The points where the curve intersect the paraboloid is (2, 0, 4).
To find the points of intersection, we set the two equations equal to each other and solve for x, y, and z.
Now, to find the point where the curve r(t) intersects the paraboloid z = x² + y², we can substitute the given value of t into the parametric equations of the curve.
The curve is defined as:
r(t) = t i + (2t - t²) k
where i and k are unit vectors in the x and y directions, respectively.
value of t is given.
Setting t = 2, we have:
x = 2
y = 2(2) - (2)² = 0
z = x² + y² = 4 + 0 = 4
So, the point of intersection is (2, 0, 4).
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_____The given question is incorrect, the correct question is given below:
At what point does the curve r(t)=ti+(2t−t2)k, where t= 2
intersect the paraboloid z=x²+y².
What is the sum of the distinct prime factors of the number 560?
A. 20
B. 14
C. 18
D. 16
E. 1488
The sum of the distinct prime factors is (b) 14
How to determine the sum of the distinct prime factorsFrom the question, we have the following parameters that can be used in our computation:
distinct prime factors of the number 560
The distinct prime factors of the number 560 are
Factors = 2, 5, 7.
When these numbers are added, we have
Sum = 2 + 5 + 7
Evaluate
Sum = 14
Hence , the sum is (b) 14
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6) Brand X sells 25 kg bags of mixed nuts
that contain 41% peanuts. To make their
product they combine Brand A mixed nuts
which contain 35% peanuts and Brand B
mixed nuts which contain 45% peanuts.
How much of each do they need to use?
Given the following cash inflow at the end of each year, what is the future value of this cash flow at 5%, 8%, and 17% interest rates at the end of year 7? What is the future value of this cash flow at 5% interest rate at the end of year 7?
A $1000 cash inflows at the end of each year would have a future value of $8,142.01, $8,922.80 and $11.772012 at the end of the year 7 for interest rates of 5% , 8% and 17% respectively.
Future Value:Annuities are a financial instrument that generates a regular stream of cash. They have both a present and future value dependent upon the value of the cash payment, the number of payment periods and the interest rate. This question does not specify the cash inflow amount so an answer will be generated that can be scaled on multiples of $1000.
Let C represent the cash inflow at the end of each year. The future value (FV) of this cash inflow is given by:
FV = [tex]C[((1+i)^n-1)/i][/tex]
where i is the annual interest rate and n is the number of years.
(a) For i = 5% and n = 7
FV = [tex]C [((1+0.05)^7-1)/0.05][/tex]
FV= C[(1.047100-1)/0.05]
FV = C [8.142008]
(b) For i = 8% and n = 7
FV = [tex]C [((1+0.08)^7-1)/0.08][/tex]
FV = C[(1.713824 - 1)/0.08]
FV = C[8.922803]
(c) For i = 17% and n = 7
FV = [tex]C [((1+0.17)^7-1)/0.17][/tex]
FV = C[(3.001242 - 1)/ 0.17]
FV = C[11.772012]
Therefore, A $1000 cash inflows at the end of each year would have a future value of $8,142.01, $8,922.80 and $11.772012 at the end of the year 7 for interest rates of 5% , 8% and 17% respectively.
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help me answer this pls
Since [tex]1 - \sin^{2}{\theta} = \cos^{2}{\theta}[/tex], the trigonometric expression [tex]\frac{\sin{\theta}}{\sqrt{1 - \sin^{2}{\theta}}} = \tan{\theta}[/tex] is proven.
