Answers
Answer:
Y= 3/5-4
Step-by-step explanation:
What is slope-intercept form? Slope intercept form is an equation for graphing. It is y=mx+b. The "m" stands for the slope, or how much coordinates it takes to move to the next point. The "b" stands for the y-intercept, or where the line is perfectly on the y-line.
Step One: The first part of the equation is the slope, so let's figure that out. Since this one a graph, it is easy to tell the slope. The points are nicely marked, so we don't have to guess which points are visible. We are going up 3 jumps and then across 5 jumps. The slope is always "rise/run" where the "rise" is the y and "run" is x. So, the slope is 3/5x.
Step Two: For the last part, we need to know the y-intercept. It is clearly shown on the graph: -4. Because it is negative, we remove the plus sign because a plus with a negative is subtraction.
Step Three: We can combine both parts and that is the answer: y=3/5x-4.
Related Questions
the ages of all the patients in the isolation ward of the hospital are 38, 26, 13, 41, and 22. what is the population variance?
Answers
To find the population variance of the ages of patients in the isolation ward, we need to calculate the average of the squared deviations from the mean.
To find the population variance, we follow these steps:
Find the mean (average) of the ages:
Mean = (38 + 26 + 13 + 41 + 22) / 5 = 28
Calculate the deviation of each age from the mean:
Deviation1 = 38 - 28 = 10
Deviation2 = 26 - 28 = -2
Deviation3 = 13 - 28 = -15
Deviation4 = 41 - 28 = 13
Deviation5 = 22 - 28 = -6
Square each deviation:
Deviation[tex]1^2[/tex] = [tex]10^2[/tex] = 100
Deviation[tex]2^2[/tex] = [tex](-2)^2[/tex] = 4
Deviation[tex]3^2[/tex] = [tex](-15)^2[/tex] = 225
Deviation[tex]4^2[/tex] = [tex]13^2[/tex] = 169
Deviation[tex]5^2[/tex] = [tex](-6)^2[/tex] = 36
Find the average of the squared deviations:
Variance = (100 + 4 + 225 + 169 + 36) / 5 = 106 / 5 = 21.2
Therefore, the population variance of the ages of patients in the isolation ward is 21.2.
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A yogurt company claims that it prints a free yogurt coupon under a randomly selected 20% of its lids. A loyal customer purchases 85 yogurt cups, and records whether each was a winner. After consuming all 85 cups, he is disappointed to see that only 12 (14.1%) of his yogurt cups contained coupon codes. He performs a 99% confidence interval for the proportion of yogurt cups containing coupon codes, obtaining (0.044, 0.238). What conclusion can the customer draw about the yogurt company’s claim?
Answers
Answer:
The customer can conclude that the company's claim is correct
Step-by-step explanation:
The percentage of lids that has a free yogurt coupon = 20%
The number of cups a loyal customer purchases = 85 yogurt cups
The number of cups that contained a coupon = 12 (14.1%)
The confidence interval performed = 99% confidence interval for the proportion of yogurt cups containing coupon codes
The interval obtained = (0.044, 0.238)
Therefore, the range of proportion within which the true proportion exists is 0.044 < [tex]\hat p[/tex] < 0.238
The range of percentage within which the true percentage exist is therefore;
0.044 × 100 = 4.4% < [tex]\hat p[/tex] × 100 < 0.238 × 100 = 23.8%
Given that the possible true percentage of lids that has a coupon is between 4.4% and 23.8% at 99% confidence level, the customer can conclude that only 12 of his yogurt cup contained coupon by chance and that the company's claim is correct.
Answer:
A, the company’s claim may be justified because 0.2 is in the confidence interval.
Step-by-step explanation:
given the system of equations x 3y z = −2 2x 5y z = −5 x 2y 3z = 1 . the determinant of the matrix of coefficients is −3. the value of z in the solution set is:: (a) z=−2/3 (b) z=5/3 (c) z=4/3 (d) z=−2 (e) None of the above
Answers
The value of z in the solution set is approximately -8.33 for the determinant of the matrix of coefficients is −3, Option E is the correct answer.
To solve the system of equations, we can use the method of determinants. The value of z can be determined by finding the determinant of the matrix of coefficients.
