[ 8 11 2 8 ] [ 1 -2 0 5]
[ 0 -7 2 -1] [ 0 7 1 5]
A = [ -3 -7 2 1], B = [ 0 4 4 0]
[ 1 1 2 4] [ 0 0 0 2]
a. use matlab to compute the determinants of the matrices a+b, a-b, ab, a^-1, and b^t. (recall that in matlab, bt is written as b'.)
b. which of the above matrices are not invertible? explain your reasoning.
c. suppose that you didn't know the entries of a and b, but you did know their determinants. which of the above determinants would you still be able to compute from this information, even without having a or b at hand? explain your reasoning.

Without specific details it is difficult to determine who the performance review belongs to as we do not have specific scores for each employee. So, based on the information we can define some data as below.

A graph in x-y axis plot is a visual representation of functions or data points. The dependent or vertical variable represented by y-axis, while the independent or horizontal variable represented by the x-axis.

Without the specific details of the performance review or the names of the employees, I cannot provide an exact answer. However, based on the information given, we can infer the following:

Person 6 : has a perfect score.

Person 3 : not achieved any of their goals.

Person 5 : excellent personality and very good job knowledge.

Person 4: more interested in hanging out at the water cooler.

Given this information, it is difficult to determine who the performance review belongs to as we do not have specific scores for each employee. We also do not have enough information to make an informed judgment about the performance of each employee. It is possible that the review could belong to any of the employees, depending on their individual scores and performance.

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Let X and Y be two matrices in A. We can write X = ((x,0),(0,y)) and Y = ((z,0),(0,w)). If we add X and Y, we get((x+z,0),(0,y+w)). The sum is in A if and only if x+z+y+w=5.

Subset of M2x2:A subset of M2x2 is a set that contains some elements of M2x2.

A subset of M2x2 can be considered as a subspace if it meets the following conditions:

To determine if A is a subspace of M2x2, we need to verify that A meets the following conditions:

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Answer: 240

You multiply them. 6x4x10 :)

The number of different outfits made by Alyssa as per the given number of shirt , skirts and shoes is equal to 240 outfits.

To find the number of possible outfits Alyssa can make, you multiply the number of choices for each item of clothing:

Number of shirts = 6

Number of skirts = 4

Number of pairs of shoes = 10

Substitute the values and multiply with each other

Total number of possible outfits

= 6 (shirts) × 4 (skirts) × 10 (shoes)

= 240 outfits.

Therefore, Alyssa can make 240 different outfits using her 6 shirts, 4 skirts, and 10 pairs of shoes.

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Answer: View answer in explanation below.

Step-by-step explanation: Let's use variables to represent the unknown quantities.

Let x be the number of $5 clearance mystery books purchased.

Let y be the number of $12 regular-priced science fiction books purchased.

We can set up a system of equations based on the given information:

5x + 12y = 126 (total amount spent)

x + y = total number of books purchased

We need to solve for x and y.

Let's use the second equation to solve for one variable in terms of the other:

y = total number of books purchased - x

Now we can substitute this expression for y into the first equation:

5x + 12(total number of books purchased - x) = 126

Simplifying and solving for x:

5x + 12total number of books purchased - 12x = 126

-7x + 12total number of books purchased = 126

-7x = -12total number of books purchased + 126

x = (12total number of books purchased - 126)/7

Since x must be a whole number (you can't buy a fraction of a book), we need to find a value of total number of books purchased that makes x a whole number. We can start by trying different values of total number of books purchased:

If total number of books purchased is 10:

x = (12(10) - 126)/7 = -6/7 (not a whole number)

If total number of books purchased is 11:

x = (12(11) - 126)/7 = 6/7 (not a whole number)

If total number of books purchased is 12:

x = (12(12) - 126)/7 = 6/7 (not a whole number)

If total number of books purchased is 13:

x = (12(13) - 126)/7 = 12/7 (not a whole number)

If total number of books purchased is 14:

x = (12(14) - 126)/7 = 18/7 (not a whole number)

If total number of books purchased is 15:

x = (12(15) - 126)/7 = 24/7 (not a whole number)

If total number of books purchased is 16:

x = (12(16) - 126)/7 = 30/7 (not a whole number)

If total number of books purchased is 17:

x = (12(17) - 126)/7 = 36/7 (not a whole number)

If total number of books purchased is 18:

x = (12(18) - 126)/7 = 42/7 = 6 (a whole number)

So, you bought 6 $5 clearance mystery books and 12 - 6 = 6 $12 regular-priced science fiction books.

