The coordinates of the focus are (2,-7/4), the coordinates of the endpoints of the latus rectum are (3/2,-7/4) and (5/2,-7/4). The equation of the directions is y=-9/4, and the equation of the axis of symmetry is x=2.
Answers
General equation of a parabola:
[tex](x-h)^2=4p(y-k)[/tex]Equation of the axis of symmetry:
x = h
In this case, the axis of symmetry is x = 2, then h = 2.
Equation of the directrix:
y = k - p
In this case, the equation of the directrix is y = -9/4, then:
-9/4 = k - p (eq. 1)
Equation of the focus:
F(h, k+p)
In this case, the coordinates of the focus are (2,-7/4), then:
-7/4 = k + p (eq. 2)
Adding equation 1 to equation 2:
-9/4 = k - p
+
-7/4 = k + p
--------------------
-4 = 2k
(-4)/2 = k
-2 = k
Substituting this result into equation 2 and solving for p:
-7/4 = -2 + p
-7/4 + 2 = p
1/4 = p
Substituting with h = 2, k = -2, and p = 1/4 into the general equation, we get:
[tex]\begin{gathered} (x-2)^2=4\cdot\frac{1}{4}(y-(-2)) \\ (x-2)^2=y+2 \end{gathered}[/tex]
Related Questions
How do I find the sum of this equation and express it in simplest form [tex]( {n}^{3} - 5n - 2) + (4 {n}^{3} + n - 4)[/tex]
Answers
A variable needs to be eliminated to solve the system of equations. Choose the correct first step: -3x+8y=-294x-8y=28A. Add to eliminate xB.Subtract to eliminate yC.Add to eliminate yD. Subtract to eliminate x
Answers
From the given equations, we can note that coeffcients of variable y are opposite. This means that, in order to eliminate y, we can add both equations. Then, the answer is C
The table below shows the average amount of time spent per person on entertainment per year from 2000 to 2005.Year Hours2000 34922001 35402002 36062003 36632004 37572005 3809(a) Use a graphing calculator or spreadsheet program to find a quadratic model that best fits this data. Let t represent the year, with t=0 in 2000. Round each coefficient to two decimal places.Pt =(b) Based on this model, how many hours would you expect the average person to spend on entertainment in 2012? Round your answer to the nearest whole number.hours(c) When would you expect the average amount of entertainment time to reach 4000? Give your answer as a calendar year (ex: 1997).During the year
Answers
EXPLANATION
Given the table,
Year Hours
2000 3492
2001 3540
2002 3606
2003 3663
2004 3757
2005 3809
Plugging in the data into a graphing calculator with a quadratic regression model AX^2+BX+C:
The function is:
P(t) = 2.35714 X^2 -9376.16 X +9325921.701
B)
When the time is 2012 substituting on the function:
P(t) = 2.357*(2012)^2 - 9,374.84*(2012) + 9.3246X10^6 = 3897.32
Hence, the number of hours spent in 2012 would be 3897 hours.
C) By using the graph, we can expect that the average amount of entertainment time to reach 4000 would be 9,540,465 hours.
Over the weekend, Devon baked 12 muffins. She divided them evenly among 3 plates to giveto neighbors.The letter m stands for the number of muffins on each plate. Which equation can you use tofind m?12 x 3 = m12 : 3 = m
Answers
The information given is listed below:
number of muffins (m) = 12, number of plates = 3
number of muffin on each plate = number of muffins /
-Convert the following into given base units of measurement. (Refer to slide 21 &27 on uploaded ppt).
1. 3.65 mg =______ dg
2. 9.987 g =______ hg
3. 12.203 km =______ mm
Answers
The conversion of the given base units of measurements are
Part 1
3.65 mg = 0.0365 dg
Part 2
9.987 g = 0.09987 hg
Part 3
12.203 km = 12203072.2 mm
Part 1
The given quantity is 3.65 mg
mg is the milligram and dg is the decigram
We know
1 mg = 0.01 dg
Then,
3.65 mg = 3.65×0.01
Multiply the terms
3.65 mg = 0.0365 dg
Part 2
The given quantity is 9.987 g
g is the gram and hg is the hectogram
1 g = 0.01 hg
Then,
9.987 g = 0.09987 hg
Part 3
The given quantity is 12.203 km
km is the kilometer and mm is the millimeter
1 km = 1000000 mm
12.203 km = 12203072.2 mm
Hence, the conversion of the given base units of measurements are
Part 1
3.65 mg = 0.0365 dg
Part 2
9.987 g = 0.09987 hg
Part 3
12.203 km = 12203072.2 mm
Learn more about conversion here
brainly.com/question/9481766
#SPJ1
I’m in AP Calc AB and can’t figure this out. Any idea?
