where does the line through (1, 0, 1) and (3, −3, 5) intersect the plane x y z = 8?
Answers
The line intersects the plane at the point (5, -6, 9).
The line passing through the points (1, 0, 1) and (3, -3, 5) can be represented by the parametric equations:
x = 1 + t(3 - 1) = 2t + 1
y = 0 + t(-3 - 0) = -3t
z = 1 + t(5 - 1) = 4t + 1
where t is a parameter.
To find the point of intersection of this line with the plane x+y+z=8, we can substitute the parametric equations for x, y, and z into the equation of the plane:
x + y + z = 8
(2t + 1) + (-3t) + (4t + 1) = 8
3t + 2 = 8
t = 2
Therefore, the point of intersection is when t = 2:
x = 2t + 1 = 5
y = -3t = -6
z = 4t + 1 = 9
So, the line intersects the plane at the point (5, -6, 9).
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Related Questions
Let (N(t))t a Poisson process with rate 3 per min. Let Sn denote
the time of the n-th event.
Find a. E[S10]
b. E[S4|N(1) = 3]
c.Var(S10).
d. E[N(4) − N(2)|N(1) = 3].
e. P[T20 > 3].
Answers
For a Poisson process with rate λ, the interarrival times between events are exponentially distributed with parameter μ = 1/λ. So, the time between the (n-1)-th and n-th event, denoted as Tn, follows an exponential distribution with parameter μ = 1/3 minutes.
Since Sn is the sum of the first n interarrival times, we have:
Sn = T1 + T2 + ... + Tn
The sum of n exponential random variables with parameter μ is a gamma random variable with shape parameter n and scale parameter μ. Therefore, Sn follows a gamma distribution with shape parameter n and scale parameter μ.
In this case, n = 10 and μ = 1/3. So, E[S10] can be calculated as:
E[S10] = n * μ = 10 * (1/3)
= 10/3 minutes.
Therefore, E[S10] = 10/3 minutes.
b. E[S4|N(1) = 3]:
Given that N(1) = 3, we know that there are 3 events in the first minute. Therefore, the time of the 4th event, S4, will be the sum of the first 3 interarrival times plus the time between the 3rd and 4th event.
Using the same reasoning as in part a, we know that the sum of the first 3 interarrival times follows a gamma distribution with shape parameter 3 and scale parameter 1/3. The time between the 3rd and 4th event, denoted as T4, follows an exponential distribution with parameter 1/3.
So, S4 = T1 + T2 + T3 + T4.
Since T1, T2, T3 are independent of T4, we can calculate E[S4|N(1) = 3] as:
E[S4|N(1) = 3] = E[T1 + T2 + T3 + T4]
= E[T1 + T2 + T3] + E[T4]
= (3/3) + (1/3)
= 4/3 minutes.
Therefore, E[S4|N(1) = 3] = 4/3 minutes.
c. Var(S10):
The variance of Sn, Var(Sn), for a Poisson process with rate λ, is given by:
Var(Sn) = n * σ^2,
where σ^2 is the variance of the interarrival times.
In this case, n = 10 and the interarrival times are exponentially distributed with parameter μ = 1/3. The variance of an exponential distribution is \(\mu^2\)So, \(\sigma^2 = \left(\frac{1}{3}\right)^2\)
= 1/9.
Substituting the values into the formula, we have:
Var(S10) = 10 * (1/9)
= 10/9.
Therefore, Var(S10) = 10/9.
d. E[N(4) − N(2)|N(1) = 3]:
Given that N(1) = 3, we know that there are 3 events in the first minute. Therefore, at time t = 2 minutes, there will be 3 - 1 = 2 events that have already occurred.
Now, we need to find the expected value of the difference in the number of events between time t = 4 minutes and t = 2 minutes, given that there were 3 events at t = 1 minute.
Since the number of events in a Poisson process follows a Poisson distribution with rate λt, where t is
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Question 8(Multiple Choice Worth 5 points)
(Experimental Probability MC)
Thirty students were surveyed about the number of siblings they have. Their results were recorded and placed on a card face down.
Outcome Frequency
1 6
2 12
3 9
4 or more 3
Determine P(2) when picking a random card.
40%
60%
70%
90%
Answers
What is Math 220 at UIUC?
Answers
Math 220 at UIUC is a calculus course offered at the University of Illinois at Urbana-Champaign.
