The approximation of the integral [tex]\int (x - 3) * e^x dx[/tex] using the composite Trapezoidal rule with n = 4 is approximately -1.670625.
We'll proceed with the default values and calculate the approximation using the composite Trapezoidal rule with n = 4.
Using the default interval [a, b] (which is not specified), we'll assume it to be [0, 1] for demonstration purposes. Therefore, a = 0 and b = 1.
First, we need to calculate the step size, h:
[tex]h = (b - a) / n\\h = (1 - 0) / 4\\h = 0.25[/tex]
Now, we can calculate the approximation using the composite Trapezoidal rule formula:
[tex]Approximation = (h/2) * [f(x_0) + 2 * (sum\ of f(x_i)) + f(x_n)]\\Approximation = (0.25/2) * [f(0) + 2 * (f(0.25) + f(0.5) + f(0.75)) + f(1)][/tex]
Let's evaluate the function at these points:
[tex]f(0) = (0 - 3) * e^0 = -3\\f(0.25) = (0.25 - 3) * e^{0.25} = -2.195\\f(0.5) = (0.5 - 3) * e^{0.5} = -1.373\\f(0.75) = (0.75 - 3) * e^{0.75} = -0.732\\f(1) = (1 - 3) * e^1 = -1.765[/tex]
Substituting these values into the formula:
[tex]Approximation = (0.25/2) * [-3 + 2 * (-2.195 - 1.373 - 0.732) - 1.765]\\Approximation = (0.125) * [-3 + 2 * (-4.3) - 1.765]\\Approximation = (0.125) * [-3 - 8.6 - 1.765]\\Approximation = (0.125) * [-13.365]\\Approximation = -1.670625[/tex]
Therefore, the approximation of the integral using the composite Trapezoidal rule with n = 4 is approximately -1.670625.
To know more about approximation, refer here:
https://brainly.com/question/29669607
#SPJ4
help with all of u can, I’d appreciate it. Have a good day
Answer:
a. -12n^3 + 8n^2 - 2n
b. n^4 - n/2
c. 6b^7 + 2b^6 - b^5
Step-by-step explanation:
btw photomath (the app) is really good for this type of stuff
2x + 7 = 15
What does x equal?
What is the area of this
Answer:
area of trapezoid = 1/2×(a+b)×height
area of trapezoid =1/2×(15m+7m)×7m
area of trapezoid =1/2×22m×7
area of trapezoid =77m²
area of trapezoid =1/2×(a+b)×height
area of trapezoid =1/2×(9ft+12ft)×4ft
area of trapezoid =1/2×21ft×4ft
area of trapezoid =42ft²
Let 2 = 3 + 6i and w = a + bi where a, b E R. Without using a calculator (a) determine z/w and hence, b in terms of a such that z/w is real; (b) determine arg{z - 9}; (c) determine =||w/w||
The correct answers for the given data are (a) b = 6, (b) arg(z - 9) = -π/4, and (c) ||w/w|| = 1.
(a) To determine z/w, we first need to express z and w in terms of their real and imaginary parts. Given 2 = 3 + 6i, we can rewrite it as z = 3 + 6i. Similarly, w = a + bi. Now, let's calculate z/w:
z/w = (3 + 6i)/(a + bi)
To make z/w real, the imaginary part of the denominator should cancel out the imaginary part of the numerator. This means 6/a = 6i/b. Simplifying further, we get ab = 6a + 6bi. Since a and b are real numbers, the only way for the equation to hold is if b = 6 and a = 1. Therefore, b = 6.
(b) To determine arg(z - 9), we need to subtract 9 from z = 3 + 6i:
z - 9 = (3 + 6i) - 9 = -6 + 6i
The argument (or angle) of -6 + 6i can be calculated as:
arg(-6 + 6i) = arctan(6/(-6)) = arctan(-1) = -π/4
(c) To determine ||w/w|| (the magnitude of w divided by the magnitude of w), we need to find the magnitude of w. Given w = a + bi, the magnitude of w is given by:
||w|| = √(a^2 + b^2)
Now, substituting a = 1 and b = 6 (from part a):
||w|| = √(1^2 + 6^2) = √37
Therefore, ||w/w|| = ||w||/||w|| = 1.
