As per the unitary method, Arun's mother would be 36 years old if Arun is 3 years old.
Let Arun's age be m years.
Let Arun's mother's age be n years.
From the problem statement, we know that n = 4m + 6. This means that Arun's mother's age is directly proportional to Arun's age, with a constant ratio of 4 and a constant difference of 6.
To solve for n, we can use the unitary method. We can set up a proportionality between the two ages as follows:
n / m = (4m + 6) / m
To solve for n, we can cross-multiply to get:
n = m x (4m + 6)
Expanding the right-hand side of the equation, we get:
n = 4m² + 6m
Therefore, Arun's mother's age is 4m² + 6m years. We can simplify this expression by factoring out 2m:
n = 2m(2m + 3)
This gives us a simpler form of the equation for Arun's mother's age. To find her age, we simply substitute Arun's age (m) into this expression and simplify.
If Arun is 3 years old (m = 15), then his mother's age would be:
n = 2m(2m + 3) = 2(3)(2(3) + 3) = 2(3)(6) = 36
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If the ratio a: b is 1 : 4 and the ratio b: c= 3:2, find the ratio (a + c) : c.
The required ratio of is (a + c) : c 11:8.
How to find ratio ?Given that a:b=1:4 and b:c=3:2.
We can simplify the ratio b:c by multiplying both sides by 4 to get b:c=12:8=3:2.
To find the ratio (a+c):c, we need to express a and c in terms of b. From the first ratio, we have [tex]a=\frac14 b$[/tex]. From the second ratio, we have [tex]c=\frac{2}{3}b$[/tex]. Substituting these values into the expression (a+c):c, we get:
[tex]$$(a+c):c = \left(\frac{1}{4}b + \frac{2}{3}b\right):\frac{2}{3}b$$[/tex]
Simplifying the expression inside the parentheses, we get:
[tex]$\frac{1}{4}b + \frac{2}{3}b = \frac{3b}{12} + \frac{8b}{12} = \frac{11b}{12}$$[/tex]
Therefore, the ratio [tex]$(a+c):c$[/tex] is:
[tex]$(a+c):c = \frac{11b}{12}:\frac{2}{3}b = 11:8$$[/tex]
Hence, the required ratio is 11:8$.
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5. If j(x) = x+8, find x such that
j(x)=10
LOVE is a kite. LV and OE are diagonals. The segments DV = 9cm and LE = 15cm, and
The lengths of LV and OE are 15cm, and the lengths of LD and EV are 3√7 cm and 9/√7 cm, respectively.
Since LOVE is a kite, LV and OE are perpendicular bisectors of each other. Let the length of LD be x, and the length of EV be y. Then, we can use the Pythagorean theorem and the fact that the diagonals bisect each other to set up two equations:
x² + (LV/2)² = DV²/4
y² + (OE/2)² = LE²/4
Simplifying each equation and substituting the given values, we get:
x² + (LV/2)² = 81/4
y² + (OE/2)² = 225/4
We also know that the diagonals bisect each other, so we can set up another equation:
LV/2 + OE/2 = LO = VE
Substituting the given value for LE, we get:
LV/2 + OE/2 = 15
Solving this equation for one of the variables, we get:
LV = 30 - OE
Substituting this expression into the first equation above, we get:
x² + ((30 - OE)/2)² = 81/4
Simplifying and rearranging, we get:
OE² - 60OE + 675 = 0
Using the quadratic formula, we get:
OE = (60 ± √(3600 - 2700)) / 2
OE = 15 or 45
If OE = 15, then LV = 30 - 15 = 15, and we can solve for x and y:
x² + 7.5² = 81/4
y² + 7.5² = 225/4
Solving these equations, we get:
x = 3√7
y = 9/√7
If OE = 45, then LV = 30 - 45 = -15, which is impossible for a length. Therefore, the solution is:
LV = OE = 15
x = 3√7
y = 9/√7
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Complete question:
LOVE is a kite. LV and OE are diagonals. The segments DV = 9cm and LE = 15cm are given. Find the lengths of the other segments of the diagonals, DV, OE, and LV.
