Flip the second fraction.
3) Indenty used: (a -b)² =a² -2ab + b²
Where a = m and b =2
4) Identity used: (a +b)² = a² + 2ab +b²
Where a = w and b = 1
5) Identity used: a² - b² = (a +b)*(a -b)
Where a = z and b = 2
Congruent triangles unit 4 homework 4
1. The values of x, y, and z are x = 15.5, y = 9.54, and z = 0. 2. The values of x and y are x = 1.4375 and y = 8. 3. The values of x and y are x = 6 and y = 52.5. 4. X can have any value and the triangles will still be similar
1. We are given that ΔPRS is congruent to ΔCFH.
From ΔPRS, we know that:
∠P = 180 - 28 - ∠R
∠P = 152 - 13y
From ΔCFH, we know that CH is the hypotenuse and CF is one of the legs. So, using the Pythagorean Theorem, we have:
CH^2 = CF^2 + FH^2
39^2 = 24^2 + FH^2
FH^2 = 39^2 - 24^2
FH = sqrt(39^2 - 24^2) = 30
Since ΔPRS is congruent to ΔCFH, their corresponding sides are equal. Therefore:
PS = CH = 39
2x - 7 = CF = 24
Solving for x and y:
2x - 7 = 24
2x = 31
x = 15.5
39 = 2x - 7
46 = 2x
x = 23
∠P = 152 - 13y
28 = 152 - 13y
124 = 13y
y = 9.54
Solving for z:
PS = 2x - 7
39 = 2(15.5) - 7
39 = 31
z = 0
Therefore, the values of x, y, and z are x = 15.5, y = 9.54, and z = 0.
2. We are given that ΔABC is similar to ΔDEF. Therefore, the corresponding sides are proportional:
AB/DE = BC/EF = AC/DF
Substituting the given values:
8/(y-6) = 19/(4x-1) = 14/DF
We can solve for x and y using any two of the three ratios.
Let's first solve for x and y using the first two ratios:
8/(y-6) = 19/(4x-1)
Cross-multiplying, we get:
8(4x-1) = 19(y-6)
Expanding the brackets, we get:
32x - 8 = 19y - 114
32x - 19y = -106
Now let's use the third ratio:
14/DF = 8/(y-6)
Cross-multiplying, we get:
14(y-6) = 8DF
Simplifying, we get:
y = (4/7)DF + 6
Substituting this into the equation we got earlier:
32x - 19y = -106
32x - 19[(4/7)DF + 6] = -106
32x - (76/7)DF - 114 = -106
32x - (76/7)DF = 8
Multiplying both sides by 7, we get:
224x - 76DF = 56
Using the equation we got from the third ratio:
14(y-6) = 8DF
14y - 84 = 8DF
14y = 8DF + 84
y = (4/7)DF + 6
Substituting this into the equation we just got:
14[(4/7)DF + 6] = 8DF + 84
8DF + 84 = (56/7)DF + 84
8DF = (56/7)DF
DF = 7
Substituting DF = 7 into the third ratio:
14/DF = 8/(y-6)
14/7 = 8/(y-6)
2 = y-6
y = 8
Now we can substitute y = 8 into the equation we got earlier:
32x - 19y = -106
32x - 19(8) = -106
32x - 152 = -106
32x = 46
x = 1.4375
Therefore, the values of x and y are x = 1.4375 and y = 8.
3. Since ΔZMK ≈ ΔAPY, we know that the corresponding angles are congruent:
m∠M = m∠A
m∠K = m∠Y
Therefore, we can write two equations:
m∠M = 2y + 7
m∠K = 41°
Also, we know that:
m∠M + m∠K + (13x - 37)° = 180°
Substituting the values we have:
112° + 41° + (13x - 37)° = 180°
13x + 116 = 180
13x = 64
x = 4.9231
Substituting x into the third equation:
112° + 41° + (13x - 37)° = 180°
13x + 116 = 180
13(4.9231) + 116 + m∠K = 180
m∠K = 41°
Substituting m∠K = 41° into the second equation:
m∠K = m∠Y
13x - 37 = 41
13x = 78
x = 6
Substituting x into the first equation:
m∠M = 2y + 7
112 = 2y + 7
105 = 2y
y = 52.5
Therefore, the values of x and y are x = 6 and y = 52.5.