How to prove the trigonometric expression?The trigonometric expression for this problem is defined as follows:
[tex]\frac{\sin{\theta}}{\sqrt{1 - \sin^{2}{\theta}}} = \tan{\theta}[/tex]
The identity used for the proof is given as follows:
[tex]\sin^{2}{\theta} + \cos^{2}{\theta} = 1[/tex]
Hence:
[tex]1 - \sin^{2}{\theta} = \cos^{2}{\theta}[/tex]
Replacing on the left side of the expression, we have that:
[tex]\frac{\sin{\theta}}{\sqrt{1 - \sin^{2}{\theta}}} = \frac{\sin{\theta}}{\sqrt{cos^{2}{\theta}}}[/tex]
Taking the square root:
[tex]\frac{\sin{\theta}}{\sqrt{1 - \sin^{2}{\theta}}} = \frac{\sin{\theta}}{\cos{\theta}}[/tex]
The tangent is given as the division of the sine by the cosine, hence:
[tex]\frac{\sin{\theta}}{\cos{\theta}} = \tan{\theta}[/tex]
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which one of the following best describes the notion of the significance level of a hypothesis test?The probability of observing a sample statistic more extreme than the one actually obtained, assuming the null hypothesis is true
The probability of the type I error
The probability of the type II error
The Hypothesis test of probability of the type I error is True.
The Hypothesis test probability of the type II error is False.
The notion of the significance level of a hypothesis test is best described by the probability of observing a sample statistic more extreme than the one actually obtained, assuming the null hypothesis is true. This is also known as the "p-value." A significance level is often set beforehand, such as alpha (α) = 0.05, and if the p-value is less than alpha, the null hypothesis is rejected.
The probability of a type I error is related to the significance level. A type I error occurs when the null hypothesis is rejected when it is actually true. The probability of a type I error is represented by alpha (α) and is the level of significance that was set for the test.
The probability of a type II error is the probability of failing to reject a false null hypothesis. It is represented by beta (β) and depends on the sample size, the true value of the parameter being tested, and the level of significance set for the test.
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Three numbers are given below. Use prime factorisation to determine the HCF and LCM 1848, 132 and 462
Answer:
The HCF is the highest common factor of 1848, 132 and 462, which is 14.Step-by-step explanation:
Prime factorisation is a mathematical method that breaks a number down into its prime factors, the smallest positive integers that are multiples of that number.The highest common factor of 1848, 132 and 462 is the smallest number that divides all three.The lowest common multiple is the smallest number that multiples all three numbers!The graph represents y = −1/4 x − 3. Which coordinate pair is NOT a solution for the equation? Responses A(−8, −1) (−8, −1) B(0, −3) (0, −3) C(−2, −4) (−2, −4) D(4, −4) (4, −4) Question 2
The equation given in the problem is shown below:
[tex]y=-\frac{1}{4} x-3[/tex]
Here are the answer choices:
a) (-8,-1)
b) (0,-3)
c) (-2,-4)
d) (4,-4)
We are asked to choose the coordinate pair that is NOT a solution, so let's just test each option!
To test answer choice "a", plug in [tex]x=-8[/tex] and [tex]y=-1[/tex] into the original equation, then simplify:
Plug in values: [tex]-1=-\frac{1}{4} (-8)-3[/tex]
Multiply: [tex]-1=2-3[/tex]
Subtract: [tex]-1=-1[/tex]
Notice that we now have a true expression, therefore option "a" IS A SOLUTION, and is thus not the correct answer.
Repeat for option "b" (0, -3):
Plug in values: [tex]-3=-\frac{1}{4}(0)-3[/tex]
Multiply: [tex]-3=-3[/tex]
Notice that we now have a true expression, therefore option "b" IS A SOLUTION, and is thus not the correct answer.
Repeat for option "c" (-2, -4):
Plug in values: [tex]-4=-\frac{1}{4}(-2)-3[/tex]
Multiply: [tex]-4=\frac{1}{2} -3[/tex]
Subtract: [tex]-4=-\frac{5}{2}[/tex]
Notice that we now have a false expression, therefore option "c" IS NOT SOLUTION, and is thus the correct answer.
To ensure we have the right option, check option "d" as well (4, -4):
Plug in values:[tex]-4=-\frac{1}{4} (4)-3[/tex]
Multiply: [tex]-4=-1-3[/tex]
Subtract: [tex]-4=-4[/tex]
Notice that we now have a false expression, therefore option "d" IS A SOLUTION, and is thus not the correct answer.