GEOMETRY:
a pile standing vertically casts a 19 ft shadow. At the same time, a 6 ft person near the beam casts a shadow 4’6’’. What is the height of the pole?
Answer:
X / 19 = 6 / 4.5 both person and pile have same ratio of shadow
X = 6 / 4.5 * 19 = 25.3 ft
a) Find the approximations T8 and M8 for the integral Integral cos(x^2) dx between the limits 0 and 1. (b) Estimate the errors in the approximations of part (a). (C) How large do we have to choose n so that the approximation Tn and Mn to the integral in part (a) are accurate to within 0.0001?
(a) Using the Trapezoidal rule, T8 = (1/16)[cos(0) + 2cos(1/16) + 2cos(2/16) + ... + 2cos(7/16) + cos(1)].
Using the Midpoint rule, M8 = (1/8)[cos(1/16) + cos(3/16) + ... + cos(15/16)].
(b) The error in the Trapezoidal rule is bounded by (1/2880)(1-0)^3(max|f''(x)|), where f''(x) = -4x^2sin(x^2) and 0 <= x <= 1. Therefore, the error in T8 is approximately 0.00014. The error in the Midpoint rule is bounded by (1/1920)(1-0)^3(max|f''(x)|), which gives an approximate error of 0.00011 for M8.
(c) Let n be the number of intervals in the approximation.
Then, the error bound for the Trapezoidal rule is (1/2880)(1-0)^3(max|f''(x)|)(1/n^2), and the error bound for the Midpoint rule is (1/1920)(1-0)^3(max|f''(x)|)(1/n^2).
Setting these equal to 0.0001 and solving for n, we get n >= 129 and n >= 160 for the Trapezoidal and Midpoint rules, respectively. Therefore, we should choose n >= 160 to ensure that both approximations are accurate to within 0.0001.
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I need help please
Answer:
136
Step-by-step explanation:
35x2+7x6+12x2
Erica's bedroom is shaped like the letter L. One of the rectangles that makes up her room measures 10 feet by 8 feet. The other rectangle measures 12 feet by 8 feet. What is the area of her entire bedroom?
the area of her entire bedroom is 176 feet².
What is rectangle?A rectangle is a parallelogram with four right angles in the Euclidean plane. It can also be described as a parallelogram with a right angle or an equiangular quadrilateral, where equiangular denotes that all of its angles are equivalent. A square is a rectangle with four equal edges.
What is area?The size of a section on a surface is determined by its area. Surface area refers to the area of an open surface or the border of a three-dimensional object, whereas the area of a plane region or plane area refers to the area of a shape or planar lamina.
Area of first rectangle = length * breadth= 10*8=80 feet²
Area of second rectangle = length * breadth= 12*8 = 96 feet²
Total area of bedroom= 80+96= 176 feet²
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suppose you start at the origin, move along the x-axis a distance of 7 units in the positive direction, and then move downward a distance of 6 units. what are the coordinates of your position? (x, y, z)
The coordinates of your position If we start at the origin, we are moving only along the x-axis of a distance of 7 units in positive direction and then only in the negative y-axis direction and z-coordinate is zero are (7,-6,0).
The origin is the point in space that has a position of (0, 0, 0), which represents the point where the x, y, and z axes intersect.
The first step is to move 7 units in the positive x direction. The positive x direction is the direction in which x values increase. Therefore, we move to the right along the x-axis to the point (7, 0). This means that we have moved 7 units along the x-axis, and our position is now (7, 0, 0).
The second step is to move downward a distance of 6 units. Since we are not moving in the x direction, we are only changing our position along the y-axis. Moving downward in the y direction means decreasing our y-coordinate. Therefore, we move 6 units downward from our current position to the point (7, -6, 0).
Therefore, the coordinates of our position are (7, -6, 0)
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30 points please help me do this question
Answer:
the area of triangle OAP is 12 square units.
Step-by-step explanation:
First, we need to find the coordinates of the center of the circle, which is (0, 0), and the radius, which is √40 = 2√10.
Since line I is a tangent to the circle at point A, it is perpendicular to the radius OA at point A. Therefore, OA is perpendicular to line I and forms a right angle with it.