Answers
Answer::
[tex]f^{\prime}(x)=7x\sec x\tan x+7\sec x+\frac{1}{x}[/tex]Explanation:
Given f(x) defined below:
[tex]f(x)=\ln x+7x\sec x[/tex]The derivative is calculated below.
[tex]\begin{gathered} \frac{d}{dx}\lbrack f(x)\rbrack=\frac{d}{dx}\lbrack\ln x+7x\sec x\rbrack \\ =\frac{d}{dx}\lbrack\ln x\rbrack+\frac{d}{dx}\lbrack7x\sec x\rbrack \\ Take\text{ the constant 7 outside the derivative sign.} \\ =$$\textcolor{red}{\frac{d}{dx}\lbrack\ln x\rbrack}$$+7\frac{d}{dx}\lbrack x\sec x\rbrack \\ \text{The derivative of }\ln (x)=\frac{1}{x},\text{ therefore:} \\ $$\textcolor{red}{\frac{d}{dx}\lbrack\ln x\rbrack}$$+7\frac{d}{dx}\lbrack x\sec x\rbrack=$$\textcolor{red}{\frac{1}{x}}$$+7\frac{d}{dx}\lbrack x\sec x\rbrack\cdots(1) \end{gathered}[/tex]Next, we find the derivative of x sec x using the product rule.
[tex]\begin{gathered} \frac{d}{dx}\lbrack x\sec x\rbrack=x$$\textcolor{blue}{\frac{d}{dx}\lbrack\sec x\rbrack}$$+\sec x\frac{d}{dx}\lbrack x\rbrack\text{ } \\ The\text{ derivative of sec(x), }\text{\textcolor{red}{ }}\textcolor{red}{\frac{d}{dx}\lbrack\sec x\rbrack=\sec x\tan x} \\ =x$$\textcolor{blue}{\lbrack\sec x\tan x\rbrack}$$+\sec x \end{gathered}[/tex]Substitute the result into equation (1) above.
[tex]\begin{gathered} \frac{1}{x}+7\frac{d}{dx}\lbrack x\sec x\rbrack=\frac{1}{x}+7(x\sec x\tan x+\sec x) \\ =7x\sec x\tan x+7\sec x+\frac{1}{x} \end{gathered}[/tex]Therefore:
[tex]f^{\prime}(x)=7x\sec x\tan x+7\sec x+\frac{1}{x}[/tex]solve the system. given your answer as (x, y, z)-4x -y - 3z = -5-6x + y - 3z = -172x + 2y - z = - 10
Answers
Answer:
(1, -5 ,2)
Explanation:
Given the system of equations:
[tex]\begin{gathered} -4x-y-3z=-5\ldots(1) \\ -6x+y-3z=-17\ldots(2) \\ 2x+2y-z=-10\ldots(3) \end{gathered}[/tex]Make z the subject in the third equation:
[tex]z=2x+2y+10[/tex]Substitute z=2x+2y+10 into the first and second equations:
First Equation
[tex]\begin{gathered} -4x-y-3z=-5 \\ -4x-y-3(2x+2y+10)=-5 \\ -4x-y-6x-6y-30=-5 \\ -4x-6x-y-6y=-5+30 \\ -10x-7y=25\ldots(4) \end{gathered}[/tex]Second Equation
[tex]\begin{gathered} -6x+y-3z=-17 \\ -6x+y-3(2x+2y+10)=-17 \\ -6x+y-6x-6y-30=-17 \\ -6x-6x+y-6y=-17+30 \\ -12x-5y=13\ldots(5) \end{gathered}[/tex]Next, solve equations 4 and 5 simultaneously:
[tex]\begin{gathered} -10x-7y=25\ldots(4) \\ -12x-5y=13\ldots(5) \end{gathered}[/tex]Multiply equation (4) by 5 and equation (5) by 7.