The car sticker information indicates a highway average of 27 mpg, while the sample mean's standard deviation is around 1.455 mpg. The mean estimate's margin of error is roughly 3.06 mpg.

The simplest approach to figure out your gas mileage is to simply divide the distance driven by the quantity of petrol your car required to fill up. That amounts to kilometers traveled divided by petrol consumed.

a) The formula for the standard deviation of the sample mean, σx¯, is:

σx¯ = σ / sqrt(n)

where σ is the standard deviation of the population, and n is the sample size. In this case, σ = 6.5 mpg and n = 20. So,

σx¯ = 6.5 / sqrt(20) ≈ 1.455 mpg

b) To find the margin of error for the mean estimate at a 95% confidence level, we can use the following formula:

Margin of error = z* (σx¯)

where z* is the critical value for a 95% confidence interval, which is 1.96.

Therefore, the margin of error = 1.96 * 1.454 = 2.85 mpg.

c) To find the 95% confidence interval for the mean highway mpg for this vehicle, we can use the following formula:

Confidence interval = x¯ ± Margin of error

where x¯ is the sample mean, which can be calculated by adding up all the mpg readings and dividing by the sample size:

x¯ = (37.2+21.0+17.4+29.2+7.4+27.0+36.9+38.8+35.3+32.3+19.0+26.1+25.8+41.4+34.4+32.5+26.5+28.2+22.1) / 20

= 29.231 mpg

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The resulting double-line graph should show the sales data for desktop and laptop computers over the five days, with a line for each type of computer.

A double-line graph is a graph that displays two sets of data on the same graph, using two lines to show how each set of data changes over time or some other variable.

To create a double-line graph of the sales data for desktop and laptop computers over five days, follow these steps:

Draw a graph with two perpendicular axes, the horizontal axis (x-axis) representing the days, and the vertical axis (y-axis) representing the number of computers sold.

Label the horizontal axis with the days from Day 1 to Day 5.

Label the vertical axis with the heading "Number of Computers Sold".

Plot the data points for desktop computer sales. For Day 1, plot a point at (1, 4), for Day 2 plot a point at (2, 1), for Day 3 plot a point at (3, 2), for Day 4 plot a point at (4, 5), and for Day 5 plot a point at (5, 1).

Connect the data points for desktop computer sales with a line.

Plot the data points for laptop computer sales. For Day 1, plot a point at (1, 5), for Day 2 plot a point at (2, 2), for Day 3 plot a point at (3, 3), for Day 4 plot a point at (4, 7), and for Day 5 plot a point at (5, 3).

Connect the data points for laptop computer sales with a line.

Use a different color or style for the line representing desktop sales and the line representing laptop sales.

Add a legend to the graph to indicate which line corresponds to desktop sales and which corresponds to laptop sales.

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Answer:

0.33

Step-by-step explanation:

To solve this, you first write the problem as an algebra equation as follows: 3x + 4 = 5

Then you solve the equation by subtracting 4 from both sides, and then divide both sides by 3. Here is the math to illustrate better:

3x + 4 = 5

3x + 4 - 4 = 5 - 4

3x = 1

3x/3 = 1/3

x = 0.33

Answer = 0.33

Joe aura 35 pommes.

40-5=35

16. The equatiοn οf the line in slοpe-intercept fοrm that passes thrοugh the pοint (-6, 5) and is parallel tο x + 2y = 14 is y = (-1/2)x + 2.

The equatiοn οf a straight line is y = mx + c, y = m x + c m is the gradient and c is the height at which the line crοsses the y -axis, alsο knοwn as the y -intercept.

16. Tο write the equatiοn οf a line in slοpe-intercept fοrm, we need tο find the slοpe and the y-intercept οf the line.

Tο find the slοpe οf the line, we can rewrite the equatiοn x + 2y = 14 in slοpe-intercept fοrm y = mx + b by sοlving fοr y:

x + 2y = 14

2y = -x + 14

y = (-1/2)x + 7

The slοpe οf the line is -1/2.

Since the line we want tο find is parallel tο this line, it will have the same slοpe οf -1/2.