We can find the equation of line I using the point-slope form:
slope of radius OA = (0 - 6) / (0 - 2) = -3
slope of line I = 1 / 3 (because it is perpendicular to OA)
equation of line I: y - 6 = (1/3)(x - 2)
simplifying, we get: y = (1/3)x + 4
To find the x-coordinate of point P, we need to solve for x when y = 0:
0 = (1/3)x + 4
x = -12
Therefore, point P has coordinates (-12, 0).
Now, we can find the coordinates of point O, which is the origin (0, 0), and the coordinates of point A, which are given as (2, 6).
To find the area of triangle OAP, we can use the formula for the area of a triangle:
Area = (1/2) x base x height
We know that OA is the base of the triangle and its length is the radius of the circle, which is 2√10.
To find the height of the triangle, we need to find the distance from point A to line I, which is the perpendicular distance. We can use the formula for the distance between a point and a line:
distance = |ax + by + c| / √(a² + b²)
where a, b, and c are the coefficients of the equation of the line, and x and y are the coordinates of the point.
In this case, the equation of line I is y = (1/3)x + 4, so a = -1, b = 3, and c = -12.
Substituting the values, we get:
distance = |(-1)(2) + (3)(6) - 12| / √((-1)² + 3²)
distance = |6| / √10
distance = 3√10 / 5
Now we can substitute the values into the formula for the area of the triangle:
Area = (1/2) x base x height
Area = (1/2) x 2√10 x (3√10 / 5)
Area = 6/5 x 10
Area = 12
Therefore, the area of triangle OAP is 12 square units.
Picture Shown Below with question:
Answer: 23
Step-by-step explanation:
Vertical angles are congruent (equal) so you first make the equations for angle A and B equal to each other and solve for x.
x + 15 = 5x - 17
32 = 4x
x = 8
Plug the x value (8) back into either equation to find the measure of angle B.
x + 15
8 + 15 = 23
solve the nonlinear system of equations for real solutions.
y = x² - 2
7x-y = 12
Answer: y=12
Step-by-step explanation: can't simplify
Aura builds model airplanes her first model airplane is 4 1/3 feet long she wants her next model airplane to be 1/4 as long as the first. How long will the next model airplane be
13/12 will be long the next airplane model. This will be because her next model is to be 1/4 as long as the first.
Fractions are referred to as the components of a whole in mathematics. A single object or a collection of objects might be entire. When we cut a piece of cake in real life from the entire cake, the part represents the per cent of the cake. The word "fraction" is derived from Roman. "Fractus" means "broken" in Latin. The fraction was expressed verbally in earlier times. It was afterwards presented in numerical form.
Given,
The length of her first model is in the fraction [tex]4\frac{1}{3}[/tex]
As her next model has to be 1/4 as long as the first model
Therefore,
Length of her new or next model
1/4 of [tex]4\frac{1}{3}[/tex]
so, 1/4 * 13 / 3
13/12
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The location of the incenter of ABC is:
A. Point D
B. Point F
C. Point E
3. Find the sine of angle in the triangle below.
8
7
Answer:
90 degrees then decreace that then turn that into a fraction
Step-by-step explanation:
Storyboards are a helpful part of the design process because the storyboard develops
A) A pseudocode description of the algorithm being designed
B) The mathematical formulas required for computing a correct answer
C) What information is needed to solve the problem, and how to present that information
D) The amount of time and space it will require to find a solution
The correct option among the four options that are given in the question is option C. The storyboard is a helpful part of the design process because the storyboard develops what information is needed to solve the problem, and how to present that information.
What is a storyboard?
A storyboard is a graphic organizer that consists of illustrations or images shown in sequence for the purpose of pre-visualizing a motion picture, animation, motion graphic or interactive media sequence. A storyboard is created to provide a visual representation of how a story will unfold on a screen.Storyboards are important in the design process because they help designers understand the complexity of a particular problem and come up with a plan to solve it. The storyboard can be used to explain how the user will interact with the software, what functions are necessary, what data is required, and how the data will be displayed on the screen. Storyboards help designers visualize the user's experience and think through the design process. They are an essential tool for designers who want to create engaging, user-friendly software or interfaces.
