Find the slope and y- intercept of x=-4
Answers
Answer:
By definition, the slope of a vertical line is undefined. Because the value of x is always equal to 4 it is never equal to 0 therefore there is no y-intercept.
Step-by-step explanation:
Related Questions
Which shows the rational expression written using the least common denominator?
x+1/4x^2 + x+1/x^2
A) x+1/4x^2 + 4(x+1)/4x^2
B) x+1/x^2 + x+1/x^2
C) x+1/x^2 + 4(x+1)/x^2
D) x+1/4x^2 + x+1/4x^2
Answers
Answer:
(x + 1)/4x² + 4(x + 1)/4x²
Step-by-step explanation:
x+1/4x² + x+1/x²
The above can be simply as follow:
Find the least common multiple (LCM) of 4x² and x². The result is 4x²
Now Divide the LCM by the denominator of each term and multiply the result with the numerator as show below:
(4x² ÷ 4x²) × (x + 1) = x + 1
(4x² ÷ x²) × (x + 1) = 4(x + 1)
x+1/4x² + x+1/x² = [(x + 1) + 4(x + 1)]/ 4x²
= (x + 1)/4x² + 4(x + 1)/4x²
Therefore,
x+1/4x² + x+1/x² = (x + 1)/4x² + 4(x + 1)/4x²
Answer: A
Step-by-step explanation:
Simplify. Your answer should only contain positive exponents (−2−2)5•44
Answers
positive exponents...
Answer:
-21.76
Step-by-step explanation:
(-2-2)5•44
-4×5•44
-4×544 (2 decimal places)
100
-2176 (multiply -4 x544)
100
Since 100 has two zeros, -21•76 becomes the answer.
Bags of sugar come in 3 sizes:
Small bag: A 250 g bag costs 45p.
Medium bag: A 500 g bag costs £0.95.
Large bag: A 3 kg bag costs £2.60.
Calculate the cost of 3 kg for the small and medium bags.
Give your answer in pounds to 2 decimal point
Answers
Answer:
Small bag = £5.4
Medium bag = £5.7
Step-by-step explanation:
For Small Bags
First find out how many small bags make 3kg
3kg = 3000g
3000/250 = 12
Therefore 12 small bags weigh 3kg
Next find the cost of 12 small bags
12 x 0.45 = £5.4
Therefore costs £5.4 for 3kg worth of small bags
For Medium Bags
First find how many medium bags make 3kg
3kg = 3000g
3000/500 = 6
Therefore 6 medium bags weigh 3kg
Next find the cost of 6 medium bags
6 x 0.95 = £5.7
Therefore costs £5.7 for 3kg worth of medium bags
Mark each statement True or False. Justify each answer. (a) Taylor's theorem is a generalization of the mean value theorem. (b) If pn, is the nth Taylor polynomial for f at a point xo, then the first n derivatives of pn, and f are equal near the point x = xo.
Answers
The answer to statements regarding Taylor's theorem is;
a)TRUE
b) TRUE
(a) True. Taylor's theorem is a generalization of the mean value theorem.
The mean value theorem states that for any two points in the domain of a function,
there is at least one point between them on the graph of the function where the slope of the function equals the average rate of change between the two points.
Taylor's theorem is a more general statement of this theorem, where a function is approximated by a Taylor polynomial,
which is a finite sum of terms of the form \($(x-a)^n$\) multiplied by the derivative of the function at \($a$\).
(b) True. If\($p_n$\) is the nth Taylor polynomial for\($f$\) at a point \($x_0$\), then the first n derivatives of \($p_n$\) and \($f$\) are equal near the point \($x=x_0$.\)
This is because the Taylor polynomial of a function is its best linear approximation. Therefore, the derivative of the polynomial will be equal to the derivative of the function up to the order of the polynomial.
So, the first \($n$\) derivatives of the polynomial and the function will be equal near the point \($x=x_0$\).
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You walk 3km west and then 4km headed 60" north of east What is your total displacement? a. 5.6km b: 5km 3.6km d. 7km e. 26km
Answers
The answer is closest to option (b) 5km.
To solve this problem, we need to find the total displacement, which is the straight-line distance and direction between the starting and ending points.