Nοw we can use the pοint-slοpe fοrm οf the equatiοn οf a line tο find the equatiοn οf the line that passes thrοugh the pοint (-6, 5) with a slοpe οf -1/2:

y - y1 = m(x - x1)

where (x1, y1) is the pοint (-6, 5), and m is the slοpe, -1/2.

y - 5 = (-1/2)(x - (-6))

y - 5 = (-1/2)x - 3

y = (-1/2)x + 2

17. The equation perpendicular to y = -(2/3)x + 4, passing through (-4, 6)

perpendicular equations slope would be negative reciprocal to the current line.

The slope in y = -(2/3)x + 4, is m = -(2/3),

The negative reciprocal of -(2/3) is 3/2

Now, applying the x and y values in pοint-slοpe fοrm

y - 6 = 3/2(x - (-4))

y =  3/2(x+4) + 6

y =  (3/2)x + 6 + 6

y =  (3/2)x + 12

18. Since the line we want tο find is parallel tο this line, it will have the same slοpe.

Lets find the slope using slope formula

[tex]\rm m = \dfrac{y_2 - y_1}{x_2 - x_1}[/tex]

[tex]\rm m = \dfrac{0 - (-1)}{2 - (-1)}[/tex]

[tex]\rm m = \dfrac{1}{3}[/tex]

Now, using the point slope form

y - 1 = 1/3(x - 3)

y = 1/3(x - 3) + 1

y = (1/3)x - 1 + 1

y = (1/3)x

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The force equation for the system is F = bV - bF, where F is the force of friction, V is the velocity of the object, and b is the coefficient of viscous friction.

Viscous friction is a force that acts to oppose the motion of an object moving through a fluid or solid. The amount of friction experienced is determined by the coefficient of viscosity, which is a measure of how easily the two surfaces move against each other. In this equation, bV is the force generated by the object's motion, and b

F is the opposing force of friction. Together, these two forces determine the net force acting on the object.

Viscous friction can be very important in understanding the behavior of a system. It helps us to understand how much energy is needed to move objects, as well as how quickly they will accelerate.

Viscous friction can also cause objects to slow down over time, as the energy it takes to move them is continually being lost to friction. Understanding the force equation for a system helps us to better predict and understand its behavior.

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The average number of beads that the girls have is 63

Let's start by using algebra to represent the given information:

Let b be the number of beads that Sally has.

Then, Kelly has 3/4 times as many beads as Sally, which can be expressed as (3/4)b.

Also, we know that Kelly has 18 more beads than Sally, which can be expressed as (b + 18).

Putting these together, we can write the equation:

(3/4)b = b + 18

Solving for b, we get:

b = 72

So, Sally has 72 beads, and Kelly has (3/4) × 72 = 54 beads.

The average number of beads that the girls have is (72 + 54)/2 = 63 beads

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The complement of the angle is 38 degrees and the supplement of the angle is 128 degrees.

The given angle is

Angle = 52 degrees

To find the complement of an angle, we need to subtract its measure from 90 degrees.

Therefore, the complement of an angle with a measure of 52 degrees is:

90 degrees - 52 degrees = 38 degrees

So, the complement of the angle shown is 38 degrees.

To find the supplement of an angle, we need to subtract its measure from 180 degrees.

Therefore, the supplement of an angle with a measure of 52 degrees is:

180 degrees - 52 degrees = 128 degrees

So, the supplement of the angle shown is 128 degrees.

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The domain of discourse of the propositional function P(x) is {1,2,3,4}, by using negation, disjunction, and conjunction are:

a)  "there does not exist an x in the domain for which P(x) is false."

b) "there exists an x in the domain for which P(x) is false."

c)  "there exist exactly three x's in the domain for which P(x) is true."

d) -(E. P(x)) can be rewritten as “Every x is not P(x)”

We are given that the domain of discourse of the propositional function P(x) is {1, 2, 3, 4}. We need to rewrite each propositional function below using only negation, disjunction, and conjunction.

a) The propositional function "Vx P(x)" means "for all x in the domain, P(x) is true." To rewrite this using only negation, disjunction, and conjunction, we can use De Morgan's law and write:

-(Ex -P(x)), which means "there does not exist an x in the domain for which P(x) is false."

b) The negation of "Vx P(x)" is "there exists an x in the domain for which P(x) is false." Using De Morgan's law again, we can rewrite this as:

Ex -P(x).

c) The propositional function "3x P(x)" means "there exist exactly three x's in the domain for which P(x) is true." To rewrite this using only negation, disjunction, and conjunction, we can break it down into two statements:

Using the symbols for negation, disjunction, and conjunction, we can write this as:

(Ex_1 P(x_1) ∧ Ex_2 P(x_2) ∧ Ex_3 P(x_3)) ∧ -(Ex P(x)).

d) The propositional function "-(E. P(x))" means "it is not true that there exists an x in the domain for which P(x) is true." To rewrite this using only negation, disjunction, and conjunction, we can use De Morgan's law and write:

Ax -P(x),

which means "for all x in the domain, P(x) is false."

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Answer: Quadratic (not 100% sure)

Jordy's first error in his proof is option (c) Jordy established all necessary conditions, but then used an inappropriate congruence criterion

Jordy's first error in his proof is that he used an inappropriate congruence criterion to prove that the two triangles are congruent. He established all necessary conditions, but AAA congruence is only valid for proving congruence of triangles in certain special cases, such as when the triangles are similar.

In general, AAA congruence is not a valid congruence criterion. This highlights the importance of choosing the correct congruence criterion when proving that two triangles are congruent, as using an invalid or inappropriate criterion can lead to an incorrect conclusion.

Therefore, the correct option is (c) Jordy established all necessary conditions, but then used an inappropriate congruence criterion

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An Inequality is a relationship between two expressions or values that aren't equal. The relationship between n and 4 is given by the inequality n> 4.

We want to find a relation between n and 4 similar that

7 *( n/ 4)> 7

still, we get

If we now divide both sides of the former inequality by 7.

7 *( n/ 4)/ 7>7/7

n/ 4> 1

So n/ 4 must be lesser than 1.

A better way to show the relationship is to multiply both sides of the inequality by 4.

4 *( n/ 4)> 4 * 1

n> 4

So the relationship between n and 4 is that n must be lesser than 4.

In mathematics, an inequality is a relationship that results in an unstable comparison of two figures or other fine expressions. It's frequently used to compare two figures on a number line grounded on their size.

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If m = 3/2, the two equations in the system are dependent and have an infinite number of solutions.

To do this, we can set the coefficients of x and y in the two equations equal to each other:

6 - 4m = 2k(2m - 1)

2n - 7 = 3k

Simplifying these equations, we get:

8m - 6 = 4km

2n - 7 = 3k

We can solve the first equation for k:

k = (8m - 6)/(4m)

Substituting this into the second equation and solving for n, we get:

n = (16m - 29)/(8m - 12)

Now we need to check if there are any values of m for which the equations are proportional. We can do this by checking if the expressions for k and n are the same for all values of m.

We find that the expressions for k and n are the same for m = 3/2.

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Complete Question:

Determine the values of m and n so that the following system of linear equations have infinite number of solutions:

(2m−1)x+3y−5=0

3x+(n−1)y−2=0

Answer: So that means the answer is $112.5

Step-by-step explanation:Percent of Discount is 80%. Sale Price is $90. The original price,. = 90 x 100 / 80. = 9000/80. = 112.5. Therefore, $112.5 is the original price.

YES THIS IS RIGHT!!!!

Meredith will take 8 hours 45 minutes to file 70% of the 10 reports given.

The time taken by Meredith to file 70% of the 10 reports given, given that each report takes an average of 75 minutes is 6 hours, 30 minutes. Therefore, the correct option is B. 6 hours, 30 minutes. How long will it take Meredith to file 70% of 10 reports, given that each report takes an average of 75 minutes to file?

Here, the total number of reports = 10

Average time to file one report = 75 minutes

To find out the time taken to file 70% of 10 reports, we will need to multiply the average time taken to file one report by the number of reports to be filed, which is 7 in this case:

75 × 7 = 525 minutes

We have calculated the time it will take Meredith to file 7 reports. Now, to convert this time to hours and minutes, we divide the total minutes by 60 to get the hours and then find out the remainder for the minutes:

525 ÷ 60 = 8 hours 45 minutes

Therefore, Meredith will take 8 hours 45 minutes to file 70% of the 10 reports given.

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Therefore, the function that matches the mosquito counts is'(w) = 8([tex]1.5^{w}[/tex]).

by the question.