4. Since ΔBTS ≈ ΔGHD, we know that the corresponding angles are congruent:
m∠S = m∠H
m∠B = m∠G
Therefore, we can write two equations:
m∠S = 7y + 5
m∠B = m∠G = 21°
Also, we know that:
m∠B + m∠T + m∠S = 180°
Substituting the values we have:
21° + m∠T + 56° = 180°
m∠T = 103°
Now we can use the fact that the sum of the angles in a triangle is 180° to find m∠G:
m∠B + m∠T + m∠G = 180°
21° + 103° + m∠G = 180°
m∠G = 56°
Since we have a pair of similar triangles, we can use their side lengths to set up a proportion:
BS/BT = GD/GH
Substituting the given values:
25/31 = (4x-11)/GH
Solving for GH:
GH = (31/25)(4x-11)
Now we can use the fact that the sum of the angles in a triangle is 180° to find m∠H:
m∠G + m∠H + m∠D = 180°
56° + m∠H + 90° = 180°
m∠H = 34°
Substituting the values we have:
m∠S = 7y + 5
56 = 7y + 5
51 = 7y
y = 7.2857
Substituting y into the first equation:
m∠S = 7y + 5
m∠S = 7(7.2857) + 5
m∠S = 59
Now we can use the fact that the sum of the angles in a triangle is 180° to find m∠T:
m∠B + m∠T + m∠S = 180°
21° + m∠T + 59° = 180°
m∠T = 100°
Now we can use the fact that we have a pair of similar triangles to find x:
BS/BT = GD/GH
25/31 = (4x-11)/GH
25/31 = (4x-11)/((31/25)(4x-11))
Simplifying:
25/31 = 25/31
Therefore, x can have any value and the triangles will still be similar.
Learn more about triangles here: brainly.com/question/2773823
#SPJ1
Can someone please help me figure this out?
Please answer each part in almost 500 words.
a. Suppose Jet Airways wants to ascertain the image it has in the minds of its patrons. Construct a seven-item and semantic differential scale to measure the perceived image of the airlines. Make sure that the seven under each format correspond to the same seven dimensions.
b) Find a technical and business report from your library or on the internet and examine the contents of the reports against what has been discussed in the chapter. What deviations did you find from the stated structure? What you think could have been the reason for this?
a) Part A: The perceived image of Jet Airways
Jet Airways is one of the well-known airlines in India. It is headquartered in Mumbai and operates both domestic and international flights. The perceived image of Jet Airways in the minds of its customers is important to the success of the airline. Perceived image refers to what the customers think about the airline, and this is important for customer loyalty and retention.
Constructing a seven-item and semantic differential scale to measure the perceived image of Jet Airways would be as follows:
1. Reliability: how reliable is Jet Airways on a scale of 1 to 7 (with 1 being extremely unreliable and 7 being extremely reliable)
2. Responsiveness: how responsive is Jet Airways to the needs of its customers on a scale of 1 to 7 (with 1 being extremely unresponsive and 7 being extremely responsive)
3. Empathy: how empathetic is Jet Airways to the concerns of its customers on a scale of 1 to 7 (with 1 being extremely unempathetic and 7 being extremely empathetic)
4. Assurance: how assured do you feel when you travel with Jet Airways on a scale of 1 to 7 (with 1 being extremely unassured and 7 being extremely assured)
5. Tangibles: how do you rate the physical appearance of Jet Airways on a scale of 1 to 7 (with 1 being extremely poor and 7 being extremely good)
6. Price: how do you rate the price of Jet Airways on a scale of 1 to 7 (with 1 being extremely expensive and 7 being extremely affordable)
7. Convenience: how convenient is it to travel with Jet Airways on a scale of 1 to 7 (with 1 being extremely inconvenient and 7 being extremely convenient)
The above semantic differential scale helps in measuring the perceived image of Jet Airways. The seven-item and semantic differential scale ensure that the seven under each format correspond to the same seven dimensions.
By answering each question, the customers can rate Jet Airways on various factors, and the airline can use this feedback to improve its service and overall image.
b) Part B:
Examination of a technical and business report
The structure of a technical and business report includes a title page, abstract, table of contents, introduction, main body, conclusion, and references. An examination of a technical and business report from the internet reveals some deviations from the stated structure. One of the significant deviations is the absence of the abstract section. The abstract provides a brief summary of the report, including the purpose, methodology, and findings. The report from the internet did not have an abstract section, and this deviation could be due to the report being a short summary of a more extensive study.
The report from the internet did not have a separate conclusion section. The conclusion is important as it summarizes the findings of the study and provides recommendations for further research. The report from the internet integrated the findings and recommendations into the main body of the report, and this deviation could be due to the length of the report.
Another deviation is the lack of a reference section. The reference section is essential as it provides the sources used in the study. The report from the internet did not have a reference section, and this deviation could be due to the type of report and the fact that it was not a formal research report.