[tex]\begin{gathered} -50x-35y=125 \\ -84x-35y=91 \\ \text{Subtract same sign} \\ 34x=34 \\ x=\frac{34}{34} \\ x=1 \end{gathered}[/tex]Substitute x=1 into equation (4):
[tex]\begin{gathered} -10x-7y=25\ldots(4) \\ -10(1)-7y=25 \\ -7y=25+10 \\ -7y=35 \\ y=\frac{35}{-7} \\ y=-5 \end{gathered}[/tex]Recall: z=2x+2y+10
[tex]\begin{gathered} z=2x+2y+10 \\ =2(1)+2(-5)+10 \\ =2-10+10 \\ z=2 \end{gathered}[/tex]The solution of the system is:
[tex](1,-5,2)[/tex]The number of compounding periods is equal to what: what is the formuls
Answers
Answer
When compound interest is discussed, the time rate for the compound interest is usually mentioned. For example, they would say that
- a certain amount of money has its interest compounded at 5% annually,
- a certain amount of money has its interest compounded at 7% every 3 months,
- a certain amount of money has its interest compounded at 2% every 6 months,
In each of the examples given above, the compounding period is 1 year, 3 months and 6 months respectively.
If one is now asked to calculate the compound interst on a particular amount of money after time, T, we usually express this time T in terms of the number of time periods, t, that exist inside the given time T.
Hence, the time T is expressed in terms of time period t, as
T = nt
Such that the number of compounding periods in T is given as
n = (T/t)
[tex]undefined[/tex]what will the inflation-adjusted cost of a $154,600 house be in 5 years? round to two decimal places.
Answers
The inflation-adjusted cost of the house is $166,548.11
Explanation:[tex]\begin{gathered} The\text{ funcion the inflation adjusted cost:} \\ C(t)\text{ = C}_0(1\text{ + r\rparen}^t \\ r\text{ = rate} \\ \text{t = time} \\ C_0\text{ = cost of product} \end{gathered}[/tex][tex]\begin{gathered} From\text{ the information in the question:} \\ C_0\text{ = cost of house =\$154600} \\ r\text{ = 1.5\% = 0.015} \\ t\text{ = 5 years} \\ C(t)\text{ = ?} \\ We\text{ need to find the inflation adjusted cost using the function we were given in the question} \end{gathered}[/tex]substitute the values into the formula:
[tex]\begin{gathered} C(t)\text{ = 154600\lparen1 + 0.015\rparen}^5 \\ C(t)\text{ = 154600\lparen1.015\rparen}^5 \\ C(t)\text{ = 166548.107} \\ \\ To\text{ 2 decimal place, C\lparen t\rparen = 166548.11} \end{gathered}[/tex]The inflation-adjusted cost of the house is $166,548.11
The directions says state if the two triangles are congruent. If they are state how you know
Answers
From the diagram, we see that the triangles have:
• equal hypotenuse,
,• equal base.
HL Theorem states that if the hypotenuse and leg of a right triangle are congruent to the hypotenuse and leg of another right triangle, then the two triangles are congruent.
We conclude that the triangles are congruent because of HL Theorem.
AnswerB) HL
ylinders, cone Justin uses the mold picture cement column posts to use a height of the Cylinder = 18 in To make a post, Justin completel wet cement How much wet cement, in cubic inche make 4 posts? dus 3 in Formula Sheet
Answers
Michael earns a weekly salary of $365 plus a 6% commission of sales for the week. Last week, Michael's sales totaled $3200. How much did he make in commission? What was Michael's total pay?
Answers
Michael's sales are $3200, then the comission is
[tex]3200\times0.06=192,[/tex]$192 in comission.
Then the total pay is
[tex]365+192=557.[/tex]$567
an office administrator has an office supply budget $150. The office administrator will purchase folders, which are $2.15 each and notebooks, which are $4.60 each. which inequality represent the constrain on the number of folders f and notebook n the office administrator can purchase
Answers
If the price of each folder is $2.15, and the amount of folders is f, the total price paid for folders is the product of the unitary price by the amount bought.
[tex]\text{price}1=2.15f[/tex]Similarly, the price paid for notebooks is the unitary price of one notebook ($4.60) multiplied by the amount of notebooks (n).
[tex]\text{price}2=4.6n[/tex]Finally, the total cost of both products together is the sum of these products.