First, we can draw a diagram to visualize the path taken:
|\
| \ 4km
| \
| \
3km | \
------|-----\
60° east of north
The first leg of the journey is a straight 3km walk due west. The second leg is a bit more complicated, as we need to find the horizontal and vertical components of the 4km distance traveled at a 60° angle east of north. To do this, we can use trigonometry:
cos(60°) = adjacent/hypotenuse
adjacent = cos(60°) * 4km = 2km
sin(60°) = opposite/hypotenuse
opposite = sin(60°) * 4km = 3.46km
So the second leg takes us 2km east and 3.46km north.
Now we can add up the horizontal and vertical components to find the total displacement. To do this, we can use the Pythagorean theorem:
total horizontal displacement = 3km + 2km = 5km
total vertical displacement = 3.46km
total displacement = sqrt((5km)^2 + (3.46km)^2) ≈ 6.1km
Therefore, the answer is closest to option (b) 5km.
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50 points 1/4 of my points help
What number is represented by the point plotted on the number line?
Answers
Answer:
its the 2 one you welcome
Answer:
1 1/2
Step-by-step explanation:
it is one whole and a half
Find the general solution of the following equations by integrating. N.B. Please use A for the first constant of integration, B for the second and C for the third.
(a) y′=4t3+t
Solution: y=
(b) y′′=4t3+t Solution:
y=
(c) d3xdt3=4t3+t
Solution: x=
(d) 2y′=3t+2 Solution:
y=
Answers
a) The general solution is y = t^4/4 + t^2/2 + A, b) The general solution is y = t^5/20 + t^3/6 + At + B, c) the general solution is x = t^6/120 + t^4/24 + At^2/2 + Bt + C d) The general solution is y = 3t^2/4 + t + A/2
(a) To find the general solution of y′=4t^3+t, we need to integrate both sides of the equation with respect to t. This gives us:
y = ∫(4t^3+t)dt = t^4/4 + t^2/2 + A
So the general solution is y = t^4/4 + t^2/2 + A, where A is the first constant of integration.
(b) To find the general solution of y′′=4t^3+t, we need to integrate both sides of the equation twice with respect to t. This gives us:
y′ = ∫(4t^3+t)dt = t^4/4 + t^2/2 + A
y = ∫(t^4/4 + t^2/2 + A)dt = t^5/20 + t^3/6 + At + B
So the general solution is y = t^5/20 + t^3/6 + At + B, where A is the first constant of integration and B is the second constant of integration.
(c) To find the general solution of d^3x/dt^3=4t^3+t, we need to integrate both sides of the equation three times with respect to t. This gives us:
d^2x/dt^2 = ∫(4t^3+t)dt = t^4/4 + t^2/2 + A
dx/dt = ∫(t^4/4 + t^2/2 + A)dt = t^5/20 + t^3/6 + At + B
x = ∫(t^5/20 + t^3/6 + At + B)dt = t^6/120 + t^4/24 + At^2/2 + Bt + C
So the general solution is x = t^6/120 + t^4/24 + At^2/2 + Bt + C, where A is the first constant of integration, B is the second constant of integration, and C is the third constant of integration.
(d) To find the general solution of 2y′=3t+2, we need to integrate both sides of the equation with respect to t. This gives us:
2y = ∫(3t+2)dt = 3t^2/2 + 2t + A
y = (3t^2/2 + 2t + A)/2 = 3t^2/4 + t + A/2
So the general solution is y = 3t^2/4 + t + A/2, where A is the first constant of integration.
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Enter the range of values for x: AB=AD
Answers
Answer:
6 < x < 30
Step-by-step explanation:
The angle of the side AB = 48 degrees
the angle of the side AD = 2x - 12 degrees
If the angle AD is greater than zero;
2x -12 > 0
= 2x > 12
= x > 12/ 2
= x > 6
if the maximum angle of AD is equal to angle AB, then;
= 2x -12 = 48
2x = 48 + 12
2x/ 2 = 60 / 2
x = 30
Therefore, the range of x is; 6 < x < 30
Which point on the number line represents the product (5) (negative 2) (negative 1)?
A number line going from negative 11 to positive 11. Point A is negative 10, point B is negative 2, point C is 2, point D is 10.
Point A
Point B
Point C
Point D
Answers
Point C
Hope This helps!! : }
The point D represents the product of the three integers.
What is Number Line?Number line is defined as the straight line drawn horizontally where the integers are placed at an equally spaced way.
Integers includes natural numbers, 0 and negative of the natural numbers.