Notice that we have now checked all possible options and only option "c" was evaluated as a false expression, therefore option C is the correct choice in regard to this question.
Let me know if you have any questions!
When a number is increased by 5%, the result is 25. What is the original number to the nearest tenth?
Anwser : 23.8
Step 1: Subtract 5% from 25.
25 - (5% of 25) = 25 - (0.05 x 25)
Step 2: Simplify the equation.
25 - (0.05 x 25) = 25 - 1.25
Step 3: Subtract 1.25 from 25.
25 - 1.25 = 23.75
Which of the following values is a rational number?
A. O √²
B. O √49+√7
C. O √225+ √169
D. O √2x √121
E. O √11x16
The expression whose value is a rational number will be √(4)² and √225+ √169. Then the correct options are A and C.
What is a rational number?If the value of a numerical expression is terminating then they are the rational number then they are called a rational number and if the value of a numerical expression is non-terminating then they are called an irrational number.
Let's check all the options, then we have
A. √(4)² = 4, is a rational number.
B. √49 + √7 = 7 + √7, is an irrational number.
C. √225+ √169 = 25 + 13, is a rational number.
D. √2 x √121 = 11√2, is an irrational number.
E. √11 x 16 = 4√11, is an irrational number.
The expression whose value is a rational number will be √(4)² and √225+ √169. Then the correct options are A and C.
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A student has a collection of 72 baseball cards. All of the cards are stored in
an album with 8 cards on each page. Which expression can be used to find the
total number of pages of baseball cards in the student's album?
The required expression that can be used to find the total number of pages of baseball cards in the student's album is P = 72 / 8.
What are equation models?The equation model is defined as the model of the given situation in the form of an equation using variables and constants.
To find the total number of pages of baseball cards in the student's album, we need to divide the total number of cards by the number of cards per page.
Let's call the number of pages "P". Then we have:
P = 72 / 8
So, the number of pages is equal to 9.
So, the expression that can be used to find the total number of pages of baseball cards in the student's album is P = 72 / 8.
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If m∠A = 50° and m∠B = 45°, what is m∠H?
(If anyone knows all the answer to any of these please provide a link.)
(It's called Chapter 5 Test, 3B Ratio, Proportion, and Similar Figures)
The measure of m∠H in the triangle is 85°.
How to find the measure of m∠H?
Similar triangles are two triangles that have the same shape but can have different sizes. More specifically, two triangles are similar if their corresponding angles are congruent and their corresponding sides are proportional.
Since ΔABC and ΔFGH are similar, we can say:
m∠A = m∠F
m∠B = m∠G
m∠C = m∠H
m∠A + m∠B + m∠C = 180° (sum of angles in a triangle)
We have m∠A = 50° and m∠B = 45°
50° + 45° + m∠C = 180°
m∠C = 180° - 50° - 45°
m∠C = 85°
Since m∠C = m∠H
Thus, m∠H = 85°
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If you flip a coin 8 times, what is the best prediction possible for the number of times it will land on tails?
Need help!
Use the Savings plan to find the amount A=? if monthly payments are $250 with APR=4% for 10 years.
