The resultant of the vectors a = 3i - 2j and b = pi - 2pj is parallel to the vector c = 2i - 3j.
a) Find the value of p
b) Find the resultant of vectors a and b.
Please help me with this question, thank you
Answers
Part (a)
The resultant vector is the vector formed by adding the two vectors a and b. So we effectively add the corresponding components.
You can use the parallelogram law as a visual alternative.
Adding a and b leads to
a+b = (3i-2j) + (pi-2pj)
a+b = (3i+pi) + (-2j-2pj)
a+b = (3+p)i - (2+2p)j
Define vector d to be d = a+b so we can use it later below.
Recall that parallel vectors point in the same direction. This means the ratio of their components or coordinates are equal.
We can say the following
(x coord of d)/(x coord of c) = (y coord of d)/(y coord of c)
(3+p)/(2) = (-(2+2p))/(-3)
Let's solve for p
(3+p)/(2) = (-(2+2p))/(-3)
(3+p)/(2) = (2+2p)/3
3(3+p) = 2(2+2p) .... cross multiply
9+3p = 4+4p
4p+4 = 3p+9
4p-3p = 9-4
p = 5
Answer: p = 5========================================================
Part (b)
Since p = 5, from part (a), we can determine vector b
b = pi - 2pj
b = 5i - 2*5j
b = 5i - 10j
Then add vectors a and b to get
a+b = (3i-2j) + (5i - 10j)
a+b = (3i+5i) + (-2j - 10j)
a+b = (3+5)i - (2+10)j
a+b = 8i - 12j
Or we can say
a+b = (3+p)i - (2+2p)j .... from part (a)
a+b = (3+5)i - (2+2*5)j ... plugging in p = 5
a+b = 8i - 12j
Note the ratio of the components of vector d and vector c are such
(x coord of d)/(x coord of c) = (y coord of d)/(y coord of c)
8/2 = -12/(-3)
4 = 4
This helps confirm the answer
You could also graph the vectors c = 2i - 3j and d = 8i - 12j to note the two lines produce the same slope -3/2. We can see that -12/8 = -3/2. Lines of the same slope are parallel lines
Answer: 8i - 12ja.
The value of p is 5
Since vector a = 3i - 2j and vector b = pi - 2pj, the resultant of vectors a and b is R = a + b
= 3i - 2j + pi - 2pj
= (3 + p)i - 2(1 + p)j
Since R is aparallel to vector c = 2i - 3j, it implies that the cross product of R and c is zero.
The cross product of two vectors a and b is a × b = absinФ where a and b are the magnitudes of a and b and Ф is the angle between them.
So, R × c = [(3 + p)i - 2(1 + p)j] × [2i - 3j]
= (3 + p)i × 2i + (3 + p)i × (-3j) + (-2(1 + p)]j × 2i + (-2(1 + p)]j×(-3j)
= 0 - 3(3 + p)k - 4(1 + p)(-k) + 0
= -3(3 + p)k + 4(1 + p)k
= [-3(3 + p) + 4(1 + p)]k
= [-9 - 3p + 4 + 4p)]k
= [-9 + 4 - 3p + 4p)]k
= [-5 + p]k
[-5 + p]k = RcsinФ.
Since R and c are parallel, Ф = 0°
So, Rcsin0° = Rc × 0 = 0
So, [-5 + p]k = 0
-5 + p = 0
p = 5
The value of p is 5
b.
The resultant of vectors a and b is R = 8i - 12j
Since p = 5 and the resultant of vectors a and b is R = (3 + p)i - 2(1 + p)j
Substituting the value of p = 5 into r, we have
R = (3 + p)i - 2(1 + p)j
R = (3 + 5)i - 2(1 + 5)j
R = 8i - 2(6)j
R = 8i - 12j
So, the resultant of vectors a and b is R = 8i - 12j
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Related Questions
can someone help my lil sister.
Answers
Answer:
78
Step-by-step explanation:
Given:
h + 9g
Required:
Evaluate when g = 8 and h = 6
Solution:
Plug in the values of the variables into the expression
Thus,
6 + 9(8)
= 6 + 72
= 78
Chord AC intersects chord BD at point P in circle Z.
AP=12 m
DP=5 m
PC=6 m
What is BP?
Enter your answer as a decimal in the box.
_______ m
Answers
The length of BP is 14.4 meters.