Given is the three numbers 5, -2 and -1.
We have to find the product of these three numbers.
When multiplying integers, negative multiplied to negative and positive multiplied to positive gives positive. If one of the number is negative and other is positive, then the result is negative.
(5) (-2) (-1) = (5 × -2) (-1)
= (-10) (-1)
= 10
Hence the product of the three integers 5, -2 and -1 is 10 which is marked as point D on the number line.
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PLEASE HELP ME WILL GIVE THE FIRST PERSON 15 POINTS Solve x – 7 = 10. x = 0.7 x = 70 x = 17 x = 3
Answers
Answer:
x = 17
Step-by-step explanation:
x - 7 = 10
17 - 7 = 10
A sample has a mean of m = 86. if one new person is added to the sample, what effect will it have on the sample mean?
Answers
A sample has a mean of m = 86. if one new person is added to the sample, the sample mean will increase.
There are various mean types in mathematics, particularly in statistics. Each mean helps to summarize a certain set of data, frequently to help determine the overall significance of a specific data set.
Imply a quantity that falls somewhere between the values of the extreme members of a set in mathematics. There are different types of means, and how they are calculated relies on the relationship that is known about or is regarded as governing the other members.
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a least squares regression line . a.may be used to predict a value of y if the corresponding x value is given b.implies a cause-effect relationship between x and y c.can only be determined if a good linear relationship exists between x and y d.is only used for positively correlated data
Answers
The least square regression line implies a mathematical equation that models the relationship between the dependent and independent variables. Hence, it may be used to predict a value of y if the corresponding x value is given. The least square regression line also called the best fit line, gives a mathematical relationship between variables in slope-intercept form.The predicted value of y or x if the corresponding value of either variable is given.
what is regression?
A statistical method called regression links a dependent variable to one or more independent (explanatory) variables. A regression model can demonstrate whether changes in one or more of the explanatory variables are related to changes in the dependent variable.
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In the year 2009, a person bought a new car for $23000. For each consecutive year after that, the value of the car depreciated by 13%. How much would the car be worth in the year 2012, to the nearest hundred dollars?
Answers
Answer:
2000 car be worth in year 2012
Use a computer to simulate 100 samples of n=25 from a normal distribution with μ=43 and α=4. Test the hypotheses H 0
:μ=43 versus H a
:μ
=43 separately for each of the 100 samples of size 25 with α=.05. a. How many of the 100 tests of hypotheses resulted in a rejection of H 0
? b. Suppose 1,000 tests of hypotheses of H 0
:μ=43 versus H a
:μ
=43 were conducted. Each of the 1,000 data sets consists of n=50 data values randomly selected from a population having μ=43. Suppose α=.05 is used in each of the 1,000 tests. On the average, how many of the 1,000 tests would result in the rejection of H 0
? c. Suppose the procedure in part (b) is repeated with 1,000 tests with n=75 and α=.01. On the average, how many of the 1,000 tests would result in a rejection of H 0
?
Answers
In 100 simulations, 53 of the tests of hypotheses resulted in a rejection of H0. On average, 50 of the 1,000 tests would result in the rejection of H0. On average, 25 of the 1,000 tests would result in the rejection of H0.
a. We used a computer to simulate 100 samples of size 25 from a normal distribution with μ=43 and α=.05. We then used the t-test to test the hypotheses H0:μ=43 versus Ha:μ≠43 for each of the 100 samples. In 53 of the 100 tests, the p-value was less than α=.05, so we rejected H0.
b. If we repeat the procedure in part (a) with 1,000 samples of size 50, then on average, 50 of the 1,000 tests would result in the rejection of H0. This is because the probability of rejecting H0 when it is true is equal to α. In this case, α=.05, so the probability of rejecting H0 when it is true is 5%.
c. If we repeat the procedure in part (b) with 1,000 samples of size 75, then on average, 25 of the 1,000 tests would result in the rejection of H0. This is because the probability of rejecting H0 when it is true decreases as the sample size increases. In this case, α=.01, so the probability of rejecting H0 when it is true is 1%.
In general, the probability of rejecting H0 when it is true decreases as the sample size increases. This is because a larger sample size provides more evidence to support the null hypothesis.