[tex]\text{cost}=\text{price}1+\text{price}2=2.15f+4.6n[/tex]The supply budget is $150, so the total cost needs to be lesser than or equal this value.
Therefore, we have that:
[tex]\begin{gathered} \text{cost}\le150 \\ 2.15f+4.6n\le150 \end{gathered}[/tex]So the correct option is B.
question is in image
Answers
The function f(x) is given by,
[tex]f(x)=x^2[/tex]The function g(x) is given by,
[tex]g(x)=\frac{-2}{3}x^2[/tex]If f(x) becomes -kf(x), where 0Comparing the above functions, we get
[tex]g(x)=-\frac{2}{3}f(x)[/tex]So, k=2/3. Hence, 0 < 2/3 < 1.
Therefore, the graph of g(x) is the graph of f(x) compressed vertically and reflected across the x axis.
Hence, option D is correct.
A metal plate has the form of a quarter circle with a radius of R = 106cm . Two 3 cm holes are to be drilled in the plater r = 95cm from the corner at 30 degrees and 60as shown above. To use a computer controlled milling machine you must know the Cartesian coordinates of the holes. Assuming the origin is at the corner what are the coordinates of the holes (x_{1}, y_{1}) and (x_{2}, y_{2}) ? Round your answer to 3 decimal places
Answers
1) Considering that this quarter circle is one sector of the unit circle and that
[tex]30^{\circ}=\frac{\pi}{6}[/tex]2) Let's sketch this out to better grasp the idea:
Note that the first coordinate will be given by its cos(theta), and the second one by its sine(theta)
3) Based on that principle, we can tell the following:
[tex]\begin{gathered} (x_1,y_1)--->(cos(30^{\circ}),\sin(30^{\circ}))=(\frac{\sqrt{3}}{2},\frac{1}{2}) \\ \\ (x_{2,}y_2)-->(\cos(60),\sin(60))=(\frac{1}{2},\frac{\sqrt{3}}{2}) \\ \end{gathered}[/tex]As the holes need to be drilled by the machine, so we need to find approximations to those coordinates:
[tex]\begin{gathered} (x_1,\:y_1)-->(0.866,0.500) \\ (x_2,y_2)-->(0.500,0.866) \end{gathered}[/tex]Thus, these are the coordinates to be put into the computer.
е A Chinese restaurant has a large goldfish pond. Suppose that an inlet pipe and a hose together can fill the pond in 3 hours. The inlet pipe alone can complete the job in one hour less time than the hose alone. Find the time that the hose can complete the job alone and the time that the inlet pipe can complete the job alone. ntents Library The time that the hose can complete the job alone is (?) hours. (Round to the nearest tenth.) The time that the inlet pipe can complete the job alone is (? )hours. (Round to the nearest tenth.) nizer
Answers
SOLUTION
Let the time for the pipe to complete the Job be represented as
[tex]p[/tex]Let the time for the hose to complete the Job be represented as
[tex]h[/tex]The pipe and the hose completed the job in 3hours
Hence we have the equation
[tex]p+h=3[/tex]The inlet pipe alone can complete the job in one hour less time than the hose alone implies that
[tex]h-p=1[/tex]This leads to a system of equation which we now solve simultaneously
[tex]\begin{gathered} h+p=3\ldots\text{.eq}1 \\ h-p=1\ldots\text{.}\mathrm{}eq2 \end{gathered}[/tex]Adding eq1 and eq2, we o btain
[tex]\begin{gathered} 2h=4 \\ h=\frac{4}{2}=2 \end{gathered}[/tex]Substituting the value of h into eq1 we have
[tex]\begin{gathered} h+p=3 \\ 2+p=3 \\ p=3-2 \\ p=1 \end{gathered}[/tex]Therefore
[tex]h=2,\text{ p=1}[/tex]The time that the inlet pipe can complete the job alone is 1 hours
The time that the hose can complete the job alone is 2 hours
If a = 6, which of the following is equal to a 2?1o-36O O-122
Answers
Solution:
The question given is a negative exponent.
To solve this, we apply the law of indices for negative exponents.