To find the length of BP, we can use the property that states that when two chords intersect inside a circle, the product of the segment lengths on one chord is equal to the product of the segment lengths on the other chord.
Using this property, we can set up the equation:
AP * PC = BP * DP
Substituting the given values:
12 m * 6 m = BP * 5 m
Simplifying:
72 m^2 = BP * 5 m
To solve for BP, divide both sides of the equation by 5 m:
72 m^2 / 5 m = BP
Simplifying:
14.4 m = BP
Therefore, the length of BP is 14.4 meters.
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Find the difference!
Answers
Answer:
2x + 10
_______
x^3 - 4x
Step-by-step explanation:
this is the answer
Write a variable expression for each statement
9. six decreased by a number 12
10. the quotient of a number and
11. the product of five and a number increased by two
12. seven less than a number
13. four times the sum of ten and a number
14. twenty less a number
15. the difference of 10 and a number
16. the quotient of 14 and a number
17. a number increased by 17
18. half of 14
19. a number increased by 6
20. the product of x and 7
Answers
Answer:
Step-by-step explanation:
I'm not doing all of them, so you can learn.
Here's the first three:
9. 6-12x
10. (and 11? dude u need to rephrase) x/(5(x+2))
Zeke and six of his friends are going to a baseball game. Their combined money totals $28.50. At the game, hot dogs cost $1.25 each, hamburgers cost $2.50 each, and sodas cost $0.50 each. Each person buys one soda. They spend all $28.50 on food and soda. Determine how many different combinations, including those combinations containing zero, of hot dogs and hamburgers Zeke and his friends can buy, spending all $28.50. ENTER
Answers
1.25x + 2.5y + 0.5z ≤ 28.5
is your inequality
Find the area of the rectangle to the right. 9 inches for width and 5y inches for the length
Answers
Answer:
The area is 45 inches
Step-by-step explanation:
L×W=A
Write an equation for the nth term of the arithmetic sequence. Then find 230 -
-9, -6, -3,0, ...
=
a30
Helpquick
Answers
Answer:
hope it helps you ✨✨✨✨✨✨
I will give brainliest who ever answer this question:) Thank you!
Answers
Answer:
2(x-4)+2(2x+5)
Step-by-step explanation:
The perimeter of a rectangle is 2(length)+2(width). Thus, the side values can be simply plugged into this equation.
Answer:
P = 2(2x+5) + 2(x-4)
Step-by-step explanation:
Perimeter is found by adding all sides
(2x+5) + (2x+5) + (x-4) + (x-4)
Notice there are two sets of sides.
If it is 11:45 a.m., what will the time be 3 hours and 15 minutes later?
4:15 p.m.
3:00 p.m.
3:15 a.m.
2:45 p.m.
Answers
Answer:
3:00 p.m.
Step-by-step explanation:
because 11:45 + 15 is 12:00 + 3 is 15:00 so it is 3:00 p.m.
How do you convert cu ft to cu yd?
Answers
To convert volume cubic feet (cu ft) to cubic yards (cu yd), you need to use the conversion factor of 1 cubic yard = 27 cubic feet.
So, to convert a given volume from cubic feet to cubic yards, you can divide the volume in cubic feet by 27. The formula for the conversion is:
Volume in cubic yards = Volume in cubic feet / 27
For example, let's say we have a volume of 54 cubic feet that we want to convert to cubic yards. Using the formula, we have:
54 cu ft / 27 = 2 cu yd
So 54 cubic feet is equal to 2 cubic yards.
Similarly, if we have a volume of 135 cubic feet, we can convert it to cubic yards as follows:
135 cu ft / 27 = 5 cu yd
Therefore, 135 cubic feet is equal to 5 cubic yards.