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Fill in the blanks below in order to justify whether or not the mapping shown represents a function.
Answer:
Step-by-step explanation:
the second blank is wrongt
Which expressions are completely factored? Select each correct answer.
A. 32y^10-24=8(4y^10-3)
B. 20y^7+10y^7=5y(4y^6+2y)
C. 18y^3-6y=3y(6y^2-2)
D. 16y^5+12y^3=4y^3(4y^2+3)
i have a tough time with math bc im a very easily distracted person, so i need a tad bit of help ^^"
Answer:
a, c and d
Step-by-step explanation:
An urn contains eight green balls and six red balls. Four balls are randomly selected from the urn in succession, with replacement. That is, after each draw the selected ball is returned. What is the probability that all four balls drawn are red. Round your answer to three decimal places
The probability of drawing four red balls in succession, with replacement, is 0.04 or 4%.
Since we are replacing the ball after each draw, the probability of drawing a red ball remains the same for each draw. The probability of drawing a red ball on any given draw is:
P(Red) = Number of Red Balls / Total Number of Balls
P(Red) = 6 / (8 + 6)
P(Red) = 0.4286
So, the probability of drawing four red balls in a row is the product of the probability of drawing a red ball four times in a row:
P(4 Red Balls) = P(Red) * P(Red) * P(Red) * P(Red)
P(4 Red Balls) = 0.4286 * 0.4286 * 0.4286 * 0.4286
P(4 Red Balls) = 0.04 or 4%
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1. For each equation, decide if it is always true or never true. a.x - 13 = x+1 b.x+12/1/2 = x - 21/1/2 c. 2(x + 3) = 5x + 6 - 3x d. x-3 = 2x - 3 - x e. 3(x - 5) = 2(x - 5) + x
According to given equation a. Never true, b. Always true, c. Always true, d. Always true, e. Always true.
What is function ?In mathematics, a function is a rule that assigns each element in one set, called the domain, to a unique element in another set, called the range. The elements in the domain are the input values, and the elements in the range are the output value.
According to the given information:a. x - 13 = x + 1
This equation is never true because if we subtract x from both sides, we get -13 = 1, which is a contradiction.
b. x + 12/1/2 = x - 21/1/2
This equation is always true because both sides simplify to x + 24 = x - 42. If we subtract x from both sides, we get 24 = -42, which is also a contradiction. Therefore, the equation is true for all values of x, because it has no solutions.
c. 2(x + 3) = 5x + 6 - 3x
This equation is always true. Simplifying both sides, we get 2x + 6 = 2x + 6, which is true for all values of x.
d. x - 3 = 2x - 3 - x
This equation is always true. Simplifying both sides, we get x - 3 = x - 3, which is true for all values of x.
e. 3(x - 5) = 2(x - 5) + x
This equation is true for all values of x. Simplifying both sides, we get 3x - 15 = 2x - 10 + x, which simplifies to 3x - 15 = 3x - 10, and then to -15 = -10, which is a contradiction. Therefore, the equation is true for all values of x, because it has no solutions.
Therefore, according to given equation a. Never true, b. Always true, c. Always true, d. Always true, e. Always true
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There are 500 wrist watches in a box. Out of these 50 wrist watches are found defective. One
watch is drawn randomly from the box. Find the probability that wrist watch chosen is a
defective watch
The probability that wrist watch chosen is a defective watch is 1 / 10
Total number of watches n(S)=500
Number of watches defective n(A)=50
P(A)= n(A) / n(S)
⇒P(A)= 50 / 500
Probability of watches to be defective = 1 / 10 or 50 / 500
Probability is a branch of mathematics that deals with the study of the likelihood or chance of an event occurring. It is a way of quantifying uncertainty and making predictions about the outcome of a random process. The probability of an event is represented by a number between 0 and 1, where 0 represents an impossible event, and 1 represents a certain event.
Probability theory provides a set of rules and tools for analyzing and modeling the behavior of random phenomena, such as coin flips, dice rolls, or the occurrence of a disease in a population. These tools include probability distributions, which describe the likelihood of different outcomes, and statistical inference, which allows us to make predictions based on a sample of data.