It is designed to introduce students to the fundamental concepts of calculus, including limits, differentiation, and integration. The course also covers applications of these concepts to real-world problems, such as optimization and modeling.
Students are expected to have a strong foundation in algebra and trigonometry before taking Math 220. The course is typically taken by students in the College of Engineering and the College of Liberal Arts and Sciences.
The textbook for the course is the 8th edition of Calculus: Early Transcendentals by James Stewart. Additionally, Math 220 students must obtain access to the online homework system MyMathLabPlus and a copy of the textbook (hard copy or eBook).
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evaluate dw/dt at t = 4 for the function w (x,y)= e^y - ln x; x = t^2, y = ln t
Answers
dw/dt at t = 4 = -2/4 + 4 = 3
We can use the chain rule to find dw/dt:
dw/dt = (∂w/∂x) (dx/dt) + (∂w/∂y) (dy/dt)
First, we need to find ∂w/∂x and ∂w/∂y:
∂w/∂x = -1/x
∂w/∂y = e^y
Next, we can substitute x = t^2 and y = ln t into these expressions:
∂w/∂x = -1/(t^2)
∂w/∂y = e^(ln t) = t
We also have dx/dt = 2t and dy/dt = 1/t. Substituting all these values into the formula for dw/dt, we get:
dw/dt = (∂w/∂x) (dx/dt) + (∂w/∂y) (dy/dt)
= (-1/(t^2)) (2t) + (t) (1/t)
= -2/t + t
Finally, we can evaluate dw/dt at t = 4:
dw/dt = -2/t + t
dw/dt at t = 4 = -2/4 + 4 = 3
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Does - 5 or 5 satisfy the equation x + 5 = 0 ?
Answers
-5 because one negative and one positive of the same number is always 0
Answer:
-5
Step-by-step explanation:
If you add 5 to -5 it will be 0 due to the - in -5. This is because negative numbers are below 0.
A parallelogram what is the order of rotational symmetry for the parallelogram?
Answers
A parallelogram possesses rotational symmetry of order 2, but no line symmetry.
What is rotational symmetry?Geometrically speaking, a shape exhibits rotational symmetry when it retains its appearance following a little amount of rotation by a partial turn. The number of different orientations in which an object appears exactly the same for each rotation is known as the degree of rotational symmetry.The least angle at which the figure can be rotated to coincide with itself is known as the angle of rotational symmetry. The number of times a figure coincides with itself while rotating through 360 degrees is known as the order of symmetry. Example: The rotational symmetry of a regular hexagon.The rotational symmetry of a parallelogram:
A parallelogram lacks line symmetry and has rotational symmetry of order 2.Therefore, a parallelogram possesses rotational symmetry of order 2, but no line symmetry.
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Answer:
in picture ....
Step-by-step explanation:
Multiply
- 4u^2(-5u^3)
Answers
\(\bold{Hello!}\\\bold{Your~Answer~Is~Below!}\)
______________________________
\(\bold{Solution~Steps:}\)
\(1.)~Multiply~Powers:\)
\(\bold{To~multiply~powers~of~the~same~base,~add~their~exponents.}\)\(\bold{2+3=5}\)\(2.)~Multiply~Bases:\)
\(\bold{-4}\) × \(\bold{-5=20}\)\(\bold{When~you~multiply~2~negatives,~the~product~will~always~be~positive.}\)______________________________
\(\bold{Answer:}\)
\(\bold{The~simplifed~version~of~the~power~is~\boxed{20u^5.}}\)______________________________
\(\bold{Hope~this~helps,}\\\bold{And~best~of~luck!}\\\\\bold{~~~~~~-TotallyNotTrillex}\)
Help me out with this question!! 50 points
Answers
C
The mistake the arrangers made is in the second inequality. They considered the number of caps to be bought should be at least 5 times greater than the number of blouses, not the other way around. The correct inequality should be C
The correct answer is D) The first inequality should be s + h ≤ 1800.
The organizers made an error in the first inequality. The given inequality 10s + 8h ≤ 1800 represents the total cost of buying shirts (10s) and hats (8h) should be less than or equal to $1800. However, this does not take into account the fact that the organizers want to buy at least 5 times as many shirts as hats, as indicated by the second inequality h ≥ 5s.