The given system of equations can be represented as:
| 1 3 1 | | x | | -2 |
| 2 5 1 | × | y | = | -5 |
| 1 2 3 | | z | | 0 |
The determinant of the matrix of coefficients is -3, which is non-zero. This means that the system of equations has a unique solution.
To find the value of z, we need to calculate the determinant of the matrix obtained by replacing the z-column with the constants column:
| 1 3 -2 |
| 2 5 -5 |
| 1 2 0 |
Using the rule of determinants for a 3x3 matrix, we can calculate the determinant:
Det = (1 × (50 - -52)) - (3 × (20 - -51)) + (-2 × (2 × -5 - 51))
= (1(0 + 10)) - (3 × (0 + 5)) + (-2 × (-10 - 5))
= (110) - (35) + (-2 × -15)
= 10 - 15 + 30
= 25
Since the determinant is non-zero, the system has a unique solution. To find the value of z, we divide the determinant of the matrix obtained by replacing the z-column with the constants column by the determinant of the matrix of coefficients:
z = Detz / Det
= 25 / -3
= -8.33
Therefore, the value of z in the solution set is approximately -8.33.
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The question is -
Given the system of equations x + 3y + z = -2
2x + 5y + z = -5
x+ 2y + 3z = 0
The determinant of the matrix of coefficients is -3. The value of z in the solution set is:
(a) z=−2/3
(b) z=5/3
(c) z=4/3
(d) z=−2
(e) None of the above
A patient is given 3 mg of morphine to control pain. About 31% of any morphine in the blood is washed out every hour. (a) Construct a function that models the level M of morphine (in mg) in the blood t hours after one dose. M = (b) How much morphine (in mg) remains in the blood after 5 hours? (Round your answer to two decimal places.) mg (c) Estimate how long, in hours, it will take for the amount of morphine left to drop to 0.1 mg. (Round your answer to two decimal places.) h
Answers
a) the function that models the level M of morphine (in mg) in the blood t hours after one dose is M = [tex]3 * (0.69)^t[/tex]
b) 0.50 mg of morphine remains in the blood after 5 hours.
c) it will take approximately 14.67 hours for the amount of morphine left to drop to 0.1 mg.
(a) To construct a function that models the level M of morphine (in mg) in the blood t hours after one dose, we can use the formula for exponential decay:
M = [tex]initial amount * (1 - decay rate)^t[/tex]
Given that the patient is initially given 3 mg of morphine and 31% (0.31) of any morphine is washed out every hour, we can write the function as:
M = [tex]3 * (1 - 0.31)^t[/tex]
Simplifying further, we have:
M = [tex]3 * (0.69)^t[/tex]
Therefore, the function that models the level M of morphine (in mg) in the blood t hours after one dose is M = [tex]3 * (0.69)^t[/tex]
(b) To find out how much morphine remains in the blood after 5 hours, we can substitute t = 5 into the function and calculate the value of M:
M = 3 * (0.69)⁵
M ≈ 3 * 0.1681
M ≈ 0.5043
So, approximately 0.50 mg of morphine remains in the blood after 5 hours.
(c) To estimate how long it will take for the amount of morphine left to drop to 0.1 mg, we need to find the value of t when M = 0.1 in the function:
0.1 = [tex]3 * (0.69)^t[/tex]
Dividing both sides by 3:
0.0333 ≈ [tex](0.69)^t[/tex]
Taking the logarithm of both sides:
log(0.0333) ≈ [tex]log[(0.69)^t][/tex]
Using the logarithm properties, we can bring down the exponent:
log(0.0333) ≈ t * log(0.69)
Now, we can solve for t by dividing both sides by log(0.69):
t ≈ log(0.0333) / log(0.69)
Calculating this expression:
t ≈ -2.3859 / -0.1625
t ≈ 14.67
So, it will take approximately 14.67 hours for the amount of morphine left to drop to 0.1 mg.