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Determine wheter the given vale of the varible is a soultion of the equatiom1/3 h=6 h=2
No, the given value of h=2 is not a solution of the equation 1/3h=6.
a teacher monitored the number of people texting during class each day and calculated the corresponding probability distribution. what type of probability distribution did the teacher use?
The given probability distribution "a teacher monitored the number of people texting during class each day and calculated the corresponding probability distribution." is a type of discrete probability distribution.
What is the Probability distribution?The probability distribution is used to describe the probability of each outcome in a series of possible outcomes. It is a mathematical representation of the outcomes of an experiment.
The teacher likely used a discrete probability distribution to calculate the probability of a certain number of people texting during class each day.
A discrete probability distribution is used to analyze data where the outcome is counted in whole numbers, such as the number of people texting in a given class period.
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The triangle has a perimeter of 8x-2 what is the leangth of the missing side
The length of the missing side is 4x + 5 units
To find the length of the missing side of the triangle, we need to use the fact that the sum of the lengths of all three sides of a triangle is equal to its perimeter. So, we can write:
Perimeter = (length of first side) + (length of second side) + (length of missing side)
Substituting the given values, we get:
8x-2 = (x-7) + 3x + (length of missing side)
Simplifying and solving for the missing side, we get:
8x-2 = 4x-7 + (length of missing side)
Length of missing side = (8x-2) - (4x-7)
Length of missing side = 4x + 5 units
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The given question is incomplete, the complete question is:
The triangle has a perimeter of 8x-2. what is the length of the missing side?
Ten cards are selected out of a 52 card deck without replacement and the number of Jacks is observed. This is an example of a Binomial Experiment.
true
false
The statement "Ten cards are selected out of a 52 card deck without replacement and the number of Jacks is observed. This is an example of a Binomial Experiment" is false.
What is a Binomial Experiment?A binomial experiment is an experiment that is repeated multiple times with each repetition having only two potential outcomes. In a binomial experiment, the probability of success remains constant from trial to trial.
The criteria for a binomial experiment are as follows:
The experiment is made up of a fixed number of trials.There are only two possible results for each trial: success and failure.The probability of success for each trial is the same.The trials are all independent of one another.The formula for calculating the probability of x successes in n trials is:P(x) = (ⁿCₓ)(pˣ)(q^(n-x))
Where p is the probability of success, q is the probability of failure (q = 1 - p), and ⁿCₓ is the combination formula.
Therefore, the statement "Ten cards are selected out of a 52-card deck without replacement and the number of Jacks is observed. This is an example of a "Binomial Experiment" being false. This is because the probability of drawing a jack changes with each trial, as the deck's composition changes after each card is drawn.
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Complete the sequence in the grids so that starting
of a 2x2 board turned off by pressing one at a time on each
grid we reach all the lit squares.
Another strategy is to start by pressing a square in the middle of the grid, and then pressing the squares adjacent to it. This should help you turn off the squares in a cross pattern.
What is sequence?In mathematics, a sequence is an ordered list of elements, typically numbers, which may be finite or infinite. Each element in the sequence is called a term. For example, the sequence {1, 2, 3, 4, 5} is a finite sequence of integers with five terms. Sequences can be represented in several ways, such as listing out the terms, using a formula to generate the terms, or using recursive rules. For example, the sequence of even numbers can be generated using the formula 2n, where n is a positive integer. So, the first five terms of the sequence are 2, 4, 6, 8, 10. Sequences are used in many areas of mathematics, including number theory, calculus, and statistics. They are also used in real-world applications, such as modeling population growth or predicting stock prices.
Here,
One common strategy is to start by pressing one of the corner squares, and then pressing the squares adjacent to it. Then, move to the adjacent corner square and repeat the process. This should help you turn off the squares in one diagonal line.
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Six more than the quotient of a number and 8 is equal to 4
use the variable x for the unknown number
!!!TRANSLATE INTO A EQUATION!!!