The correct way to represent this constraint is by using the equation s + h ≤ 1800, which ensures that the total number of shirts and hats purchased does not exceed $1800 in cost. This is because the organizers want to make sure that the total cost of shirts and hats combined does not exceed the budget of $1800.
help me with this question
Answers
the coffee pub has cans of coffee that weigh 3 1/4 pounds each. the pub has 8 1/2 cans of coffee left. what is the total weight of 8 1/2 cans ? show your work
Answers
Final Answer: \(27\frac{5}{8}\) pounds
Final Answer Reason: The total weight of \(8\frac{1}{2}\) cans would be \(27\frac{5}{8}\) pounds
Steps/Reasons/Explanation:
We'll need to find the total weight of \(8\frac{1}{2}\) cans, so we would need to multiply \(3\frac{1}{4}\) cans by \(8\frac{1}{2}\) cans. We are solving for the total weight of \(8\frac{1}{2}\) cans.
Question: The coffee pub has cans of coffee that weigh \(3\frac{1}{4}\) pounds each. The pub has \(8\frac{1}{2}\) cans of coffee left. What is the total weight of \(8\frac{1}{2}\) cans?
Solve For: The total weight of \(8\frac{1}{2}\) cans.
Steps: Multiply to find total weight of \(8\frac{1}{2}\) cans.
\(3\frac{1}{4}\) × \(8\frac{1}{2}\)
= \(\frac{13}{4}\) × \(\frac{17}{2}\)
= \(\frac{221}{8}\)
= \(27\frac{5}{8}\)
~I hope I helped you :)~
Given a function f(x) = x+y, 0≤x+2y≤2 , otherwise = 0 (a) Show that f is a PDF. (b) Find the marginal of X and Y . (c) Find the Cov(X, Y ).
Answers
a) f(x) is a PDF. b) the marginal of X and Y is (y/2 + 1) / 2 c) the covariance of X and Y is: -1/18
What is meant by PDF?
In probability theory, a probability density function (PDF) is a function that describes the relative likelihood for a continuous random variable to take on a given value.
What is covariance?
Covariance is a statistical measure that quantifies the degree to which two random variables are linearly associated.
According to given information:(a) To show that f(x) is a probability density function (PDF), we need to show that it satisfies the following two conditions:
Non-negativity: f(x) is non-negative for all x in its domain.
Normalization: The integral of f(x) over its domain is equal to 1.
The domain of f(x) is given by the inequality 0 ≤ x + 2y ≤ 2. To find the integral of f(x) over its domain, we need to integrate it with respect to y from (0-x/2) to (2-x/2), and then integrate the result with respect to x from 0 to 2:
∫(0 to 2) ∫(0-x/2 to 2-x/2) (x+y) dy dx
Solving the inner integral with respect to y, we get:
∫(0 to 2) [xy + \(y^2\)/2] |_0-x/\(2^{(2-x/2)\) dx
= ∫(0 to 2) (\(x^2\)/4 - \(x^3\)/12 + 1) dx
= [\(x^3\)/12 - \(x^4\)/48 + x] |_\(0^2\)
= 2 - 2/3 + 2 = 8/3
Since the integral is finite and positive, the first condition of non-negativity is satisfied. To satisfy the normalization condition, we divide the function by the integral:
f(x) = (x+y) / (8/3)
Therefore, f(x) is a PDF.
(b) To find the marginal of X, we integrate f(x,y) over the range of y:
f(x) = ∫(0-x/2 to 2-x/2) (x+y) / (8/3) dy
= (x/2 + 1) / 2
Similarly, to find the marginal of Y, we integrate f(x,y) over the range of x:
f(y) = ∫(0 to 2) (x+y) / (8/3) dx
= (y/2 + 1) / 2
(c) To find the covariance of X and Y, we use the formula:
Cov(X, Y) = E[XY] - E[X]E[Y]
To find E[XY], we integrate xy*f(x,y) over the range of x and y:
E[XY] = ∫(0 to 2) ∫(0-x/2 to 2-x/2) xy*(x+y)/(8/3) dy dx
= ∫(0 to 2) [\(x^3\)/6 - \(x^4\)/24 + \(x^2\)/4] dx
= 2/3
To find E[X] and E[Y], we integrate xf(x) and yf(y) over their respective ranges:
E[X] = ∫(0 to 2) x*(x/2+1)/2 dx
= 7/3
E[Y] = ∫(0 to 2) y*(y/2+1)/2 dy
= 7/6
Therefore, the covariance of X and Y is:
Cov(X, Y) = E[XY] - E[X]E[Y] = 2/3 - (7/3)*(7/6) = -1/18
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For what values of h is b in the plane spanned by a1 and a2?
a1=(1; 0; -h) a2=(0; 1; 2) b=(h; -1; 3h)
2
-1
-2
0
Answers
The b is in the plane spanned by a1 and a2 for h = ±1. For any other value of h, b is not in the plane spanned by a1 and a2.