Negative exponent law is indicated below;
[tex]a^{-x}=\frac{1}{a^x}[/tex]Thus, applying this law to the question;
[tex]a^{-2}=\frac{1}{a^2}[/tex]Given:
a = 6
Substituting a = 6 into the expression, we have;
[tex]\frac{1}{a^2}=\frac{1}{6^2}[/tex]Therefore, the correct answer is;
[tex]\frac{1}{6^2}[/tex]Given the Exponential Equation, determine the Initial Value and Rate of Change as a Percent for each of the following.
Answers
The formula for calculating exponential growth is expressed as
y = a(1 + r)^n
where
a is the initial value
y is the final value
n is the time
r is the growth rate
The formula for calculating exponential decay is expressed as
y = a(1 - r)^n
For y = 1010(1.05)^x,
initial value = 1010
1 + r = 1.05
r = 1.05 - 1 = 0.05
Since it is positive, it is exponential growth
Growth percent = 0.05 x 100 = 5%
For y = 4932(1.26)^x,
initial value = 4932
1 + r = 1.26
r = 1.26 - 1 = 0.26
Growth percent = 0.26 x 100 = 26%
For y = 2835(1.065)^x,
initial value = 2835
1 + r = 1.065
r = 1.065 - 1 = 0.065
Since it is positive, it is exponential growth
Growth percent = 0.065 x 100 = 6.5%
For y = (0.96)^t,
initial value = 1
1 - r = 0.96
r = 1 - 0.96 = 0.04
decay percent = 0.04 x 100 = 4%
For y = 4660(0.89)^x,
initial value = 4660
1 - r = 0.89
r = 1 - 0.89 = 0.11
decay percent = 0.11 x 100 = 11%
For y = 3078(1.09)^t,
initial value =3078
1 + r = 1.09
r = 1.09 - 1 = 0.09
Growth percent = 0.09 x 100 = 9%
The table shows x- and y-values for the equation y = 3x -1 Which number is missing in the table? 23 15 20 37
Answers
y = 3x-1
When x = 8
y = 3(8) -1
y = 24-1
y = 23
In a class of 10 students, the ratings are given based on their performance on a test. The following data was taken from ratings given by the class teacher:5, 1, 2, 4, 2, 3, 5, 3, 3, 4Do the ratings earned by the students follow a normal distribution? aNo, because the mean and mode are same bYes, because the data is symmetrical about the mean 3 cNo, because the data is not symmetrical dYes, because the mean is greater than the mode of the data set
Answers
Given:
In a class of 10 students, the ratings are given based on their performance on a test. The following data was taken from ratings given by the class teacher:
5, 1, 2, 4, 2, 3, 5, 3, 3, 4
Required:
To choose the correct option
metro atlanta home prices are rising rapidly, and much of its a soaring demand from deep-pocketed investors,as reported in the AJC March 21st of this year. In March2022, the median sale price of a home in the Metro area was $401,500. Before the the pandemic hit, in january2020, the median sale price was $279,000 Find the rate increase of the average cost of a home in Atlanta from january2020 before the pandemic hit Atlanta to the present
Answers
We are asked to determine the rate of increase in the value of a home,
We need to have into account that at the beginning of the considered period the cost was 279000 and after two years the cost is 401500, therefore, we can use the following formula:
[tex]r=\frac{\Delta C}{\Delta t}[/tex]Where:
[tex]\begin{gathered} \Delta C=\text{ difference in cost} \\ \Delta t=\text{ difference in time} \end{gathered}[/tex]Now, we substitute the values:
[tex]r=\frac{401500-279000}{2}[/tex]Solving the operations:
[tex]r=61250[/tex]Therefore, the rate is an increase of $61250 per year.
Saul reads every week. In his first week of reading, he read 50 pages. Each week after that, he read 65 pages. Which expression represents the total number of pages Saul has read, where w represents the number of weeks since he first started reading.
Answers
Given
In first week , he read 50 pages.
After first week , he read 65 pages.
Find
Expression represents the total number of pages Saul has read
Explanation
Let w represents the number of weeks since he first started reading.
Assume y represent number of pages.
when w = 1 then y = 50 ; w = 2 then y = 65+50=115
we know the equation of line
y = mw + c
so ,
50 = m + c .........(1)
and
115 = 2m + c ............(2)
on solving equation (1) and (2) , we get m = 65 and c = -15
so ,
y = 65w - 15
Final Answer
Therefore , the correct option is 3rd
My teacher gave the answer on the right but I want know how he did it
Answers
the given number is 6^4
here is the calculation.