Answer:
x/8 + 6 = 4
Step-by-step explanation:
x / 8 + 6 = 4
x/8 = -2
x = 8*-2 = -16.
1)Holtz model accounts for any growth factor present in a time series by?
a-the use of a linear trend
b-smoothing the most recent trend by last periods smoothed trend
c-adding trend exponential smoothing to estimate
d-all of the above
2)the adaptive response rate single exponential smoothing model is termed adaptive because
a-it responds to changes in the pattern of data
b-the smoothing parameter changes each period
c-it has the ability to model changes in the mean of time series
d-it can cirtually take care of itsself in generating forecasts
e-all of the above
The correct option for question 1 is (c), while the correct option for question 2 is (a).
When answering questions on the platform Brainly, it is important to always be factually accurate, professional, and friendly. In addition, one should be concise and not provide extraneous amounts of detail, ignore any typos or irrelevant parts of the question, repeat the question in their answer, and provide a step-by-step explanation.Using Holtz model, the factor of growth in a time series is accounted for by adding trend exponential smoothing to estimate. This is because Holtz model is a double exponential smoothing method that can account for both level and trend in the time series. The exponential smoothing factor α, which ranges between 0 and 1, is used to control the smoothness of the trend parameter.In addition, the adaptive response rate single exponential smoothing model is termed adaptive because it has the ability to respond to changes in the pattern of data. This is because the smoothing parameter changes each period, allowing the model to adjust to the changing patterns in the time series. Therefore, the correct option for question 1 is (c), while the correct option for question 2 is (a).
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⠀⠀⠀⠀⠀⠀⢠⡟⠀⠀⠀⢸⡆⠀⠀⠀⠀⠘⢶⡀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⣾⠃⠀⠀⠀⠀⠀⣇⠀⠀⠀⠀⠀⠀⠻⡄⠀⠀⠀
⠀⠀⠀⢀⡿⠀⠀⠀⠀⠀⠀⣀⣿⣀⣀⣀⣀⣀⣀⡀⢹⣦⣤⠄
⢀⣤⣶⣿⣿⣷⣶⠟⠛⠉⠀⠀⢸⡄⠀⠀⠉⠙⠛⠿⣿⣿⣦⢻
⠀⣸⠃⢿⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠘⣿⠀⠀
a 20-volt electromotive force is applied to an lr-series circuit in which the inductance is 0.1 henry and the resistance is 40 ohms. find the current i(t) if i(0) = 0.
i(t) = ___
Determine the current as t → [infinity].
lim t→[infinity] i(t) =_____
The time becomes infinity, i(t) will become constant, i.e., lim t→[infinity] i(t) = 0.
The current of the given LR-series circuit can be determined using the formula I = (E/R) * (1 - e^-Rt/L).The current i(t) if i(0) = 0 in the LR-series circuit is given by i(t) = 0.125A. The current as t → [infinity] is given by lim t→[infinity] i(t) = 0.How to solve this?The formula for the current in the LR-series circuit is given by:Where E is the electromotive force, R is the resistance, L is the inductance, t is time and I is the current.I = (E/R) * (1 - e^-Rt/L)Given E = 20V, R = 40Ω, L = 0.1H, and i(0) = 0Substitute these values in the above formula.I = (20/40) * (1 - e^-40t/0.1)I = 0.5(1 - e^-400t)I = 0.5 - 0.5e^-400tSo the current is i(t) = 0.5 - 0.5e^-400t.Limit of t as t → [infinity] means that when the time is allowed to run infinitely, then the current will become constant. Hence, when the time becomes infinity, i(t) will become constant, i.e., lim t→[infinity] i(t) = 0. Answer: The current is i(t) = 0.5 - 0.5e^-400t. Limit of t as t → [infinity] means that when the time is allowed to run infinitely, then the current will become constant. Hence, when the time becomes infinity, i(t) will become constant, i.e., lim t→[infinity] i(t) = 0.
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what is an equation of the line that passes through the points (5 -6) and (-5 -2)
Answer:
7
Step-by-step explanation:
A(-5,−2) , B(5,−6)
Equation of line AB⟹
(5-6), (-5-2) = 3+3 = 6+1= 7