To determine for what values of h is b in the plane spanned by a1 and a2.
We need to check if b can be written as a linear combination of a1 and a2.
If b can be written as a linear combination of a1 and a2 then it is in the plane spanned by a1 and a2.
Otherwise,
It is not in the plane.
We can write the equation for a plane using a point on the plane and the normal vector to the plane.
Since a1 and a2 are in the plane, we can find the normal vector by taking the cross product of a1 and a2:
n = a1 x a2
n = <0 -h 1> x <1 0 -h>
n = <-h -1 0>
So, the equation for the plane spanned by a1 and a2 is:
-h(x) - y = 0
We can substitute b = (h, -1, 3h) into this equation and see if it satisfies the equation.
-h(h) - (-1) = 0
-\(h^2\) + 1 = 0
\(h^2\) = 1
h = ±1
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a handful of coins has the value of 1 dollar and 79 cents there are 3 times as many dimes as quarters and 5 more pennies than dimes if there are only 3 types of coins how many of each type of coin are there
Answers
Answer:
3 Quarters 9 dimes 14 pennies
Step-by-step explanation:
so dimes are x, quarters are y, and pennies are z. Next we know that x*3 y is what dimes are and 5 more pennies then dimes so z+5. Now we do 3 quarters since thats about 100 but less then 3*3=9 so 190 we have 90+75 cents now then we add 14 the cursed number lol but we add 14 because 9+5 is 14 and there are 5 more pennies then dimes.
plz help it's due tomorrow
4.Congratulations! You won a free grill in a sweepstake! You know that you can fit a rectangular grill in your truck that has a width of 2 1/2 feet. The length of the grill can be up to three times the width. What is the largest possible perimeter your new grill can have to fit in your taco truck? Show your work.
2. Based on customer reviews, you decide to lower the ratio of jalapenos and corn in your recipe. This can be represented by the expression (-7x + 9) - 2(3x – 4). In simplest form, what is the new ratio of jalapenos and corn in your recipe? Show your work.
Answers
Answer:
-7x + 9 -6x + 8
collect the like terms
-7x -6x +9 +8
-13x +17
a cheese merchant examines the data set about the product sales of cheese as a % of total sales, in which the sample mean is 15.8 and the sample standard deviation is 8.9. find the 68% confidence interval.
Answers
The lowest level of the 68% confidence interval estimate for wholesale sales in cheese establishments, given the provided data, can be determined with the sample size.
To calculate the confidence interval, we need the sample mean and the sample standard deviation. The sample mean represents the average wholesale sales in the sample, while the sample standard deviation measures the variability or spread of the data around the mean.
In this case, the sample mean of wholesale sales in cheese establishments is given as 3,324.3, and the sample standard deviation is 2,463.8.
The 68% confidence interval estimate is based on the concept that if we were to repeat the sampling process multiple times and calculate the confidence interval each time, approximately 68% of those intervals would contain the true population mean.
To calculate the lowest level of the 68% confidence interval estimate, we need to determine the margin of error, which is a measure of uncertainty associated with our estimate. The margin of error is determined by multiplying the sample standard deviation by a critical value, which corresponds to the desired level of confidence.
For a 68% confidence interval, the critical value is approximately 1, since the remaining 32% is divided equally into the upper and lower tails of the distribution.
The formula to calculate the margin of error is:
Margin of Error = Critical Value * (Sample Standard Deviation / √Sample Size)
Since the sample size is not given, we cannot calculate the exact margin of error. However, we can estimate the lowest level of the confidence interval by subtracting the margin of error from the sample mean.
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Complete Question:
The following data set provides information on wholesale sales by establishments and by total sales.
