The vectors [8 -2 6] and [12 -3 9] are option (c) linearly independent because neither vector is a multiple of the other.
A vector is an entity that has both magnitude and direction. It is represented by an ordered set of numbers, which correspond to the coordinates of its endpoint in a given coordinate system.
In this problem, we are given two vectors: [8 -2 6] and [12 -3 9]. To determine if they are linearly independent or not, we need to check if one vector can be expressed as a linear combination of the other.
Let us assume that the first vector can be expressed as a linear combination of the second vector. That is, there exist constants a, b, and c such that:
[8 -2 6] = a[12 -3 9] + b
where b is a vector. Simplifying the above equation, we get:
8 = 12a + b1
-2 = -3a + b2
6 = 9a + b3
where b1, b2, and b3 are the respective components of vector b. Now, we can solve for a, b1, b2, and b3 using the system of linear equations. Solving for a, we get a = 2/3. Substituting this value in the remaining equations, we get:
b1 = -4/3, b2 = -2/3, and b3 = 2/3
Therefore, the vector b is [-4/3 -2/3 2/3]. We can verify that the first vector cannot be expressed as a linear combination of the second vector and b. Hence, the given vectors are linearly independent.
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Find each angle measure to the nearest degree.
3) sin U = 0.9945
4) tan C = 3.7321
The measure of angle U = 84° and the measure of angle C = 75°
The inverse of a trigonometric function.The sine, cosine, tangent, cotangent, secant, and cosecant functions are the fundamental trigonometric functions. Inverse trigonometric functions are just the inverse functions of these functions. They can also be referred to as antitrigonometric functions or arcus functions. To find the angle for any trigonometric ratio, these inverse trigonometric functions are applied.
Given that:
sin U = 0.9945
U = sin⁻¹ (0.9945)
U = 83.988°
U ≅ 84° ( to the nearest degree)
tan C = 3.7321
C = tan⁻¹ (3.7321)
C = 75°
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I've been working on this problem for the last hour and can't quite seem to get it right.
A tank is full of water. Find the work required to pump the water out of the spout. Use the fact that water weighs 62.5 lb/ft3. (Assume a = 4 ft, b = 5 ft, and c = 6 ft.)
The work required to pump the water which weighs 62.5 lb/ft3 out of the spout is 15000 foot-pounds.
To find the work required to pump the water out of the spout, we need to calculate the weight of the water in the tank and then multiply by the height of the spout to find the potential energy of the water.
First, we need to find the volume of the tank, which is given by:
V = a * b * c = 4 ft * 5 ft * 6 ft = 120 ft^3
Next, we can find the weight of the water in the tank, using the fact that water weighs 62.5 lb/ft^3:
W = V * ρ = 120 ft^3 * 62.5 lb/ft^3 = 7500 lb
So the weight of the water in the tank is 7500 pounds.
Now, we can find the potential energy of the water by multiplying the weight by the height of the spout. Let's assume the spout is 2 feet above the top of the tank:
PE = W * h = 7500 lb * 2 ft = 15000 ft-lb
So the work required to pump the water out of the spout is 15000 foot-pounds (ft-lb). This means that if we used a pump that was 100% efficient, it would require 15000 ft-lb of work to pump all the water out of the tank. However, in reality, pumps are not 100% efficient, so the actual work required would be greater than 15000 ft-lb.
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Your credit card has a balance of $4500 and an interest rate of 22%. The credit card requires a minimum payment of 3%.
What is your minimum payment?
What is your interest for 1 month?
What is your new balance?
Answer: Your welcome!
Step-by-step explanation:
Your minimum payment would be $135 ($4500 x 0.03 = $135).
Your interest for 1 month would be $99 ($4500 x 0.22 = $990 x 0.1 = $99).
Your new balance would be $4634 ($4500 + $99 - $135 = $4664).
X
5
Z
10
5√3
Y
Find sin cos tan
The trigonometry ratios have their values to be
sin(x) = √3/2cos(x) = 0.5tan(x) = √3How to determine the trigonometry ratiosThe complete question is added as an attachment
From the question, we have the following parameters that can be used in our computation:
Hypotenuse = 10
Adjacent = 5
Opposite = 5√3
Using the above as a guide, we have the following:
sin(x) = Opposite/Hypotenuse
cos(x) = Adjacent/Hypotenuse
tan(x) = Opposite/Adjacent
Using the above as a guide, we have the following:
sin(x) = 5√3/10 = √3/2
cos(x) = 5/10 = 0.5
tan(x) = 5√3/5 = √3
The above are the values of the trigonometry ratios based on the attached figure
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An train station has determined that the relationship between the number of passengers on a train and the total weight of luggage stored in the
baggage compartment can be estimated by the least squares regression equation y = 200+ 23x. Predict the weight of luggage for a flight with
57 passengers.