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What is the product of the complex numbers below? (4 - 21)(1 + 7) O A. 18 - 307 - OB B. -10 - 301 O C. -10 + 261 + O + D. 18 + 261
Answers
Given:
\((4-2i)(1+7i)\)To find: The product of two complex numbers:
Explanation:
On expansion we get,
\((4-2i)(1+7i)=4+28i-2i-14(i^2)\)As we know,
\(i^2=-1\)So, we w
pls help me with this
Answers
Answer:
x-intercept coordinates: (9, 0)
y-intercept coordinates: (0, 21)
Step-by-step explanation:
Put the equation in slope-intercept form, y = mx + b
3y = -7x + 63 divide both sides by 3
y = -7/3x + 21
y-intercept = b = 21
y-intercept coordinates: (0, 21)
Find x intercept by setting y = 0 and solving for x:
0 = -7/3x + 21
7/3x = 21
x = 21(3/7) = 9
x-intercept coordinates: (9, 0)
A car is traveling at a steady speed. It travels 2 1/2 miles in 3 1/3 minutes. How far will it travel in 41 minutes? In 1 hour
Answers
Answer:
120 miles
Step-by-step explanation:
You multiply 41 times 4 equal 120 miles.
Answer:
30 3/4 miles, 45 miles
Step-by-step explanation:
First we find the unit rate, in miles per minute:
2 1/2 miles 5/2 mi 1/2 mi 1 mi
--------------------- = --------------- = ------------- = -------------- = 3/4 mile/min
3 1/3 minutes 10/3 min 2/3 min 4/3 min
In 41 minutes the car will travel (3/4 mi/min)(41 min) = 123/4 mi = 30 3/4 mi
In 1 hour, or 60 minutes, the car will travel (3/4)(60) mi = 45 mi
Use a t-distribution to find a confidence interval for the difference in means ud = M1 – U2 using the relevant sample results from paired data. Assume the results come from random samples from populations that are approximately normally distributed, and that differences are computed using d = x1 – x2. = A 95% confidence interval for Hd using the paired difference sample results id 3.2, sd = 1.9, nd = 30. Give the best estimate for Hd, the margin of error, and the confidence interval. Enter the exact answer for the best estimate, and round your answers for the margin of error and the confidence interval to two decimal places. Best estimate = i 3.2 Margin of error = i The 95% confidence interval is i to i
Answers
The best estimate for Hd is 3.2, the margin of error is 0.71, and the confidence interval is (2.49, 3.91).
To find a confidence interval for the difference in means (ud = M1 – M2) using paired data, we can use the t-distribution.
Given the following sample results:
d = 3.2 (sample mean of the differences)
sd = 1.9 (sample standard deviation of the differences)
nd = 30 (sample size)
To calculate the confidence interval, we need to determine the critical value from the t-distribution based on the desired confidence level. For a 95% confidence level with 29 degrees of freedom (nd - 1), the critical value is approximately 2.045.
The best estimate for Hd is the sample mean of the differences, d, which is 3.2.
The margin of error is calculated as the critical value multiplied by the standard error, where the standard error is given by:
SE = sd / √nd
SE = 1.9 / √30 ≈ 0.346
The margin of error is then:
Margin of Error = critical value * standard error
Margin of Error ≈ 2.045 * 0.346 ≈ 0.707
Finally, the confidence interval is constructed by subtracting and adding the margin of error from the best estimate:
Confidence Interval = d ± Margin of Error
Confidence Interval = 3.2 ± 0.707
Rounded to two decimal places, the confidence interval is approximately (2.49, 3.91).
Therefore, the best estimate for Hd is 3.2, the margin of error is 0.71, and the confidence interval is (2.49, 3.91).
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Homework: Section 11.1 Question 7. Complete the square to find the x-intercepts of the function given by the equation listed. f(x)=x² +34x+104 What are the x-intercepts? **** (Simplify your answer. T
Answers
Answer:
x² + 34x + 104 = 0
x² + 34x = -104
x² + 34x + ((1/2)(34))² = -104 + ((1/2)(34))²
x² + 34x + 17² = -104 + 17²
x² + 34x + 289 = 185
(x + 17)² = 185
x + 17 = +√185
x = -17 + √185
Look at this quadrilateral ABCD, which is not drawn accuratrly. Choose a name for the quadrilateral when the values of the interior angles are as shown below (see attachment for questions)
Answers
The solution is, the quadrilateral ABCD is a trapezium.
What is Quadrilateral ?In geometry a quadrilateral is a four-sided polygon, having four edges and four corners. The word is derived from the Latin words quadri, a variant of four, and latus, meaning "side".
here, we have,
from the given figure we get,
the figure has four sides, which are not all equal, and, two of them are parallel to each other.
here we get,
angle A = angle C = 80
angle B = angle D = 100
and, two sides are parallel to each other.
Hence, The solution is, the quadrilateral ABCD is a trapezium.