To determine which function matches the mosquito counts, we can plot the given data points on a graph and see which function fits the curve. Here are the counts for the first few weeks:

Week Mosquito Count

0 8

1 20

2 50

3 125

4 312

Plotting these points on a graph with weeks on the x-axis and mosquito count on the y-axis, we get:

mosquito graph

Looking at the graph, we can see that the curve increases rapidly and seems to be exponential. This rule out option A (which is linear), leaving us with options B, C, and D.

To determine which of these options matches the data, we can try plugging in the week numbers and seeing which one gives us values close to the actual counts. We can also use a calculator or graphing technology to help us with this.

Option B gives us the following mosquito counts for the first five weeks:

Week Mosquito Count

0            8

1         19.5

2        47.25

3       114.19

4       276.32

Option C   gives us:

Week Mosquito Count

0       8

1        12

2       18

3       27

4       40.5

Option D is not a function of mosquito counts with weeks as the input variable, so we can rule it out.

Comparing the values from options B and C to the actual counts, we can see that option C is the closest match.

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Answer:

The answer is the standard error is a measure of the accuracy of the sample mean as an estimate of the population mean.

Step-by-step explanation:

The length of RV for the right triangle is equal to 6 to the nearest whole number using the Pythagoras rule.

The Pythagoras rule states that in a right-angled triangle, the square of the hypotenuse is equal to the sum of the squares of the other two sides. 

so by Pythagoras rule we can evaluate for the length RV by considering the following right triangles:

For ∆TVU:

13² = 5² + TV²

TV = √(13² - 5²) {make TV the subject}

TV = √(169 - 25)

TV = √144

TV = 12

For ∆TVS:

15² = 12² + SV²

SV = √(15² - 12²) {make SV the subject}

SV = √(225 - 44)

SV = √81

SV = 9

For ∆RVS:

11² = 9² + RV²

RV = √(11² - 9²) {make RV the subject}

RV = √(121 - 81)

RV = √49

RV = 6.3246

Therefore, the length of RV for the right triangle is equal to 6 to the nearest whole number using the Pythagoras rule.

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Consequently, C = 17.2° as by the result of the Rule of Cosines , rounded to the nearest tenth.

A geometric figure known as an angle is created by two lines that share an endpoint and are referred to as the angle's sides and vertex, respectively. The quantity of rotation required to align one side with the other side around the vertex is the angle's unit of measurement. Typically, angles are expressed as degrees or radians, where a complete rotation equals 360 degrees or 2 radians. Angles are frequently used to define the position and orientation of lines and shapes in geometry, trigonometry, and other branches of mathematics.

given

As a result of the Rule of Cosines, we have:

A2 Plus B2 - 2ab cos = c2 (C)

Adding the specified values:

c² = 26² + 29² - 2(26)(29) cos(50°)

c² = 676 + 841 - 1508 cos(50°)

c² = 1517 - 1508 cos(50°)

c ≈ √(1517 - 1508 cos(50°))

c ≈ 17.2° (rounded to the closest tenth)

Consequently, C = 17.2° as by the result of the Rule of Cosines , rounded to the nearest tenth.

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Answer:

C= 23.22

This is the answer this question.

Answer:

The given equation is in vertex form y = a(x - h)^2 + k, where (h, k) is the vertex of the parabola. Comparing the given equation with the vertex form, we have a = -3, h = -3 and k = 4.

Since a = -3 < 0, the parabola opens downwards and has a maximum point.

To find the maximum value of y, we need to evaluate y at the x-coordinate of the vertex:

x = -3

y = -3(-3+3)^2 + 4 = 4

Therefore, the parabola y = -3(x+3)2 + 4 contains a maximum point and the maximum value of y is 4.

Hence, the answer is option C

Answer:

C)  Maximum point; 4

Step-by-step explanation:

Given parabola:

[tex]y=-3(x+3)^2+4[/tex]

The given parabola is in vertex form:

[tex]\boxed{y = a(x - h)^2 + k}[/tex]

where:

By comparing the given equation with the vertex form, we can see that:

As a < 0, the parabola opens downwards. Therefore, the vertex of the parabola is a maximum point.

The vertex of the parabola is (h, k) = (-3, 4).

Therefore, the maximum value of y is 4, which occurs at x = -3.

Hence, the abbreviated formula is -7 + 0i, or just -7.