A cheese merchant is looking to expand her business. She looks at the data set about cheese establishments in six categories, in which the sample mean is 3,324.3 and the sample standard deviation is 2,463.8.
Find the lowest level of the 68% confidence interval estimate.
Round your answer to ONE decimal place.
what is the value of this expression when c=4 c^3/2
Answers
Answer:
8
Step-by-step explanation:
c ^ 3/2
Let c = 4
4 ^ 3/2
Rewriting 4 as 2^2
2 ^2 ^3/2
We know that a^b^c = a^(b*c)
2 ^(2*3/2)
2 ^3
8
the right answer is 8.
please see the attached picture for full solution
Hope it helps
Good luck on your assignment....
Kim sold half of his comic books and then bought 16 more. He now has 36. With how many did he start with?
Answers
Answer: 40
Step-by-step explanation: Subtract 16 from 36 and you get 20. It says half so you multiply by 2 and get 40.
A temperature recorded in Antarctica was -121 degrees Fahrenheit the temperature recorded in the Sahara Desert was 133 degrees Fahrenheit how many degrees warmer is 133 degrees than -121 degrees Fahrenheit
Answers
Answer:
254
Step-by-step explanation:
133+121=254
In the parallelogram below, solve for x and y.
I have y but i can’t figure out x
Answers
Step-by-step explanation:
how did you get y, when you don't know how to get x ?
the easiest way to solve this is to base on the fact that the opposite angles must be identical.
so,
2x + 32 = 4x - 12
32 = 2x - 12
44 = 2x
x = 22
and the to be sure
-8y - 14 = -5y + 4
-3y = 18
y = -18/3 = -6
or, the sum of 2 consecutive angles must be 180°.
2x + 32 - 5y + 4 = 180
2x - 5y + 36 = 180
2x - 5y = 144
-8y - 14 + 4x - 12 = 180
-8y + 4x = 206
-4y + 2x = 103
-5y + 2x = 144
- -4y + 2x = 103
------------------------
- y 0 = 41
y = -41
-4×-41 + 2x = 103
164 + 2x = 103
2x = -61
x = -30.5
ha, your teacher either set a trap or made a mistake.
these given angles do not belong to a parallelogram.
there is no solution for x and y with these angle expressions to create a parallelogram.
every condition that has to be true creates a different and inconsistent set of solutions (and implausible ones at that creating single angles larger than 200° and even 300°, or smaller than 0°).
Solve: 4x^2 = 32 thanks
Answers
Answer:
D.Step-by-step explanation:
It is difficult to describe, but you just need to follow through the steps acorddingly.The members of a student council held a car wash to earn money for a field trip. The equations represent how they calculated their earnings.
5c+8v=234
c=2v
If c
represents the number of cars and v
represents the number of vans, which pair of sentences best describe the results of the fundraiser?
Answers
There are 26 automobiles and 13 vans available for the field excursion.
What is equation?An algebraic equation, also known as a polynomial equation, is a mathematical equation of the form P=0, where P is a polynomial with coefficients in some field, most commonly the field of rational numbers. A mathematical statement that expresses the connection between two values is simply characterized as an equation. In an equation, the two values are usually equated by an equal sign. Linear equations are first-order equations. Lines in the coordinate system are determined by linear equations. A linear equation in one variable is defined as an equation with a homogeneous variable of degree 1 (i.e. only one variable). A linear equation can include several variables.
Here,
If c represents the number of cars and v represents the number of vans,
5c+8v=234
c=2v
10v+8v=234
v=234/18
v=13 vans
c=26 cars
The number of cars for field trip is 26 and number of vans is 13.
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Find X round to the nearest tenth.
Answers
Answer:
38.3 =x or x=141.8
Step-by-step explanation:
Using the law of sines
sin 27 sin x
----------- = ------------
11 15
Using cross products
15 sin 27 = 11 sin x
15/11 sin 27 = sin x
Taking the inverse sin of each side
sin^-1 (15/11 sin 27 )= sin ^-1(sin x)
38.24883302 = x
To the nearest tenth
38.2 =x
or
x=141.8
Answer:
38.2 degrees
Step-by-step explanation:
Use the law of sines
(sin 27)/11=(sinx)15
15sin(27)=11sin(x)
[15sin(27)]/11=sin(x)
x=arcsin[15sin(27)]/11
rounded to nearest tenth, x=38.2
sin² x + cos²x = 1
Which Trigonometric Identity is given above?