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Find the volume of the solid obtained by rotating the region bounded by the given curves about the specified axis. y = x^8, y = 1; about y = 3
Answers
Therefore, the volume of the solid of revolution is given by: V = π∫[1,3](y18/8 - 3)2 dy
The given curves are y = x8 and y = 1, and the region to be rotated around the axis of rotation is the region between y = 1 and y = x8, that is, the region bounded by the curves. This region is given by the following figure:
The solid formed is a solid of revolution, and it is given by rotating the region around the line y = 3.
The resulting solid is the portion of the solid that is above the line y = 3.
The distance between y = 1 and y = 3 is 2 units, so the volume of the solid formed by rotating the region about the axis of rotation is given by:
V = π∫[a,b]R2(y)dy
where R(y) is the radius of the disk for a given value of y, which is given by R(y) = x(y) - 3, and x(y) is given by x(y) = y18/8.
Expanding the square, we have:V = π∫[1,3] y183/16 - 6y9/4 + 9 dy
Integrating term by term, we have:
V = π [y218/288 - 6y13/52 + 9y]23 from 1 to 3V
= π [(3)218/288 - 6(3)13/52 + 9(3)] - [(1)218/288 - 6(1)13/52 + 9(1)]23V
= π [2813/288 - 109/13]23
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plss answer it correctly...I need asap
Answers
Answer:
sorry I cannot understand that
A car travels 28 miles south and then 45 miles east around a lake. A boat leaves from the same place and arrives at the same place but travels directly from point A to point B. Calculate how many miles the boat and the car each traveled total. Then calculate who arrived first if the car was traveling at 40miles per hour and the boat traveled at 25 miles per hour.
Answers
Answer:
The car travelled 73 miles
The boat travelled 53 miles
The car arrived 17.7 minutes before the boat
Step-by-step explanation:
The total distance the car travelled from Point A to Point B = 28+45 = 73 miles
The total distance the boat travelled is given by the displacement; Using Pythagorean theorem = 53miles.
Time taken by the car = Distance/Speed = 73/40 = 1.825 hrs or 109.5 minutes
Time taken by the boat = Distance/speed = 53/25 = 2.12 hrs or 127.2 minutes.
The time taken by the car is the shortest, therefore it arrives first before the boat.
(◔‿◔)
(5 points) Write out the first five terms of the sequence (-17 (+6) determine whether the sequence converges, and it so find its limit n=1 Enter the following information for an (6) 01 ag a = as lim (-1)^2 (n+6) (Enter DNE if limit Does Not Exist) Does the sequence converge (Enter yes" or "no")
Answers
Finally, we need to determine if this sequence converges. Since the terms alternate between -1 and 1 and do not approach a specific number, the sequence oscillates and does not converge. Therefore, the answer is "no".
The first five terms of the sequence (-17 (+6) are -17, -11, -5, 1, 7. To determine if the sequence converges, we need to check if it approaches a specific number as n (the term number) gets larger and larger. However, since the sequence is increasing without bounds, it does not converge to a specific number. Therefore, the limit does not exist (DNE).
For the second part of the question, we need to find the value of a for the sequence given by\(a_n = (-1)^{n+2).\) To do this, we can simply plug in n=1 to get\(a_1 = (-1)^{(1+2)} = -1.\)Therefore, a=-1.
Finally, we need to determine if this sequence converges. Since the terms alternate between -1 and 1 and do not approach a specific number, the sequence oscillates and does not converge. Therefore, the answer is "no".
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The numbers 1 through 8 are to be placed in the circles in the diagram shown such that the sum of the numbers on each side of the figure is 15. Find the values of x, y, and z. Then copy the diagram on a piece of paper and fill in each circle with the appropriate number. Be sure to show all your work. Upload the finished problem below.
Note: x satisfies –4(x – 2) = –4,
y satisfies 9 + 2(y – 3) = 3(y – 2) + 1,
and z satisfies z/3 + 1/2 = 5/2.
Answers
Answer:
ff
Step-by-step explanation:
f
Compute the y-intercept if x-bar = 57, y-bar = 251, sx= 12, sy= 37 and r = 0.341. A)244.40 B)191.1 C)1.05
Answers
Answer:
C
Step-by-step explanation:
The y-intercept is approximately 191.1. The correct option is (B).