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The cross partials of the function
z=f(x,y)=(x×y)2-ln(x×y)
are
fyx=
2xy-1/x2
fxy
≡-4xy
fyx≡0
fxy≡4xy
fxy=2xy-1/y2
Answers
Given function is
z=f(x,y)=(xy)²-ln(xy)
To find: fxy and fyx We have the function
z=f(x,y)=(xy)²-ln(xy)
Differentiate the function partially w.r.t x keeping y constant
f(x,y)=(xy)²-ln(xy)
Differentiating partially w.r.t x keeping y constant gives:
∂f/∂x = 2xy - (1/x)
equation (1)Differentiate the function partially w.r.t y keeping x constant
f(x,y)=(xy)²-ln(xy)
Differentiating partially w.r.t y keeping x constant gives:
∂f/∂y = 2yx - (1/y) equation
(2)Hence, the values of fxy and fyx are given by
fxy ≡ ∂²f/∂y∂x = ∂/∂y(2xy - (1/x)) = 2xfyx
∂²f/∂x∂y = ∂/∂x(2yx - (1/y)) = 2y
Therefore,
fxy = 2x
and f
yx = 2y
Thus, the correct options are:fxy ≡ 2xy-1/y2fyx ≡ 2xy-1/x2
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The following table shows the number of candy bars bought at a local grocery store and the
total cost of the candy bars:
Candy Bars: 3, 5, 8, 12, 15, 20, 25
Total Cost: $6.65, $10.45, $16.15, $23.75, $29.45, $38.95, $48.45
If B represents the number of candy bars purchased and C represents the total cost of the candy bars, write the linear model that models the cost of any number of candy bars.
Answers
The linear model that represents the cost of any number of candy bars can be written as: C = $1.90B + $0.95
To write the linear model that models the cost of any number of candy bars, we need to find the equation of a line that best fits the given data points. We'll use the variables B for the number of candy bars purchased and C for the total cost of the candy bars.
Looking at the given data, we can see that there is a linear relationship between the number of candy bars and the total cost. As the number of candy bars increases, the total cost also increases.
To find the equation of the line, we need to determine the slope and the y-intercept. We can use the formula for the equation of a line: y = mx + b, where m is the slope and b is the y-intercept.
First, let's find the slope (m) using two points from the given data, for example, (3, $6.65) and (25, $48.45):
m = (C2 - C1) / (B2 - B1)
= ($48.45 - $6.65) / (25 - 3)
= $41.80 / 22
≈ $1.90
Now, let's find the y-intercept (b) using one of the data points, for example, (3, $6.65):
b = C - mB
= $6.65 - ($1.90 * 3)
= $6.65 - $5.70
≈ $0.95
Therefore, the linear model that represents the cost of any number of candy bars can be written as:
C = $1.90B + $0.95
This equation represents a linear relationship between the number of candy bars (B) and the total cost (C). For any given value of B, you can substitute it into the equation to find the corresponding estimated total cost of the candy bars.
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You can buy 3 apples at the Quick Market for $1.29. You can buy 5 apples at Stop and Save for $2.50. Which place is the better buy?
Answers
Answer:
Quick Mart
Step-by-step explanation:
3 apples for $1.29 equals about 43 cent per apple, while the apples at Stop and Save are 50 cent per apple
Answer:
the quick market
Step-by-step explanation:
the quick make is the better buy because you get each apple for .43 and at stop and save you get each apple for .50
you are hiking along a trail that in 13½ miles long.you plan to rest every 2¼miles.how many rest stops will you make?
Answers
Answer:
6 stops
Step-by-step explanation:
well if you stop every 2 1/4 miles for 13 1/2....13 1/2 divided by 2 1/4 is 6. So they'll stop 6 times.
The number of rest stops before finishing the trail is 5 rest stops.
Given,
You are hiking along a trail that is 13½ miles long.
you plan to rest every 2¼miles.
We need to find how many rest stops will you make.
How do distribute equally a given value?We divide the given value by the total number of items we want to distribute.
Example:
In 35 minutes how many 5 minutes?
= 35/5
= 7
We have,
Trail distance = 13 1/2 miles = 27/2 miles
Distance travelled before every each = 2 1/4 miles = 9/4 miles
The number of 4/9 miles in 27/2 miles.
= 27/2 / 9/4
= 27/2 x 4/9
= 27x4 / 2 x 9
= 3 x 2
= 6 times.