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___ divided by 3x3 =12
Answers
Answer:
108
Step-by-step explanation:
Answer:
108 hope this helps! :)
I need some answer plssss help me
Answers
A. Find the unknown term of each proportion.
1. Answer: X=5
Step-by-step explanation:
x/7=15/21 ==> 21x=7(15) ==> 21x=105
21x/21=105/21 ==> x=5
2. Answer: X=40.5
Step-by-step explanation:
27/x=x/3 ==> 27(3)=x(x) ==> 81=2x
81/2=2x/2 ==> x=40.5
3. Answer: X=16
Step-by-step explanation:
8/x+2=4/9 ==> 8(9)=4(x+2) ==> 72=4x+8
72-8=4x+8-8 ==> 64=4x ==> 64/4=4x/4 ==> x=16
4. Answer: X=8
Step-by-step explanation:
3/x=30/80 ==> 3(80)=30x ==> 240=30x
240/30=30x/30 ==> x=8
5. Answer: M=56
Step-by-step explanation:
m/8=m+7/9 ==> 9m=8(m+7) ==> 9m=8m+56
9m-8m=8m-8m+56 ==> m=56
B. Solve the following.
1. Answer: 80 and 100
Step-by-step explanation:
4:5 ==> 4x+5x=180 ==> 9x=180
9x/9=180/9 ==> x=20
4(20)= 80 5(20)=100
2. Answer: 235.29
Step-by-step explanation:
3400/8 ==> 425
100,000/425= 235.29
A triangle has sides with lengths of 14 feet, 48 feet, and 50 feet. Is it a right triangle?
Answers
Answer:
Yes, it is a right triangle
Step-by-step explanation:
Answer: Yes it is
Note that a right triangle is a triangle with a right angle.
A random poll of 800 middle school students found that 9% are ESL (English as a Second Language) learners. Estimate the actual percentage of ESL learners by constructing a 95% confidence interval. Separately, a local school board member claimed that 15% of students are ESL learners. Is the board member's claim plausible? The 95% confidence interval is 7% to 11% and, yes the board member's claim of 15% is plausible since his claim is inside of the confidence interval The 95% confidence interval is 7% to 11% and, no the board member's claim of 15% is not plausible since his claim is outside of the confidence interval The 95% confidence interval is 9% and, no the board member's claim of 15% is not plausible since his claim is outside of the confidence interval The 95% confidence interval is 0% to 18% and, yes the board member's claim of 15% is plausible since his claim is inside of the confidence interval QUESTION 26 A stationary time series is one whose properties depend on the time the series is observed and are likely to exhibit trends and seasonality. True False
Answers
The given statement "A stationary time series is one whose properties depend on the time the series is observed and are likely to exhibit trends and seasonality" is false.
The confidence interval provides a range of values in which the actual value of a population parameter is likely to fall.
A random poll of 800 middle school students found that 9% are ESL (English as a Second Language) learners.
The confidence interval estimates the actual percentage of ESL learners by constructing a 95% confidence interval.
Let us calculate the 95% confidence interval to check the board member's claim.
The point estimate is:9%
The margin of error is calculated as:
ME=1.96×√(pˆ(1−pˆ)/n)=1.96×√(0.09(1−0.09)/800)=0.0228
Since the margin of error is small enough relative to the point estimate, we can approximate the confidence interval using:
pˆ±ME=0.09±0.0228
=(0.0672,0.1128)
The 95% confidence interval is (0.0672, 0.1128).
Now we can check if the board member's claim of 15% is plausible or not:
15% falls outside the 95% confidence interval of (0.0672, 0.1128).
Hence, we can conclude that the board member's claim of 15% is not plausible since his claim is outside of the confidence interval.
False is the correct answer to the given question.
A stationary time series is one whose properties do not depend on the time the series is observed and do not exhibit trends and seasonality.
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The riddle family income is 3400 per month. They spend 1088 per month on housing. Use information to determine the percent of the budget spent on housing
Answers
Answer:
32%
Step-by-step explanation:
[tex]\frac{1088}{3400}[/tex]=[tex]\frac{x}{100}[/tex]
(1088)(100)=(3400)(x)
108800=3400x
x=32
32%
The percent of the budget spent on housing is 31.76%.
What is percentage?
Percentage is a mathematical term which means number or ratio expressed in terms of fractions of 100. it can be calculated by dividing given value to the whole value and multiplied by 100. we represent it through ' %'.
Given that, The riddle family income is 3400 per month.
They spend 1088 per month on housing.
We know the formula for percentage which is;
Percentage = (given value/whole value)*100,
Percentage = (1080/3400)*100
Percentage = 31.76
Hence, The percentage is 31.76%.