To compute the y-intercept, we need to use the equation of the regression line, which is:
y = a + bx
where a is the y-intercept, b is the slope, x is the independent variable (in this case, x-bar), and y is the dependent variable (in this case, y-bar).
The formula for the slope of the regression line is:
b = r * (sy/sx)
where r is the correlation coefficient, sx is the standard deviation of x, and sy is the standard deviation of y.
Substituting the given values, we get:
b = 0.341 * (37/12) = 1.05025
Now, we can use the formula for the y-intercept:
a = y-bar - b * x-bar
Substituting the given values, we get:
a = 251 - 1.05025 * 57 = 191.10925
Therefore, the y-intercept is approximately 191.1.
The answer is B) 191.1.
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Tickets for an Amtrak train cost $21 for children and $49 for adults. Josie paid $3,332 for a total of 88 tickets. How many children tickets and how many adult tickets did Josie buy?
Answers
SOLUTION:
Case: System of equation word problem
Required: Find the number of adults and children tickets Josie bought.
First we create a system of equation. One for the total number of tickets, the other for the total cost of tickets.
Assumption: Let the number of adult tickets be a and the number of children tickets c.
Sytems of equations:
\(\begin{gathered} a\text{ + c= 88. (ticket equation)} \\ 49a\text{ + 21c = 3332. (Cost equation)} \end{gathered}\)Solving the system of equation, using substitution method
\(\begin{gathered} \text{Make c the isolated variable from ticket equation} \\ c=\text{ 88-a} \\ \text{Substitutute in Cost equation.} \\ 49a\text{ + 21c = 3332. } \\ 49a\text{ + 21(88-a) = 3332. } \\ 49a\text{ + 1848 - 21a = 3332. } \\ \text{Taking like terms} \\ 49a\text{ - 21a = 3332 - 1848} \\ 28a\text{ = }1484 \\ Divide\text{ both sides by 28} \\ a=53 \end{gathered}\)Next we find the value of c
\(\begin{gathered} We\text{ plug in the value }a\text{ in the isolated variable equation} \\ c=\text{ 88 - a} \\ c=\text{ 88 - 53} \\ c=\text{ 35} \end{gathered}\)Final answers:
The total number of children tickets bought were 35 WHILE
The total number of adult tickets bought were 53.
Graph y = - 2x + 5 will give brainilist if correct
Answers
Answer:
Step-by-step explanation:
That's the graph. The slope is -2 and 5 means where the y intersects.
Help?
g(x)= 1/2x^2+2
Evaluate the function above for g(6)
Answers
g(6)= 1/2(6)^2+2
g(6)= 1/2(36)+2
g(6)= 18+2
g(6)= 20
What does it mean to bisect a segment or an angle? in your own words.
Answers
The economy is in a recession. Real GDP is well below potential GDP. If the government wants to increase real GDP so that it is closer to potential GDP, it could ____. (Select all that apply.) Group of answer choices -increase government spending -decrease government spending -decrease taxes -increase taxes
Answers
To increase real GDP and bring it closer to potential GDP during a recession, the government could increase government spending and/or decrease taxes.
During a recession, when real GDP is below potential GDP, the government can use fiscal policy tools to stimulate economic growth and close the GDP gap. The two options that can be effective in this situation are increasing government spending and decreasing taxes.
Increase government spending: By increasing spending on infrastructure projects, education, healthcare, or other sectors, the government can create demand in the economy, which leads to increased production and employment, ultimately raising real GDP.
Decrease taxes: Reducing taxes can provide individuals and businesses with more disposable income, encouraging consumption and investment. This increased spending and investment can boost aggregate demand, leading to higher production levels and closing the GDP gap.
Decreasing government spending and increasing taxes, on the other hand, would have contractionary effects, potentially exacerbating the recessionary conditions by reducing overall demand in the economy. Therefore, these options are not suitable for increasing real GDP during a recession.
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A nurse provides a back massage as a palliative care measure to a client who is unconscious, grimacing, and restless. Which of the following findings should the nurse identify as indicating a therapeutic response? (Select all that apply.)
A. the shoulders droop
B. the facial muscles relax
C. the RR increases
D. the pulse is within the expected range
E. the client draws his legs into a fetal position
Answers
A nurse provides a back massage as a palliative care measure to a client who is unconscious, grimacing, and restless.