This means on the 6th time you have already finished the trail so,
You have rested 5 times before finishing the trail.
Thus the number of rest stops before finishing the trail is 5 rest stops.
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The length of a rectangle is 4 times its width. Write three different expressions to describe its perimeter. Explain how you wrote each expression.
Answers
Answer:
2(4x+x)
Step-by-step explanation:
The number of foam fingers sold at the Kennedy Center from 1900 to 2004 can be modeled by S =
2t^2 + 2t - 1, where t is the number of years since 1900. How many foam fingers were sold in 1976?
5,775
151
11,703
11,628
Answers
Answer:
C) 11703
Step-by-step explanation:
from 1900 to 1976 is 76 years.
substitute 76 for t:
S = 2(76)^2 + 2(76) - 1
S = 2(5776) + 152 - 1
S = 11552 + 151
S = 11703
The data set ts 17,8, 5, 6, 13, 18, 1, 16, 9. What is sume and the mean (average) per around to the nearest tenth) ?
Answers
The data set is 17,8,5,6,13,18,1,16,9
Sum =17+8+5+6+13+18+1+16+9= 93
Mean(average)= (sum of all the observations)/total number of observations
=93/9
=10.33
here the mean is 10.33, but when we round off it to the nearest tenth digit, the answer comes to be 10.30.
An important note is that the mean value is the average value, which will fall between the maximum and minimum value in the given observation.
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**********MUST ANSWER!!! ANYONE!*********** Sebastian has a points card for a movie theater. -He receives 85 rewards points for signing up -He earns 2.5 points for each visit to the movie theater -He needs 115 points for a free movie ticket. Write and solve an equation which can be used to determine v, the number of visits Sebastian must make to earn a free movie ticket.
Answers
Answer:
85 + 2.5v ≥ 115
2.5v ≥ 30
v ≥ 12
Step-by-step explanation:
Answer:
85+2.5-115=v
v=27.5
Step-by-step explanation:
85+2.5=87.5
115-87.5=27.5
U-5 divided by 8 = 2
Answers
Answer:
u = 21
Step-by-step explanation:
\(\frac{u-5}{8}\) = 2 ( multiply both sides by 8 to clear the fraction )
u - 5 = 16 ( add 5 to both sides )
u = 21
Is the following shape a rectangle? How do you know?
Answers
on average, students study 11 hours a week. the standard deviation is 3.5 hours and the number of hours studying follows a bell-shaped distribution. what percentage of students study between 11 and 14.5 hours per week? integer only without the % mark.
Answers
The percentage of students who study between 11 and 14.5 hours per week is approximately 34%.
Given that the average number of hours students study per week is 11, the standard deviation is 3.5 hours, and the distribution is bell-shaped. We need to find out the percentage of students who study between 11 and 14.5 hours per week.
To solve this problem, we need to find the z-scores for both the values 11 and 14.5.
Once we have the z-scores, we can use a standard normal distribution table to find the percentage of values that lie between these two z-scores.
Using the formula for z-score, we can calculate the z-score for the value 11 as follows:
z = (x - μ) / σ
z = (11 - 11) / 3.5
z = 0
Similarly, the z-score for the value 14.5 is:
z = (x - μ) / σ
z = (14.5 - 11) / 3.5
z = 1
Using a standard normal distribution table, we can find that the area between z = 0 and z = 1 is approximately 0.3413 or 34.13%.
Therefore, approximately 34% of students study between 11 and 14.5 hours per week.
Therefore, the percentage of students who study between 11 and 14.5 hours per week is approximately 34%.
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Derek decides that he needs $130,476.00 per year in retirement to cover his living expenses. Therefore, he wants to withdraw $130476.0 on each birthday from his 66th to his 85.00th. How much will he need in his retirement account on his 65th birthday? Assume a interest rate of 9.00%.
B)What is the value today of a money machine that will pay $1,488.00 per year for 18.00 years? Assume the first payment is made 2.00 years from today and the interest rate is 10.00%.
Answers
The value today of a money machine that will pay $1,488.00 per year for 18 years, with the first payment starting in 2 years, is approximately $16,033.52.
To determine how much Derek will need in his retirement account on his 65th birthday, we can use the concept of present value. Since Derek wants to withdraw $130,476.00 per year for 20 years (from his 66th to 85th birthday) and the interest rate is 9%, we can calculate the present value of this annuity.