Answer: pounds
The residual sum of squared values is reduced using the least-squares method. The predicted weight of luggage for a flight with 57 passengers is 1511 Pounds.
What is meant by least-squares method?
The least-squares method is a statistical technique used to find the best fit line for a set of data points. It works by minimizing the sum of the squared differences between the observed values of a dependent variable and the values predicted by a linear function of one or more independent variables.
In other words, the least-squares method finds the line that best represents the relationship between two or more variables, such that the sum of the squared errors (the difference between the observed values and the predicted values) is minimized. The resulting line is known as the regression line or best-fit line, and it can be used to make predictions about future values of the dependent variable based on the values of the independent variable.
Based on the given least squares regression equation, we have:
y: the total weight of luggage stored in the baggage compartmentx: the number of passengers on the train200: the intercept term of the regression equation23: the slope of the regression equationTo predict the weight of luggage for a flight with 57 passengers, we simply substitute x = 57 into the regression equation:
y = 200 + 23x
= 200 + 23(57)
= 200 + 1311
= 1511
Therefore, the predicted weight of luggage for a flight with 57 passengers is 1511 pound.
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Kendallyn wants to know the height of a sailboat mast. if the sailboat mast casts a shadow 45 meters long and a nearby marble column that is 8 meters tall casts a shadow 15 meters long, then the sailboat mast is___ meters long. Write your answer as a whole number or a decimal.
The sailboat mast casts a shadow 45 meters long and a nearby marble column that is 8 meters tall casts a shadow 15 meters long, then the height of the sailboat mast is 24 meters.
We can use proportions to solve this problem. Let's let h be the height of the sailboat mast, then we have:
h/45 = 8/15
Cross-multiplying, we get:
15h = 8 * 45
Simplifying, we get:
15h = 360
Dividing by 15, we get:
h = 24
Therefore, the height of the sailboat mast is 24 meters. This means that the sailboat mast is 3 times as tall as the marble column, since its shadow is 3 times as long.
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what is the kinetic energy of 1500 kg pick-up truck traveling at 31.0 m/sec.
The kinetic energy of a 1500 kg pick-up truck traveling at 31.0 m/sec will be 720 kJ.
What is kinetic energy?If the body of the mass (m) is moving with a velocity (v), then the body possesses the energy which is known as kinetic energy. The SI unit of the kinetic energy is Joule. Then the formula is given as,
KE = 1/2 x mv²
The kinetic energy of a 1500 kg pick-up truck traveling at 31.0 m/sec is given as,
KE = 1/2 x 1500 x 31²
KE = 720,750 Joule
KE = 720 kJ
The kinetic energy of a 1500 kg pick-up truck traveling at 31.0 m/sec will be 720 kJ.
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Contessa is solving an absolute value inequality. She writes the compound inequality -7<=8-3q<=7 as her first step. Which inequality is Contessa solving?
The inequality that Contessa is solving is obtained as 5 ≥ q ≥ 1/3.
What is an inequality?
In Algebra, an inequality is a mathematical statement that uses the inequality symbol to illustrate the relationship between two expressions. An inequality symbol has non-equal expressions on both sides. It indicates that the phrase on the left should be bigger or smaller than the expression on the right, or vice versa.
The given compound inequality is = -7 ≤ 8 - 3q ≤7
To solve this compound inequality, start by subtracting 8 from each part of the inequality -
-15 ≤ -3q ≤ -1
Next, divide each part by -3, remembering to flip the direction of the inequalities since it is getting divided by a negative number -
5 ≥ q ≥ 1/3
So the solution to the inequality -7 ≤ 8-3q ≤ 7 is the set of all q values that lie between 1/3 and 5, including the endpoints 1/3 and 5.
Note that this solution set is different from the solution set of the absolute value inequality |8-3q| < 7, which does not include the endpoints.
Therefore, the inequality is 5 ≥ q ≥ 1/3.
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Jennifer was given $600. She decided to save 15% of the money.
How much did she save? $____.00
Do not type in the dollar sign. Just type in the missing amount.
Answer: She saved 90 dollars.
To solve this we must find amount of 600 that makes 15 percent.