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with 09) Let x, y be random variables joint probability density function f(x,y) = K (2x+ +y) of as 4 of y=2 443 Find K and (Hind : draw P CY
Answers
K = 1/4, fY(y) = (8 - Y)/9
Random variables X and Y have a joint probability density function f(x,y) = K(2x+y) where 0<=x<=1, 0<=y<=2 and f(x,y) = 0 elsewhere. Also, Y = 2^(-X) + 3. Let's determine the value of K.
Determination of K
The probability density function f(x,y) must satisfy the following condition:
i.e., the integral of f(x,y) over the entire range of (x,y) should be equal to 1.
f(x,y) = 0 elsewhere implies that f(x,y) = 0 for x<0 and x>1 and y<0 and y>2. Hence, the range of integration should be [0,1] for x and [0,2] for y.
The integral of f(x,y) over the entire range of (x,y) can be expressed as follows:
[tex]∫∫K(2x+y)dydx = 1[/tex]
On integrating with respect to y first, we get:
[tex]∫(2x+y)dy = [2xy + (1/2)y^2][/tex]evaluated from 0 to 2
= 4x + 2
On integrating with respect to x, we get:
[2x^2 + 2x] evaluated from 0 to 1
= 4
On equating the integral value with 1, we get:
[tex]4K = 1K = 1/4[/tex]
Determination of probability density function of Y
We have [tex]Y = 2^(-X) + 3[/tex]. Therefore, for a given value of Y, the range of X can be determined as follows:
[tex]2^(-X) = Y - 3= > X = -log2(Y-3)[/tex]
Hence, the probability density function of Y can be obtained as follows:
[tex]fY(y) = ∫f(x,y)dxfY(y) = ∫f(x,2^(-X) + 3)dx[/tex]
From the given expression, we can observe that f(x,y) = 0 elsewhere implies that f(x,2^(-X) + 3) = 0 for x<0 and x>1 and y<3 and y>2. Also, the range of integration for x can be determined as follows:
For y<=3, X>=-log2(y-3). For y=2, the minimum value of X can be obtained by taking the limit as y tends to 2 from the right. The minimum value of X is therefore equal to [tex]-∞[/tex]. Therefore, the range of integration for x is [tex][-∞,1].[/tex]
fY(y) =[tex]∫f(x,2^(-X) + 3)dx = ∫(1/4)(2x + 2^(-X) + 3)dx[/tex]
fY(y) = (1/4)(x^2 - 2^(-X)x + 3x) evaluated from [tex]x=-∞ to x=1[/tex]
fY(y) = [tex](1/4)(1 - 2^(log2(Y-3)) + 3)[/tex]= (8 - Y)/9
Let's draw the probability density function of Y. The probability density function of Y is as follows:
fY(y) = (8 - Y)/9
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with 09) Let x, y be random variables joint probability density function f(x,y) = K (2x+ +y) of as 4 of y=2 443 Find K and (Hind : draw P CY<SX ) a picture )
Find the area of rhombus with diagonals 6 mm and 9 mm.
Answers
What is the greatest common factor of 24, 40 and 32?
A. 1
B. 2
C. 4
D. 8
Answers
Answer:
your answer is D. 8
Step-by-step explanation:
Which mapping represents y as a function?
Answers
Answer:
a
Step-by-step explanation:
Answer: J
Step-by-step explanation:
Can someone explain this step by step pls and no links
Answers
Answer: 12
Step-by-step explanation: Use the quadratic equation to solve the equation.
a = 1
b = -8
c = 12
Answer:
x=6 is the answer
Step-by-step explanation:
x squared -8 x +12=0
6 squared=36
36-8x +12=0
x= 6 so 8*6 =48
36-48+12=0
36-48= -12
-12+12=0
hope this helps
Just need the answer of what the surface area is
Answers
Answer:
54
Step-by-step explanation:
#8 Tessa has a plan for a set of stairs made of concrete, as shown. Each stair is 1 point the same width and height and is taller than the previous one by the same amount. What is the volume of concrete needed for the set of stairs?
Picture below:
Answers
Answer: 2.43m^3
Step-by-step explanation:
Find a vector with magnitude 14 in the same direction as (2,6, -3)
Answers
To find a vector with a magnitude of 14 in the same direction as (2, 6, -3), the vector (4, 12, -6) has a magnitude of 14 and is in the same direction as (2, 6, -3).
we need to scale the original vector while preserving its direction. By normalizing the vector, we can determine its unit vector and then multiply it by the desired magnitude to obtain the final vector. magnitude = √(x² + y² + z²), where x, y, and z are the components of the vector. In this case, the magnitude of the vector (2, 6, -3) is √(2² + 6² + (-3)²) = √(4 + 36 + 9) = √49 = 7.