The therapeutic response that the nurse should identify in the client after a back massage includes relaxing of facial muscles and the pulse remaining within the expected range.
Massage is a fundamental nursing measure that is often utilized as part of palliative care for patients. The purpose of back massage is to promote relaxation, improve blood circulation, reduce muscle tension, and alleviate pain, stress, and anxiety. The nursing assessment of the patient before and after the massage is essential to determine its effectiveness as a therapeutic intervention for the patient.
When providing back massage as a palliative care measure to an unconscious, grimacing, and restless client, the nurse should identify several therapeutic responses as follows;
The shoulders droop: The nurse should expect the shoulders of the client to relax during massage therapy. If this occurs, it is a sign that the patient is experiencing relaxation and tension relief.
The facial muscles relax: Relaxation of the facial muscles is a common therapeutic response during back massage. The nurse should observe the patient's face for any signs of relaxation, which may include softening of facial lines, eyelids drooping, or a general expression of peacefulness.
The respiratory rate (RR) decreases: The nurse should expect the client's respiratory rate to decrease during a back massage. This is because relaxation stimulates the parasympathetic nervous system, resulting in decreased respiratory rate, heart rate, and blood pressure.
The pulse is within the expected range: The nurse should expect the client's pulse to remain within the expected range during a back massage. A normal pulse rate is between 60-100 beats per minute for adults. If the pulse remains within this range, it is a sign that the patient is responding positively to the massage therapy.
In conclusion, providing back massage as a palliative care measure to an unconscious, grimacing, and restless client can help to promote relaxation, improve blood circulation, reduce muscle tension, and alleviate pain, stress, and anxiety. The nurse should identify therapeutic responses in the patient during the massage therapy, which may include relaxation of the shoulders, facial muscles, decreased respiratory rate, and pulse remaining within the expected range.
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What is Dangerous on living for 7 days on a can of sardines Questions. . . .
Answers
Answer:
YOU MIGHT FALL OFF
Step-by-step explanation:
that's the answer
-kenma #3
The area values of the circles given in the attachment are :
28.26 cm²50.24 in²314 m²12.56 cm²254.34 ft²4.52 km²7850 in²379.94 m²19.63 cm²200. 96 ft²1256 m²78.5 cm²7.07 m²113.04 in²200. 96ft²38.47 cm²0.28 km²3.14 cm²Area of a circle =
\( {\pi} {r}^{2} \)
Where, r = Radius
\( \frac{\pi {d}^{2} }{4} \)
d = diameter
\(\pi = 3.14\)
1.)
r = 3cm
Area = 3.14 × 3² = 28.26 cm²
2.)
r = 4 in
Area = 3.14 × 4² = 50.24 in²
3.)
r = 10 m
Area = 3.14 × 10² = 314 m²
4.)
r = 2cm
Area = 3.14 × 2² = 12.56 cm²
5.)
r = 9 ft
Area = 3.14 × 9² = 254.34 ft²
6.)
r = 1.2 km
Area = 3.14 × 1.2² = 4.52 km²
7.)
r = 50 in
Area = 3.14 × 50² = 7850 in²
8.)
r = 11 m
Area = 3.14 × 11² = 379.94 m²
9.)
r = 2.5 cm
Area = 3.14 × 2.5² = 19.63 cm²
10.)
d = 16 ft
Area = (3.14 × 16²) ÷ 4 = 200. 96ft²
11.)
d = 40 m
Area = (3.14 × 40²) ÷ 4 = 1256 m²
12.)
d = 10 cm
Area = (3.14 × 10²) ÷ 4 = 78.5 cm²
13.)
d = 3 m
Area = (3.14 × 3²) ÷ 4 = 7.07 m²
14.)
d = 12 in
Area = (3.14 × 12²) ÷ 4 = 113.04 in²
15.)
d = 16 ft
Area = (3.14 × 16²) ÷ 4 = 200. 96ft²
16.)
d = 7cm
Area = (3.14 × 7²) ÷ 4 = 38.47 cm²
17.)
d = 0.6 km
Area = (3.14 × 0.6²) ÷ 4 = 0.28 km²
18.)
d = 2 cm
Area = (3.14 × 2²) ÷ 4 = 3.14 cm²
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Please answer correctly !!!!! Will mark Brianliest !!!!!!!!!!!!!!
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Answer:
the second one