[tex]{ \qquad\qquad\huge\underline{{\sf Answer}}} [/tex]
Here we go ~
The required formula is :
[tex] \qquad \dashrightarrow \sf \: A = P \times \dfrac{{\bigg(1 + \dfrac{APR}{n} \bigg) }^{ny} - 1}{\dfrac{APR}{n}}[/tex]
[tex] \textsf{A = Total accumulated savings } [/tex][tex] \textsf{P = regular deposit } [/tex][tex] \textsf{APR = annual percentage rate } [/tex][tex] \textsf{n = number of payment period per year} [/tex][tex] \textsf{y = number of years } [/tex]Now, plug in the values ~
[tex] \qquad \dashrightarrow \sf \: A = 250 \times \dfrac{{\bigg(1 + \dfrac{0.04}{12} \bigg) }^{(12 \times 10)} - 1}{\dfrac{0.04}{12}}[/tex]
[tex] \qquad \dashrightarrow \sf \: A = 250 \times \dfrac{{\bigg(1 + 0.0033 \bigg) }^{(12 0)} - 1}{0.0033}[/tex]
[tex] \qquad \dashrightarrow \sf \: A = 250 \times \dfrac{{\bigg(1.0033 \bigg) }^{(12 0)} - 1}{0.0033}[/tex]
[tex] \qquad \dashrightarrow \sf \: A = 250 \times \dfrac{1.4908- 1}{0.0033}[/tex]
[tex] \qquad \dashrightarrow \sf \: A = 250 \times \dfrac{0.4908}{0.0033}[/tex]
[tex] \qquad \dashrightarrow \sf \: A = 250 \times 147.249[/tex]
[tex] \qquad \dashrightarrow \sf \: A = 250 \times 147.2498[/tex]
[tex] \qquad \dashrightarrow \sf \: A = 250 \times 147.2498[/tex]
[tex] \qquad \dashrightarrow \sf \: A =\$ 36812.45[/tex]
That's the required value ~
What is the equation of this graph
In this equation, the value of x is fixed at 2, which means that every point on the graph will have the same x-coordinate value of 2. This creates a vertical line that passes through the point (2, y), where y can be any real number.
Therefore, the proper equation for the graph presented is:
[tex]x=2[/tex]
{10x + 7y= - 12
9x+ 5y = -16
Answer: x=-4, y=4
Step-by-step explanation:
We can use elimination method to solve this problem.
Let's eliminate y.
In equation 2, use the coefficient of y (i.e 5) to multiply equation 1. DO the same for other equation. Thus,
5(10x+7y=-12)
7(9x+5y=-16)
=> 50x+35y=-60
63x+35y= -112
clearly, y can be eliminated by subtraction.
Therefore,
-13x = 52 [-63+50 and 112-60)]
x = -4.
When x = -4,
9x+5y =-16
9(-4) +5y =-16
5y = 36-16
y=4.
Alexa earns 5% commission as a salesperson. She sold a gold necklace that cost $78. How much commission did Alexa earn?
Answer:
Step-by-step explanation:
= 5 /100 * 78 = 39 /10 = 3.9
$3.90
Use the Exterior Angle Theorem to find the measure of each angle.
mangleC =
°
mangleD =
°
mangleDEC
The Exterior Angle Theorem states that the measure of an exterior angle of a triangle is equal to the sum of the measures of the 2 nonadjacent interior angles. That means that the measure of angle DEF is equal to the sum of measure of angle C and measure of angle D. Substituting known values gives you 2y + 9 + 6y + 10 = 115, then you can solve
8y + 19 = 115
8y = 96
y = 12
The measure of angle C is 33 degrees, the measure of angle D is 82 degrees, and because the measure of angle DEF is 115 degrees, its supplement angle (DEC) measures 65 degrees.
Help !!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!
Evaluate each algebraic expression for the given values.
1. 9.8t^2 + 20t + 8 for t = -2, 0, 3.5
2. -3(2.1x - 7.9) for x = -18.1, -0.3, 14.4
The numeric values for each of the expressions are given as follows:
1. 9.8t² + 20t + 8:
t = -2: 7.2.t = 0: 8.t = 3.5: 198.05.2. -3(2.1x - 7.9):
x = -18.1: 137.73. x = -0.3: 25.59x = 14.4: -67.02.How to find the numeric value of a function or of an expression?To find the numeric value of a function or of an expression, we replace each instance of the variable in the function or in the expression by the value at which we want to find the numeric value.
Then the numeric values are given as follows:
1. 9.8t² + 20t + 8:
t = -2: 9.8(-2)² + 20(-2) + 8 = 7.2.t = 0: 8. 9.8(0)² + 20(0) + 8 = 8.t = 3.5: 9.8(3.5)² + 20(3.5) + 8 = 198.05.2. -3(2.1x - 7.9):
x = -18.1: -3 x (2.1(-18.1) - 7.9) = 137.73.x = -0.3: -3 x (2.1(-0.3) - 7.9) = 25.59.x = 14.4: -3 x (2.1(14.4) - 7.9) = -67.02.Learn more about the numeric values of a function at brainly.com/question/28367050
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If the measure of angle f g h is 64 degrees and the measure of angle e g d is (4 x + 8) degrees, what is the value of x?.