15 % of 600 is 90. This means that Jennifer saved up 90 dollars
I hope that this helps & Good Luck <3 !!!
Referring to the figure, use the graph to estimate the
roots of the equation: y = x2 - 2x - 8
Answer:
The roots are -2 and 4
Step-by-step explanation:
Using the graph, we can estimate the roots of the equation by seeing where it crosses the x axis.
It appears to cross the x axis at -2 and 4.
The roots are -2 and 4
consider a system using a multilevel feedback queue scheduler. its scheduler is configured to have four queues, which are, in order of highest priority to lowest priority: q1, q2, q3, and q4. the queues have quantums sized 5s, 10s, 20s, and 40s, respectively. for each of the following three processes, determine which queue it is in when it begins its final quantum
In this example, process A completed its final quantum in q4, process B completed its final quantum in q4, and process C completed its final quantum in q4.
To determine which queue each process is in when it begins its final quantum, we need to know the length of time each process has been running and how many times it has already used each queue's quantum. Without that information, we cannot determine which queue a process will be in at a specific point in time. However, we can provide an example of how a process might move between the queues over time.
Let's consider the following three processes:
Process A - CPU burst time = 100s
Process B - CPU burst time = 30s
Process C - CPU burst time = 50s
Assume that all three processes arrive at the scheduler at the same time and are added to q1, the highest priority queue.
When the scheduler begins, it will select the first process in q1, which is process A. Since q1 has a quantum of 5s, process A will run for 5s before it is preempted and placed at the back of q2.
The next process in q1 is B. B will also run for 5s before being preempted and placed at the back of q2.
Next, the scheduler will select process C from q1. C will run for 5s before being preempted and placed at the back of q2.
Now the scheduler has completed one round-robin cycle through q1, and all the processes in q1 have used up their q1 quantum. The scheduler will move on to q2 and select the first process in that queue, which is process A. Since q2 has a quantum of 10s, process A will run for an additional 5s before being preempted and placed at the back of q3.
The next process in q2 is B. B will run for 10s before being preempted and placed at the back of q3.
Next, the scheduler will select process C from q2. C will run for 10s before being preempted and placed at the back of q3.
Now the scheduler has completed one round-robin cycle through q2, and all the processes in q2 have used up their q2 quantum. The scheduler will move on to q3 and select the first process in that queue, which is process A. Since q3 has a quantum of 20s, process A will run for an additional 10s before being preempted and placed at the back of q4.
The next process in q3 is B. B will run for 20s before being preempted and placed at the back of q4.
Next, the scheduler will select process C from q3. C will run for 20s before being preempted and placed at the back of q4.
Now the scheduler has completed one round-robin cycle through q3, and all the processes in q3 have used up their q3 quantum. The scheduler will move on to q4 and select the first process in that queue, which is process A. Since q4 has a quantum of 40s, process A will run for an additional 20s before completing its CPU burst.
The next process in q4 is B. B will run for 30s before completing its CPU burst.
Finally, the scheduler will select process C from q4. C will run for 40s before completing its CPU burst.
However, it's important to note that the exact behavior of the scheduler will depend on the length of time each process has been running and how many times it has already used each queue's.
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Evaluate h - 3 for h = 1
The result of the function is h = 1 is equal to -2
Evaluating linear equationsLinear equations are equations that has a leading degree of 1.
Given the linear equation f(h) = h - 3
We need to determine the resulting value when h is equal to 1
f(1) = 1 - 3
f(1) = -2
Hence the value of the function given if the value of h is 1 is -2
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find the mean and median of each of the following sets of data. determine the deviation from the mean for each data point within the sets and find the mean deviation for each set. 24.49 24.68 24.77 24.83 24.73
The average distance from the mean is 0.09.
The mean is also known as the average and is calculated by adding up all the values in the set and then dividing the sum by the total number of values.
So, for the given set of data: 24.49, 24.68, 24.77, 24.83, 24.73, the mean would be calculated as follows:
Mean = (24.49 + 24.68 + 24.77 + 24.83 + 24.73) / 5
= 24.70
It tells us what the typical value is within the data set. In this case, the mean value of the data set is 24.70.
Next, let's find the median of the set of data. The median is the middle value of a data set when it is arranged in numerical order. In this case, the data set is already arranged in numerical order, so we can easily find the median.
The median value of the data set is the middle value, which is 24.77.
Now, we will calculate the deviation from the mean for each data point within the set. The deviation from the mean tells us how far each value is from the mean value. This is calculated by subtracting the mean from each value in the set.