To obtain a vector with a magnitude of 14, we need to scale the original vector by a factor of 14/7. This ensures that the new vector has the desired magnitude while maintaining the same direction. Scaling a vector involves multiplying each of its components by the scaling factor. Therefore, we can calculate the new vector as follows: New vector = (2, 6, -3) * (14/7) = (2 * 14/7, 6 * 14/7, -3 * 14/7) = (4, 12, -6).
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need help please.........
Answers
Answer:
Yes. it is 5. bc u need to trust me
ra elaborar un pastel de 2 kg, se necesitan, ¾ de kg de harina y 4 huevos (con un peso de 100 gr cada uno), además de otros ingredientes. ¿Cuál es el peso que tienen los demás ingredientes del pastel?
Answers
Based on the above, the weight of the other ingredients in the cake is about 850 grams.
What is the weight about?To determine the weight of the other ingredients in the cake, one need to subtract the weight of the flour as well as the eggs from the total weight of the cake.
Note that from the question:
Weight of flour = ¾ kg = 750 gNumber of eggs = 4Weight of each egg = 100 gSo: Weight of flour and eggs = (Weight of flour) + (Number of eggs × Weight of each egg)
= 750 g + (4 × 100 g)
= 750 g + 400 g
= 1150 g
Hence: The Total weight of the cake = 2 kg = 2000 g
Going further:
Weight of other ingredients = Total weight of the cake - Weight of flour and eggs
= 2000 g - 1150 g
= 850 g
Therefore, the weight of the other ingredients that is seen in the cake is 850 grams.
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See text below
To make a 2 kg cake, ¾ kg of flour and 4 eggs (weighing 100 g each) are needed, in addition to other ingredients. What is the weight of the other ingredients in the cake?
PLEASE HELP! 15 POINTS! Select the statement that describes this expression: fraction 1 over 2 x (734 − 246). (2 points)
Group of answer choices
Half the sum of 734 and 246
fraction 1 over 2 the difference between 734 and 246
fraction 1 over 2 the quotient of 734 and 246
2 times the difference between 734 and 246
Answers
Answer:
fraction 1 over 2 the difference of 734 and 246.
help i really need help WILL GIVE BRAINLIEST
Answers
Answer:
3 and 4
Step-by-step explanation:
The distance from the
coffee shop to the
school is 10 miles. On
the map, the coffee
shop is 7.5 inches from
the school. Which one
of the following gives
the scale used
on the map?
A. 5 inches = 2 miles
B. 4 inches = 3 miles
C. 2 inches = 5 miles
D. 3 inches = 4 miles
Answers
Please can someone help me?
Answers
Answer:
weight of a water=0.5
spherical ball is filled With water=0.95.
so dear for
22\7*0.5*0.95=1.49
please help!!
Explain how you could figure out the formula for the surface area of a cylinder if all you knew was the formula for surface area of a right rectangular prism. k
Answers
If you know the formula for the surface area of a right rectangular prism, you can use that knowledge as a basis to derive the formula for the surface area of a cylinder.
Deriving the surface area of a cylinder from the surface area of a right rectangular prismRecall the formula for the surface area of a right rectangular prism:
SA_prism = 2lw + 2lh + 2wh
where l, w, and h represent the length, width, and height of the prism, respectively.
Consider a cylinder as a special case of a prism with a circular base and a height. The circular base can be thought of as a rectangle with a length equal to the circumference of the base (2πr) and a width equal to the height (h) of the cylinder.
The curved surface of the cylinder can be "unrolled" and flattened to form a rectangle, with the length equal to the circumference of the base (2πr) and the width equal to the height (h) of the cylinder.
Thus, the surface area of the curved part of the cylinder is equal to the surface area of the rectangular prism with dimensions 2πr and h.
Thus, the formula for the surface area of the cylinder can be derived as follows: SA_cylinder = 2πrh.
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LEGIT BEG PLEASE HELP
Answers
Answer:
help with what problem?
Step-by-step explanation:
Answer:
Sure
Step-by-step explanation:
One hundred draws will be made at random with replacement from one of the following boxes. Your job is to guess what the sum will be, and you win $1 if you are right to within 10. Which box is best? Worst?