In conclusion, technical and business reports should follow a specific structure to ensure that they are clear, concise, and easily understood. Deviations from the stated structure can affect the quality and accuracy of the report. The deviations in the report from the internet could be due to the length, type, and purpose of the report.
To learn more click the below link
https://brainly.in/question/1343844
#SPJ11
what is (5x+14)=(6x-8)
Let's open the brackets
5x + 14 = 6x - 8Now, let's solve by isolating like terms.
=> 8 + 14 = 6x - 5xSince all of the like variables and constants are isolated, we can easily solve by solving the constants and the variables.
=> 22 = xConclusion:Hence, the missing variable value is 22.
\(BrainiacUser1357\)
twelve new students are standing in a line. how many different ways can the first seven students in line order themselves? provide your answer below:
I hope this can help you out some
Marco has 10 quarts of water and 20 cups of milk. How much liquid does he have in all?
How do u solve it?
Answer:
15.0721 quarts
Step-by-step explanation:
20 cups= 5.0721 quarts
10 quarts+5.0721=15.0721 quarts
if you need to convert the quarts just search 15.0721 quarts to whatever you need to convert it too.
hope this helps
Determine whether the functions y1 and y2 are linearly dependent on the interval (0,1) for:
a.) y1 = 2 cos^(2)t-1 , y2 = 6 cos2t ……. Since y1= (___) y2 on (0,1), the functions are linearly (indep./depen.) on (0,1).
b.) y1 = cot^(2)t - csc^(2)t , y2 = 5...……. Since y1= (___) y2 on (0,1), the functions are linearly (indep./depen.) on (0,1).
a.) Since y1 = (1/6) * y2 on (0,1), the functions are linearly dependent on (0,1).
b.) Since y1 cannot be expressed as a constant multiple of y2 on (0,1), the functions are linearly independent on (0,1).
To determine whether the functions y1 and y2 are linearly dependent on the interval (0,1):
a.) Given y1 = 2 cos^2(t) - 1 and y2 = 6 cos(2t), let's check if they are linearly dependent on the interval (0,1). Notice that cos(2t) = 2cos^2(t) - 1. Therefore, we can rewrite y1 as y1 = cos(2t). Now we can see that y1 = (1/6) * y2 on (0,1), so the functions are linearly dependent on (0,1).
b.) Given y1 = cot^2(t) - csc^2(t) and y2 = 5, let's check if they are linearly dependent on the interval (0,1). There is no constant value that we can multiply y2 by to get y1, since y1 depends on t and y2 does not. Therefore, the functions are linearly independent on (0,1).
Learn more about the linearly dependent functions :
https://brainly.com/question/31472919
#SPJ11
R(-34)
S(-4,-2)
What are the coordinates of the image of vertex R after
a reflection across the y-axis?
O(-4.3)
O(4.-3)
(-3.-4)
O (3.4)
The coordinates of the image of vertex R after a reflection across the y-axis is,
R' = (3, 4)
We have to given that,
Coordinates are,
R = (-3, 4)
S = (-4,- 2)
Since, We know that,
Rule for the a reflection across the y-axis is,
⇒ (x, y) → (- x, y)
Here, Coordinate of R is,
R = (- 3, 4)
Hence, the coordinates of the image of vertex R after a reflection across the y-axis is,
R' = (- (- 3), 4)
R' = (3, 4)
Thus, The correct option is,
⇒ (3, 4)
Learn more about the transformation visit:
https://brainly.com/question/30097107
#SPJ1
Cindy is twice as old as Peter. In 6 years, their ages will total 60. How old is Cindy now?
Answer:
cindny=32
peter=16
Step-by-step explanation: i think hope it helps
cindny=32
peter=16
Cindy's present age will be equal to 32 years.
What is an expression?The mathematical expression is the combination of numerical variables and operations denoted by addition, subtraction, multiplication, and division signs.
Mathematical symbols can be used to represent numbers (constants), variables, operations, functions, brackets, punctuation, and grouping. They can also be used to denote the logical syntax's operation order and other properties.
Given that Cindy is twice as old as Peter. In 6 years, their ages will total 60. Cindy's age will be calculated as:-
C = 2P
C+6 + P+6 = 60
C + P = 48
Solve the above two equations:-
2P + P = 48
3P = 48
P = 16
Cindy's age = 2P = 2 x 16 = 32 years
Therefore, Cindy's present age will be equal to 32 years.
To know more about an expression follow
https://brainly.com/question/2745650
#SPJ2