Deviation from the mean for each data point:
-0.21, -0.02, 0.07, 0.13, 0.03
As you can see, some values are above the mean, and some are below the mean. The deviation from the mean can be used to determine how spread out the data is from the mean value.
Finally, we will calculate the mean deviation for the set. The mean deviation is the average of the absolute values of the deviation from the mean.
Mean deviation = (|(-0.21)| + |(-0.02)| + |0.07| + |0.13| + |0.03|) / 5
= 0.09
The mean deviation tells us the average distance from the mean value.
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Bacteria colonies can increase by 45% every 7 days. If you start with 200 bacteria microorganisms, how large would the colony be after 35 days? First, identify I, the starting amount. Future Amount = [?](1+ Remember: Future Amount = (1 + r)t
After 35 days, the colony will be 1281.95.
What are Exponential Functions?Exponential functions are functions where the independent variable, x is in the exponent.
Given that,
Bacteria colonies can increase by 45% every 7 days.
We know that,
Future amount = l (1 + r)^t
where l is the starting amount, r is the growth rate and t is the time.
Here,
l = 200
r = 45% = 45 / 100 = 0.45
t = 35 / 7 = 5
Substituting,
Future amount = (200) (1 + 0.45)⁵
= 1281.95
Hence the required amount is 1281.95.
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Decide how many solutions this equation has:
x2 - 2x + 1 = 0
An experiment observing the growth of two germ strand populations finds these patterns.
• The population of the first germ is represented by the function A(x) = (1.3)^x+9
• The population of the second germ is represented by the function B (x) = ^4x+1
Which function best represents function R, the ratio of the population of the second germ to the population of the first germ?
A. R(x) = (1.3)^3x-8
B
An experiment observing the growth of two germ strand populations finds these patterns.
• The population of the first germ is represented by the function A(x) = (1.3)^x+9
• The population of the second germ is represented by the function B (x) = ^4x+1
Which function best represents function R, the ratio of the population of the second germ to the population of the first germ?
A. R(x) = (1.3)^3x-8
B. R(x) = (1.3)^5x+10
C.R(x) = (2.6) ^3x-8
D. R(X) =(2.6) ^4x^2+9
The right answer, based on the provided assertion, is (C) R(x) = 2.6³ˣ⁻⁸.
What does an arithmetic the expression mean?Mathematical expressions consist of at least two integers or factors, a minimum of one math procedure, and a sentence. It's possible to multiply, divide, add, or remove with this mathematical procedure. An expression's form is as follows: Expression: (Math Operator, Number/Variable, Math Operator)
To find the ratio of the population of the second germ to the population of the first germ, we can divide the function for the population of the second germ by the function for the population of the first germ. That is:
R(x) = B(x) / A(x)
Plugging in the given functions, we get:
R(x) = (x+1) / (1.3)ˣ⁺⁹
To simplify this expression, we can use the properties of exponents and rewrite it as:
R(x) = 2.6ˣ⁻⁸
Therefore, the function that best represents the ratio of the population of the second germ to the population of the first germ is R(x) = 2.6ˣ⁻⁸
So, the correct option is (C) R(x) = (2.6)³ˣ⁻⁸.
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Add. Write your answer in simplest form.
3/8 + 2/5 WILL GIVE BRAINLIST IF RIGHT!!!
Predict the missing component in the nuclear equation.
The missing component in the nuclear equation.137Cs55 → X + -e will be 137Ba56. option B is correct.
What is nuclear reaction?The particles in the nucleus are changed, and one element is transformed into another element when particles in the nucleus are gained or lost.
Nuclear reactions are processes in which one or more nuclides are produced from the collisions between two atomic nuclei or one atomic nucleus and a subatomic particle.
This was the first observation of an induced nuclear reaction, that is, a reaction in which particles from one decay are used to transform another atomic nucleus.
The most notable man-controlled nuclear reaction is the fission reaction which occurs in nuclear reactors. A target nucleus is within the range of nuclear forces for the time allowing for numerous interactions between nucleons.
therefore, option B is correct.
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Part 2
Bc my autocorrect messed up my other question.
Make a word using all of these letters
RrCsVb
This doesn't have to be an actual word but one that is memorable. Please use all of the words
Answer:
CrabSVR
BRscrV
ScarbRV
VRbScCr
Step-by-step explanation:
I can suggest that some of these words might be memorable because they are short and have a combination of consonants and vowels that make them sound unique and catchy. For example, "ScrubVR" has a rhythmic and playful sound to it, while "BRscrV" has a more abbreviated and tech-like feel to it. Ultimately, what makes a word memorable is highly subjective and varies from person to person.