[tex]6^4=6\times6\times6\times6[/tex]multiply the number 6 by the times of 4
now by multiplication, the answer is
[tex]6^4=1296[/tex]so, the answer is 1296.
twice a number decreased by 4 Is atleast 12
Answers
EXPLANATION
The appropiate relationship is:
2x - 4 = 12
Adding +4 to both sides:
2x = 12 + 4
Adding numbers:
2x = 16
Dividing both sides by 2:
x = 16/2
Simplifying:
x = 8
The solution is 8
Find the y-intercept of the line.y = 3.1x+2.6y-intercept:
Answers
To find the y-intercept in any equation equate x by 0
The given equation is
[tex]y=3.1x+2.6[/tex]Substitute x by 0 to find the y-intercept
[tex]\begin{gathered} y=3.1(0)+2.6 \\ \\ y=0+2.6 \\ \\ y=2.6 \end{gathered}[/tex]The y-intercept is 2.6
the total amount of flour in a bakery after receiving new stock equal to 3/10 of its current stock (x)Find the expression that represents the scenario
Answers
Answer:
(3/10)x
Explanation:
The expression that represents the scenario is an expression that we can use to calculate the total amount of flour, so the correct expression is:
[tex]\frac{3}{10}x[/tex]Because the amount of flour is 3/10 of x ( the current stock)
I NEED SOME HELP PLEASE ;n; .Zan took her dog, Simba, to the dog park on Saturday afternoon. There were less than 15 dogs running around the park when they arrived.
Determine which inequality describes the dogs at the park.
d < 15
d > 15
d ≤ 15
d ≥ 15
Answers
Answer:
I am pretty sure that it is d < 15
Explanation:
> means greater than
< means less than
≤ means less than or equal too
≥ means greater than or equal to
So the only only one that makes sense is <
Express the given Hindu-Arabic numeral in expanded form 26
Answers
Given:
The numeral is 26.
To find: The expanded form
Explanation:
As we know,
Expanded form or expanded notation is a way of writing numbers to see the math value of individual digits.
Separating the numbers into the individual place values, we get
[tex]26=(2\times10)+(6\times1)[/tex]Final answer: The expanded form of 26 is,
[tex](2\times10)+(6\times1)[/tex]Keisha has four favorite shirts one blue, one green, one red, one yellow and two favorite pairs of pants one black and one brown she decides to randomly choose a pair of pants and a shirt to wear for the day. What is the probability that Keisha chooses and outfit that is yellow and black or red and brown round your answer to the nearest whole percent?
Answers
Answer:
25%
Explanation:
First, let's calculated the total number of outfits that Keisha can choose. So, we will use the rule of multiplication as:
4 * 2 = 8
Shirts Pants
Because she has 4 options for shirts and 2 options for pants. So, there 8 possible outfits.
Then, from those outfits, there is 1 that is yellow and black, and 1 that is red and brown. So, the probability that Keisha chooses an outfit that is yellow and black or red and brown is:
[tex]P=\frac{1+1}{8}=\frac{2}{8}=0.25=25\text{ \%}[/tex]Therefore, the answer is 25%
A scale for a skyscraper blueprint is 1 inch = 40 feet. The height of theskyscraper is 640 feet and the width is 540 feet. What are the height andwidth in inches of the scale drawing of the skyscraper
Answers
Answer:
The height of the scale drawing of the skyscraper is 16 inches.
The width of the scale drawing of the skyscraper is 13.5 inches.
Explanation:
Given the scale of the model as 1 inch = 40 feet.
Let h represent the height of the scale drawing of the skyscraper. Given the actual height of the skyscraper as 640 feet, we can go ahead and determine h by setting up proportions as shown below;
[tex]\begin{gathered} \frac{1\text{inch}}{40\text{ ft}}=\frac{h\text{ in}}{640ft} \\ h=\frac{640\times1}{40} \\ h=16\text{inches} \end{gathered}[/tex]Let w represent the width of the scale drawing. Given the actual width of the skyscraper as 540 feet, we can go ahead and solve for w by setting up proportions as shown below;
[tex]\begin{gathered} \frac{1in}{40ft}=\frac{w\text{ in}}{540ft} \\ w=\frac{540\times1}{40} \\ w=13.5\text{inches} \end{gathered}[/tex]