By the help of congruent , the measure of angle f g h is 64 degrees and the measure of angle e g d is (4 x + 8) degrees and the value of x is 14
Things that have precisely the same size and shape are said to be congruent. The shapes and sizes need to hold true regardless of how we flip, spin, or rotate the forms. Two triangles that are identical in size and shape are said to be congruent triangles. Even if we flip, turn, or rotate one of two congruent triangles, the other two remain congruent.Two triangles must have the same angles and, as a result, must be congruent if their sides are the same.The equal sides and angles may not be in the same location if there is a turn or flip, but they are still there.
The are congruent So,
4x+8=64
Solve for x
X=14
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A Ferris wheel has a radius of 218 feet. What is the
total distance covered if the Ferris wheel makes 6
rotations? Write an exact answer in terms of Pi.
The total distance covered by the Ferris wheel after 6 rotations is 2616π feet
What is an equation?An equation is an expression that shows the relationship between two or more numbers and variables using mathematical operations. An equation can be linear, quadratic, cubic and so on, depending on the degree of the variable.
The Ferris wheel has a radius of 218 feet. The total distance covered if the Ferris wheel makes one rotation is the perimeter of the wheel.
Perimeter = 2π * radius = 2π * 218 feet = 436π
For 6 rotations:
Total distance covered = 6 * 436π = 2616π
The total distance is 2616π feet
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What value for x makes the equation −13(x + 11) + 12x = -26 true
Answer:-117
Step-by-step explanation:
-13x-143+12x=-26
-x=-26+143=117
x=-117
Is 1/3(36m+12) and 12m+4 equivalent expressions
The expressions 1/3(36m+12) and 12m+4 are equivalent
What are equivalent expressions?
Equivalent expressions are defined as algebraic expressions that have the same solution but differ in the mode of the arrangement of values.
These expressions are known to have variables, constants, terms, coefficients, and factors.
They are also made up of mathematical operations.
We have the expression;
1/3(36m+12)
Now, expand the bracket
36m/3 + 12/3
Divide the values
12m + 4
Hence, the expression is 12m + 4
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What is the distance d between the student and the mirror?
Using the fact that the two triangles must be similar, we will see that d = 7.5 ft
What is the distance between the student and the mirror?To find the distance d we will use the fact that the two triangles must be similar triangles.
That means that the quotients between the legs must be equal.
For the triangle on the left side, the quotient is:
50ft/30ft
For the triangle on the right side, the quotient is:
d/height of the student.
We know that the height of the student is 4.5ft, so that quotient is:
d/4.5ft
Now we can write the equation:
d/4.5ft = 50ft/30ft
Solving this for d, we will get:
d = 4.5ft*(50ft/30ft) = 7.5 ft
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Three friends go to a book fair. Allen spends $2.60. Maria spends 4 times as much as Allen. Akio spends $3.55 less than Maria.
How much does Akio spend?
PLS NEED THE HELP!!
Answer:
$6.85
Step-by-step explanation:
$2.60 x 4 is 10.4 and that is how much Maria spends. Akio spends $3.55 less than Maria. So, 10.4 - 3.55 which is 6.85 and that is the answer.
based on each set of triangles or parallel lines crest a proportion and solve it to find the missing value
pls help
The value of the x in the given triangle is 7.5 units.
What is proportion?Proportion definition, comparative relation between things or magnitudes as to size, quantity, number.
Given is a triangle having sides, 12, 4 and 10 there is a missing side x we need to find is value,
Using the concept of parallel lines crest a proportion,
x / 10 = 12 / 16
x = 120 / 16
x = 7.5
Hence, the value of the x in the given triangle is 7.5 units.