Answer: he right
Step-by-step explanation:
A television and DVD player cost total of $1192. The cost of the television is three times the cost of the DVD player. Find the cost of each, item.
Cost of television:
Cost of DVD player:
The cost of the DVD player and the cost of the television will be $298 and $894, respectively.
What is the solution to the equation?An answer to a formula is any variable value that fulfills the equal outcomes, that is, it tends to make the Left Hand Side (LHS) and Right Hand Side (RHS) of the formula equal. To solve an equation, you must locate the feasible solution) to that formula.
A television and DVD player cost a total of $1192. The cost of the television is three times the cost of the DVD player.
Let 'x' be the cost of the DVD player and 'y' be the cost of the television. Then the equations are given as,
x + y = 1,192 ...1
y = 3x ...2
From equations 1 and 2, then we have
x + 3x = 1192
4x = 1192
x = $298
Then the value of 'y' is given as,
y = 3 (298)
y = $894
The cost of the DVD player and the cost of the television will be $298 and $894, respectively.
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The population of Lcavetown is 123,000 people, and is decreasing at a rate of 9,4% per year What will the population of Leavetown be 100 years from now? (round to the nearest person)
Answer:
6
Step-by-step explanation:
You want the population of Leavetown in 100 years if it is 123,000 now and decreasing at the rate of 9.4% per year.
Exponential equationThe exponential equation that models the population is ...
p = 1230000·(1 -0.094)^t
where t is the number of years later.
ApplicationFor t=100, the attached calculation shows the population in 100 years is about 6 persons.
Forty percent of what number is 18?
Answer:
45
Step-by-step explanation:
Y = forty percent of blank to make 18
18 = 40/100 x Y
Y = 18 x 100/40
Y = 18 x 100 divided by 40
Y = 45
d. In this situation, what does the solution to the equation C(t) = 2 tell us? Find
that solution.
e. Write an equation that would allow us to find the age of the car when we know
C(t).
ora 1 Unit 4
n 17
CC BY 2019 by Illustrative Mathematics®
The equation C(t) = 2 tells us that at a moment of t, the numeric value of the variable C is of 2 units.
How to define the ordered pair and how it relates to the numeric value?The general format of an ordered pair is given as follows:
(x,y).
The meaning of an ordered pair (x,y) is that y = f(x), meaning that the numeric value of the function at the value of x is of y.
The ordered pair for this problem is given as follows:
(t, C(t)) = (t,2).
Meaning that at a moment of t, the numeric value of the variable C is of 2 units.
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The equation:
(x³+2x²) (3x²+2x+1)=x³ (3x² + 2x+1) + 2x² (3x² + 2x+1) is an example of which method/property?
A. Distributive Property
B. FOIL
C. Vertical multiplication
D. Collect like terms
Suppose the data have a bell-shaped distribution with a mean 30 and a standard deviation of 5. Use the empirical rule to determine the percentage of data between 15 and 45.
Select one:
a. 95.00%
b. 97.35%
c. 99.70%
d. 81.50%
According to the empirical rule, for a bell-shaped distribution with a mean of 30 and a standard deviation of 5 is approximately 99.7%,
Using the empirical rule, we know that for a normal distribution with a mean of 30 and a standard deviation of 5, approximately:
68% of the data falls within 1 standard deviation of the mean, which in this case is between 25 and 35.95% of the data falls within 2 standard deviations of the mean, which in this case is between 20 and 40.99.7% of the data falls within 3 standard deviations of the mean, which in this case is between 15 and 45.Therefore, the percentage of data between 15 and 45 is approximately 99.7%, which corresponds to option c.
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Find the area of the isosceles triangle
The area of the isosceles triangle is 96 ft²
How to determine the areaThe formula for area of a triangle is expressed as
Area = 1/2bh
Where , b is the base and h is the height
We have that;
Base = 16ft
Using the Pythagorean theorem, we have;
20² - 16² =h²
Find the squares
h = √144
h= 12ft
Substitute the values
Area = 1/2 × 12 × 16
Multiply the values
Area = 96 ft²
Hence, the value is 96 ft²
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what is the equation of the secant line connecting the point (1,f(1)) to the point (0.9,f(0.9))? the equation of this secant line is y
(a) The equation of the secant line connecting (1, f(1)) and (0.9, f(0.9)) is y = -x + 2.1.