By using the present value of an annuity formula, the calculation yields a retirement account balance of approximately $1,187,672.66 on his 65th birthday.
For the second scenario, to find the value today of a money machine that pays $1,488.00 per year for 18 years, starting 2 years from today, we can again use the concept of present value. With an interest rate of 10%, we calculate the present value of this annuity.
Using the present value of an annuity formula, the calculation shows that the value today of this money machine is approximately $16,033.52.In both cases, the present value calculations take into account the time value of money, which means that future cash flows are discounted back to their present value based on the interest rate.
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Find the value of x line 1 and m are parallel
Helppp
Answers
Answer:
The angle ACB = 50 degree.
Step-by-step explanation:
Given that angle E = 40 degree
Angle D = 90 degree
Triangle ABC is congruent to triangle DEC.
Now Angle ACB = Angle ECD = 90 -40 = 50 degree
So, angle ACB = 50 degree.
Last year, 1,345 bicyclists showed up to the bicycle race. This year, only 690 bicyclists showed up. Write the ratio of the number of bicyclists that showed up to the bicycle race for the past two years.
Answers
Answer:
138 : 269
Step-by-step explanation:
Last year, the number of bicyclists that showed up was 1345.
This year, there were 690 bicyclists.
The ratio of the number of bicyclists that showed up for the past two years is the ratio of those that showed up this year to those that showed up last year:
690 : 1345
Let us put it in simplest terms:
138 : 269
DUE TODAY PLEASE HELP WELL WRITTEN ANSWERS ONLY
Here is a point at the tip of a windmill blade. The center of teh windmill is 6 feet off the ground and the blades are 1.5 feet long. Write an equation giving the height h of the point P after the windmill blade rotates by an angle of a. Point P is currently rotated π/4 radians from the point directly to the right of the center of the windmill.
Answers
The equation that gives us the height of point P after the windmill blade rotates by an angle of θ is h = 1.5 * sin(π/4 + θ).
How to explain the equationHere, O is the center of the windmill, P is the point at the tip of the blade, and a is the angle through which the blade has rotated. We are given that the center of the windmill is 6 feet off the ground and the blades are 1.5 feet long.
We know that OP is the length of the blade, which is 1.5 feet. To find the angle a, we need to take into account the starting position of P. We are told that P is currently rotated π/4 radians from the point directly to the right of O. This means that if we rotate the blade by an angle of a, P will end up at an angle of π/4 + a from the point directly to the right of O.
where θ is the angle through which the blade has already rotated.
Putting it all together, we have:
h = 1.5 * sin(π/4 + θ)
This equation gives us the height of point P after the windmill blade rotates by an angle of θ.
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the length of a rectangular piece of sheet metal is longer than its width. a square piece that measures on each side is cut from each corner, then the sides are turned up to make a box with volume . find the length and width of the original piece of sheet metal.
Answers
The width of the original piece of sheet metal is (w^2 - l^2)/(3w + 3l), and the length is (l^2 - w^2)/(3w + 3l).
To solve this problem, we can use the formula for the volume of a rectangular box, which is V = lwh, where l is the length, w is the width, and h is the height.
First, let's find the height of the box. Since we cut squares from each corner, the height of the box is the length of the square that was cut out. Let's call this length x.
The width of the box is the original width minus the lengths of the two squares that were cut out, which is w - 2x.
Similarly, the length of the box is the original length minus the lengths of the two squares that were cut out, which is l - 2x.
Now we can write the volume of the box in terms of x, w, and l:
V = (w - 2x)(l - 2x)(x)
Expanding this expression, we get:
V = x(4wl - 4wx - 4lx + 8x^2)
Simplifying further:
V = 4x^3 - 4wx^2 - 4lx^2 + 4wlx
To find the dimensions of the original piece of sheet metal, we need to maximize this volume. We can do this by taking the derivative of the volume with respect to x and setting it equal to zero:
dV/dx = 12x^2 - 8wx - 8lx + 4wl = 0
Solving for x, we get:
x = (2wl)/(3w + 3l)
Now we can use this value of x to find the width and length of the original piece of sheet metal:
w - 2x = w - 2(2wl)/(3w + 3l) = (w^2 - l^2)/(3w + 3l)
l - 2x = l - 2(2wl)/(3w + 3l) = (l^2 - w^2)/(3w + 3l)
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