(i) 1 9 (ii) 4 6 (iii) 5 5
A. Box (i) is the best and Box (iii) is worst.
B. Box (i) is the best and Box (ii) is worst.
C. Box (ii) is the best and Box (i) is worst.
D. Box (ii) is the best and Box (iii) is worst.
E. Box (iii) is the best and Box (ii) is worst.
F. Box (iii) is the best and Box (i) is worst.
Answers
The answer is:Option (F) Box (iii) is the best and Box (i) is worst, for the given one hundred draws will be made at random with replacement from one of the following boxes based on expected-probability.
Given the three boxes:
(i) 1 9(ii) 4 6(iii) 5 5
One hundred draws will be made at random with replacement from one of the above boxes.
Let us now calculate the expected value of the sum for each of the boxes:
(i) Expected value of sum = (1+9)/2 × 100
= 500.
(ii) Expected value of sum = (4+6)/2 × 100
= 500.
(iii) Expected value of sum = (5+5)/2 × 100
= 500.
Box (i) and (ii) have the same expected value, so we can choose either of them.
However, it is important to note that in Box (ii) the numbers are closer together than in Box (i),
so the sum is more likely to be near the expected value.
This makes Box (ii) the best option.
Box (iii) is the worst option as it has a smaller range than the other two boxes,
Which means that it is less likely to produce a sum close to the expected value.
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Let S be any sample space, and E, F and G be any three events. Describe the event that E and F occur, and G does not occur.
a) ( E ∪ Fc ) ∩ G
b) ( E ∪ F ) ∩ G
c) ( E ∪ F ) ∩ Gc
d) ( E ∩ F ) ∪ Gc
e) E ∩ F ∩ Gc
f) None of the above.
Answers
The event that E and F occur, and G does not occur is E ∩ F ∩ Gc. So, correct option is E.
The event that E and F occur, and G does not occur can be represented by the expression (E ∩ F) ∩ Gc. Let's break down the options provided to determine the correct representation:
a) (E ∪ Fc) ∩ G: This represents the event where either E or the complement of F occurs, and G occurs. It does not capture the condition that both E and F occur.
b) (E ∪ F) ∩ G: This represents the event where either E or F occurs, and G occurs. It does not exclude the possibility of E and F occurring together.
c) (E ∪ F) ∩ Gc: This represents the event where either E or F occurs, and G does not occur. However, it does not specify that E and F occur together.
d) (E ∩ F) ∪ Gc: This represents the event where either E and F occur together or G does not occur. It does not exclude the possibility of E and F occurring without G.
e) E ∩ F ∩ Gc: This correctly represents the event where both E and F occur together, and G does not occur. This is the desired outcome as stated in the question.
Therefore, the correct representation for the event is option e) E ∩ F ∩ Gc.
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please answer and explain and i’ll give brainliest
Answers
Step-by-step explanation:
I really want to help you but there's no question.
Dose anyone know this question I will give brainless bc I dont know this
Answers
Answer:
3.5
Step-by-step explanation:
Answer:
LxWxH
Step-by-step explanation:
thats how you find area
use a known maclaurin series to obtain a maclaurin series for the given function. f(x) = xe5x
Answers
The maclaurin series for the given function xe⁵ˣ = x + 5x² + (25x³)/2! + (125x⁴)/3! + ...
To find the Maclaurin series for the function f(x) = xe⁵ˣ, we can utilize the Maclaurin series expansion of the exponential function, eˣ:
eˣ = 1 + x + (x²)/2! + (x³)/3! + ...
Substituting 5x for x in the above expansion, we have:
e⁵ˣ = 1 + 5x + (5x)²/2! + (5x)³/3! + ...
Multiplying the above series by x, we get:
xe⁵ˣ = x + 5x² + (25x³)/2! + (125x⁴)/3! + ...
This is the Maclaurin series for the function f(x) = xe⁵ˣ.
The calculation involves applying the Maclaurin series expansion of the exponential function to the function f(x) = xe⁵ˣ by substituting 5x for x in the series expansion. Then, multiplying the resulting series by x gives us the desired Maclaurin series for f(x).
The series can be continued by following the pattern of increasing powers of x, with the coefficients determined by the corresponding terms in the expansion.
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