- Pythagorean Identity
- Lagrange's Trigonometric Identity
- Angle Sum and Difference Identity
- Tangent Identity
Answers
The Trigonometric Identity sin² x + cos²x = 1 is: A. Pythagorean Identity.
What is Pythagorean Identity?The Pythagorean Identity which tend to asserts that for every angle x, the sum of the squares of the sine and cosine of x is equal to one is known as or called a trigonometric identity.
The Pythagorean identity can be expressed as:
sin² x + cos² x = 1
This identity is crucial to understanding trigonometry and tend to have several uses in numerous branches of science and engineering.
Therefore the correct option is A.
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A circle has a diameter with endpoints at 5 + 18i and –3 + 2i. What is the center of the circle?
–11 –16i
1 + 10i
2 + 20i
4 + 8i
Answers
Answer:
so there is a real and imaginary axis
the midpoint is just the average of them
average between the reals is (5-3)/2=2/2=1
average between imaginaries is (18i+2i)/2=20i/2=10i
center is 1+10i
Step-by-step explanation:
Answer: B. 1+10i
Step-by-step explanation:
edge
cam sone ine please help me ASAP
Answers
Answer:
x = 63°
Step-by-step explanation:
The exterior angle of a triangle is equal to the sum of the 2 opposite interior angles.
∠ DAB is an exterior angle of the triangle, thus
x + 65 = 128 ( subtract 65 from both sides )
x = 63
Answer:m
Step-by-step explanation:m
solve the equation for a? z=mab. a)a=z+mb b)a=z-mb c)a= mb/z d)a=z/mb
Answers
Answer:
a = z/mb
Step-by-step explanation:
Given:
\(\displaystyle \large{z=mab}\)
To solve for a, divide both sides by the variables mb to isolate a-term.
\(\displaystyle \large{\dfrac{z}{mb}=\dfrac{mab}{mb}}\)
Simplify the expression and we finally have solved for a-term.
\(\displaystyle \large{\dfrac{z}{mb}=a}\\\\\displaystyle \large{a=\dfrac{z}{mb}}\)
Therefore, the answer to this question is a = z/mb.
Please let me know if you have any questions regarding my answer or explanation!
On Earth day, a local community wants to distribute 800 flyers, 300 banners, and 250 badges to volunteers in packets containing the three items. What is the greatest number of packets that can be made using all these items if each type of item is equally distributed among the packets?
Answers
Answer:
800 flyersOn Earth day, a local community wants to distribute 800 flyers, 300 banners, and 250 badges to volunteers in packets containing the three items. What is the greatest number of packets that can be made using all these items if each type of item is equally distributed among the packets?
Which equation is modeled below?
4 x tiles and 2 negative 1 tiles = 2 x tiles and 4 1 tiles.
2 x + (negative 2) = negative 2 x + 6
4 x + (negative 2) = negative 2 x + 6
2 x + 4 = 6 x + 2
Negative 2 x + 4 = 6 x + (negative 2)
(Ignore the filled in bubble)
Answers
Answer:
B
Step-by-step explanation:
4 (x) + 2 (-1) = 2 (-x) + 6(1)
4x + -2 = -2x + 6
The equation for the given figure is 4x-2=-2x+6. Therefore, option B is the correct answer.
What is an equation?In mathematics, an equation is a formula that expresses the equality of two expressions, by connecting them with the equals sign =.
From the given figure,
x+x+x+x+(-1-1)=(-x-x)+(1+1+1+1+1+1)
⇒ 4x-2=-2x+6
So, equation modeled as 4x-2=-2x+6
The equation for the given figure is 4x-2=-2x+6. Therefore, option B is the correct answer.
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Can someone please help me with these? Thank You!
Answers
Step-by-step explanation:
9. f(x) is x² so -4² will give you 16 under the f(x)
-4= 16
-2= 4
0= 0
1= 1
6 = 36
10. f(x) is x² -4 therefore f(x) is (-3)² -4= 5
-3= 5
-1= -3
0= -4
2= 0
5= 21
(20m + 3) - (7 m - 5)
Find the difference
Answers
3--5=8
13m+8
Answer:
This can be done in two ways -
- horizontal
- vertical
so I chose Vertical :