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What is terminal value formula ?
The terminal value formula helps estimate the value of a business beyond the explicit forecast period,
the terminal value formula = FCFF 6 / (WACC – Growth Rate)
We can say that in a DCF model with a five-year free cash flow projection, the terminal value formula = FCFF 6 / (WACC – Growth Rate)
It could be accountable that in finance, the terminal value (also known as “continuing value” or “horizon value” or "TV") of a security is the present value at a future point in time of all future cash flows when we expect stable growth rate forever. It is most likely often used in multi-stage discounted cash flow analysis and also allows for the limitation of cash flow projections to a several-year period; see Forecast period (finance). Forecasting results beyond such a period is impractical and exposes such projections to a variety of risks limiting their validity, primarily the great uncertainty involved in predicting industry and macroeconomic conditions beyond a few years.
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What are the zeros of the function f(x) = x² - 4x² - 5?
+√5 ti
±2, ti
±5, ti
O +√2 ti
You must check the box below prior to submitting your exam!
The zeros of the function f(x) = x² - 4x - 5 are given as follows:
x = -1 and x = 5.
How to solve the quadratic function?The quadratic function for this problem is defined as follows:
f(x) = x² - 4x - 5
The coefficients are given as follows:
a = 1, b = -4, c = -5.
Then the discriminant is given as follows:
D = b² - 4ac
D = (-4)² - 4(1)(-5)
D = 36
Hence the zeros are given as follows:
x = (4 + sqrt(36))/2 = 5.x = (4 - sqrt(36))/2 = -1.More can be learned about quadratic functions at https://brainly.com/question/1214333
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What is 76 degree F in C?
76 degrees Fahrenheit was found to be equal to approximately 24.4 degrees Celsius using the formula of conversion.
To convert Fahrenheit to Celsius, you can use the following formula:
Celsius = (Fahrenheit - 32) x 5/9
Plugging in 76 degrees Fahrenheit, we get:
Celsius = (76 - 32) x 5/9
Celsius = 44 x 5/9
Celsius = 220/9
Celsius ≈ 24.4
Therefore, 76 degrees Fahrenheit is approximately 24.4 degrees Celsius.
On the Fahrenheit scale, water freezes at 32 degrees Fahrenheit (°F) and boils at 212 °F, at standard atmospheric pressure.
On the Celsius scale, the freezing point of water is defined as 0 degrees Celsius (°C), and the boiling point of water is defined as 100 °C, at standard atmospheric pressure.
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Why is the lac curve called the envelope curve?
The lac curve, also known as the envelope curve, is a curve that shows the maximum amount of work that can be done in a given period of time.
It is defined by the equation: W = min {W1 + W2, W3, W4, ..., Wn}, where W1, W2, W3, W4, ..., and Wn are the individual work tasks. The envelope curve is called such because it forms an envelope that encompasses all of the individual tasks on the graph, visually representing the maximum amount of work that can be done within the given timeline. This curve can be used to assess the efficiency of a task or project, as well as to analyze the impact of changes in the workload, deadlines, and resources.
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Help please the question is in the picture
Answer:
a) [tex]W(x) = 0.50 (3^x)[/tex]
W = tickets worth in $
x = number of balloons popped
b) For 8 balloons popped, number of tickets = 6,561
Tickets worth = [tex]\$ 3,280.50[/tex]
Step-by-step explanation:
The relation between number of balloons popped(x) and the number of tickets is
[tex]f(x) =3 ^ x\\\\f(1) = 3^1 = 3\\\\f(2) = 3^2 = 9\\\\f(3) = 3^3 = 27\\\\f(4) = 3^4 = 81[/tex]
each ticket is worth 50 cents
So for x tickets
[tex]W(x) = 0.50 (3^x)[/tex]
Number of tickets for 8 balloons popped
f(x) = 3^8
= [tex]f(x) = 3^8 = 6,561[/tex]
Ticket worth = [tex]0.5 \times 6,561 = \$ 3,280.50[/tex]