(b) The slope of the tangent line to f at x is f'(x) = -cos(x), and the equation of the tangent line at (x, f(x)) is y = -cos(x)*x + sin(x) + cos(x)*x.
In contrast to the tangent line, which meets a curve just once and has the same slope as the curve at that point, the secant line is a straight line that connects two locations on a curve. In this task, we are required to determine the equations of the secant and tangent lines at various places given a function f(x).
Using the two provided locations, we determine the slope of the secant line in section (a), which is equal to the difference between the y- and x-coordinates. The equation of the line is therefore written using the point-slope form, and it is y = -x + 2.1.
In part (b), we use the definition of the derivative to find the slope of the tangent line at a given point x. We then use the point-slope form of a line to write the equation of the tangent line, which has the same slope as the derivative and passes through the point (x, f(x)). In this case, the slope of the tangent line is -cos(x), and the equation of the tangent line is
y = -cos(x)*x + sin(x) + cos(x)*x.
The complete question is provided in the image below.
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10. Usando el metodo de la iteracion del punto fijo
¿Para que raiz el porcentaje de error es del
16.1%?
*
(4 puntos)
f (x) = x − (√5x – e^x)comenzando en xo = 0.5
O 1.7278
O 1.7351
O 1.4482
O 0.9226
Answer: Your welcome!
Step-by-step explanation:
O 1.7278
El porcentaje de error del 16.1% se refiere a la raíz de la ecuación f(x) = x - (√5x - e^x), comenzando en xo = 0.5. Utilizando el método de iteración del punto fijo, se obtiene que la raíz de esta ecuación es 1.7278.
Answer:
Step-by-step explanation:
Para encontrar la raíz de la ecuación f(x) = x - (√(5x) - e^x) con un porcentaje de error del 16.1%, podemos utilizar el método de iteración de punto fijo con la siguiente fórmula:
x1 = f(x0) + x0
Donde x0 es el valor inicial, f(x) es la función y x1 es el siguiente valor de la raíz aproximada.
Primero, evaluamos la función en x0 = 0.5:
f(0.5) = 0.5 - (√(5*0.5) - e^0.5) = -0.2749
Luego, usamos la fórmula para encontrar el siguiente valor:
x1 = f(0.5) + 0.5 = 0.2251
Continuamos iterando hasta que el porcentaje de error sea menor o igual al 16.1%. Podemos calcular el porcentaje de error relativo por iteración con la siguiente fórmula:
Error relativo (%) = |(x_nuevo - x_viejo) / x_nuevo| * 100%
donde x_nuevo es el valor actual de la raíz aproximada y x_viejo es el valor anterior de la raíz aproximada.
Después de algunas iteraciones, encontramos que la respuesta que tiene un porcentaje de error del 16.1% es 1.7351.
Choose the number of possible combinations shown by this tree diagram.
2 combinations
4 combinations
5 combinations
6 combinations
The number 345,600 can be expressed as 2^a*3^b*5^b for integers a, b and c. What is the value of the product abc?
For a number 345,600 which is expressed as 2ᵃ × 3ᵇ × 5ᶜ, ae integers a, b and c. Then the value of the product abc is equals to the 54.
We have, a number 345,600, which can be expressed as 2ᵃ × 3ᵇ × 5ᶜ. That is it can be written as 345,600 = 2ᵃ × 3ᵇ × 5ᶜ, which is prime factorazation of number. To determine the value of a , b , c, we have to do prime factorization of number 345,600. Prime factorzation of a number contains all prime factors of a number. So,
345600 = 3456×100 = 576× 6 × 100
= 24² × 2×3 × 10² = ( 2×2×2×3)² × 2× 3×(2× 5)²
= 2⁶ × 3² × 2× 3×2²× 5²
345,600 = 2⁹ × 3³ × 5²
but 345,600 = 2ᵃ × 3ᵇ × 5ᶜ,
=> 2ᵃ × 3ᵇ × 5ᶜ = 2⁹ × 3³ × 5²
On comparing the powers of 2, 3, and 5 in above equation, we get a = 9 , b = 3 , c = 2.
Therefore, the value of product of a, b, and c
= abc = 9×3×2 = 54
Hence, the value of product is 54.
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Complete question:
The number 345,600 can be expressed as 2ᵃ × 3ᵇ × 5ᶜ for integers a, b and c. What is the value of the product abc?