The terms in the parentheses can be immediately simplified. So, we can carry out the operations indicated by the brackets in the following order: multiplication, addition, subtraction, division. Note: The brackets should be shortened in the following order: (),, []. Simplify: 14 + (8 - 2 3) for Example 2.

We must combine like terms in order to make the phrase simpler.

First, we can individually merge the real and made-up parts:

The genuine parts add out to -3 - 4 = -7.

i - i = 0 is the imaginary part's total.

Hence, the abbreviated formula is -7 + 0i, or just -7.

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Complete question:

Please simplify the following expression while performing the given operation. (-3+i)+(-4-i)

Answer:

y = 12

Step-by-step explanation:

if a tangent and a secant are drawn from an external point to a circle, then the square of the measure of the tangent is equal to the product of the measures of the secant's external part and the entire secant , that is

y² = 8(8 + 6 + 4) = 8 × 18 = 144 ( take square root of both sides )

y = [tex]\sqrt{144}[/tex] = 12

Thursday’s high temperature was 6.5 degrees more than Wednesday’s high temperature.

Average temperature is calculated as (Monday's temperature plus Tuesday's temperature plus Wednesday's temperature plus Thursday's temperature)/Total days.

Temporary for Monday and Tuesday plus Temperatures for Wednesday and Thursday.

The sum of the temperatures for Monday, Tuesday, Wednesday, and Thursday is equal.

As stated, the 6.5 degree average for the days of Tuesday, Wednesday, Thursday, and Friday.

using the formula no.

Average temperature is equal to (Tuesday's temperature plus Wednesday's temperature plus Thursday's temperature plus Friday's temperature)/Total days.

Thus, Thursday’s high temperature was 6.5 degrees more than Wednesday’s high temperature.

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the complete question is

Write a positive or negative number to represent each change in the high temperature.

1. Tuesday’s high temperature was 4 degrees less than Monday’s high temperature. ?

2. Wednesday’s high temperature was 3.5 degrees less than Tuesday’s high temperature. ?

3. Thursday’s high temperature was 6.5 degrees more than Wednesday’s high temperature. ?

4. Friday’s high temperature was 2 degrees less than Thursday’s high temperature. ?

The equation of the required line in slope-intercept form is y = -1/4x + 8.

Here are the steps to find the equation of the line:

Step 1: Find the slope of the given line in slope-intercept form

y = mx + c

-4x + y = 43 ⇒ y = 4x + 43... (1)

Here, the slope (m1) of the given line is 4.

Step 2: Find the slope of the required line as the two lines are perpendicular to each other.

m1 × m2 = -1

[As the given line and the required line are perpendicular to each other]

4 × m2 = -1 ⇒ m2 = -1/4

So, the slope (m2) of the required line is -1/4.

Step 3: Write the equation of the required line in point-slope form.

y - y1 = m(x - x1)

[Using the point-slope formula]

Let (x1, y1) = (-8, 10)m = -1/4

Putting the values in the above formula, we get

y - 10 = -1/4(x - (-8)) ⇒ y - 10 = -1/4(x + 8)... (2)

Step 4: Simplify the above equation to get the required equation of the line in slope-intercept form.

y - 10 = -1/4x - 2 ⇒ y = -1/4x + 8... (3)

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[tex]3[/tex] days [tex]0[/tex] hours. The answer is three because the function [tex]W[/tex] that solves the differential equation gives the number of weeds in a large garden.

A number is calculated and represented using a decimal, which is an algebra quantity. In handwriting, numerical symbols like "3" are used to represent numbers. A counting system is a logical way of expressing numbers that uses digits or symbols to represent them.

Vets Day and Memorial Day are commonly celebrated on November 11 in the United States and overseas, respectively. The history, mythology, and mathematical importance of this particular time and date are all explained here.

[tex]\frac{dw}{dt}=\frac{1}{12}(-318+24W)[/tex]

[tex]\frac{d^{2}W }{dt^{2} }=\frac{d}{dt}[\frac{1}{12} (-318+24W)][/tex]

When [tex]W=14, \frac{dW}{dt}[/tex]

[tex]=\frac{1}{12}(-318+24*14)[/tex]

[tex]=\frac{18}{12}=1.5[/tex]

[tex]=2\frac{dW}{dt}=2*1.5[/tex]

[tex]=3[/tex]

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