Learn more about imaginary parts click here:
brainly.com/question/13389642
#SPJ11
16. Use the distributive property of multiplication to find the product of 2x5²
We have:
[tex]2x \cdot (5^2)[/tex]
[tex]= 2x \cdot 25[/tex]
[tex]= \boxed{50x}[/tex]
[tex]\sqrt{x} 196
can someone help me
Answer:
14
Step-by-step explanation:
√196
Calculate the square root of 196 and get 14.
14
what is the probability rule for deciding whether events a and b are independent
Events A and B are considered independent if and only if the probability of their intersection (P(A ∩ B)) is equal to the product of their individual probabilities (P(A) * P(B)).
Independence: Two events A and B are independent if the occurrence or non-occurrence of one event does not affect the probability of the other event.
Joint Probability: The joint probability P(A ∩ B) represents the probability of both events A and B occurring together.
Multiplication Rule: According to the multiplication rule for independent events, if events A and B are independent, the probability of their intersection is equal to the product of their individual probabilities.
P(A ∩ B) = P(A) * P(B)
Interpretation: If the equation holds true, events A and B are considered independent since the probability of their intersection can be determined solely by multiplying their individual probabilities.
Dependence: If the equation does not hold true, it implies that the occurrence of one event affects the probability of the other event, indicating dependence between the two events.
In summary, the multiplication rule for independent events states that events A and B are independent if and only if P(A ∩ B) = P(A) * P(B).
Know more about the joint probability click here:
https://brainly.com/question/32099581
#SPJ11
I will mark brainlyist! Can anyone answer and explain how to do these? Thank you!
Answer:
2) $1797
3) $152
4) $5,378
i need help asap.!!!!!
The sheet of metal has dimensions 56 cm by 33 cm. It sis melted down
and recast into discs of the same thickness and radius 7 cm. How many
disces will be cast ?
Answer:
12
Step-by-step explanation:
To determine the number of discs, divide the area of the metal sheet by the area of the discs
The metal sheets are in the shape of a rectangle, thus the area of a rectangle would be used to determine the area of the sheet
Area of a rectangle = length x breadth
56 x 33 = 1848 cm^2
The disc is in the shape of a circle.
area of a circle = πr²
π = 3.14
r = radius
3.14 x 7² = 153.86 cm²
Number of discs = 1848 /153.86 = 12
1,3x + 3,9x = 0
Pls someone explain the steps for this. Like how do I find the x1 and x2.
Answer:
x=0
I used phone math!!!!!!!!
Can someone help me in proving theorems in square pleasee ASAP
Step-by-step explanation:
[tex]90 = 4x - 6 \\ 96 = 4x \\ x = 24[/tex]
[tex]2x - 8 = \\ = 48 - 8 = \\ = 40[/tex]
In a study of the accuracy of fast food? drive-through orders, Restaurant A had 239 accurate orders and 70 that were not accurate.
a. Construct a 95?% confidence interval estimate of the percentage of orders that are not accurate
The 95% confidence interval estimate of the percentage of orders that are not accurate is approximately (17.37%, 27.83%)
Let's denote p as the proportion of orders that are not accurate.
The sample proportion of orders that are not accurate is given by:
p(bar) = 70 / (239 + 70)
= 70 / 309
≈ 0.226
The standard error of the proportion is calculated as:
SE = √[(p(bar)(1 - p(bar))) / n]
= √[(0.226(1 - 0.226)) / 309]
≈ √(0.1785 / 309)
≈ 0.0267
To find the margin of error, we need to multiply the standard error by the critical value corresponding to a 95% confidence level. For a 95% confidence level, the critical value is approximately 1.96.
Margin of error = 1.96 × SE
≈ 1.96 × 0.0267
≈ 0.0523
Now we can construct the confidence interval:
Lower limit = p(bar) - Margin of error
= 0.226 - 0.0523
≈ 0.1737
Upper limit = p(bar) + Margin of error
= 0.226 + 0.0523
≈ 0.2783
Therefore, the 95% confidence interval estimate of the percentage of orders that are not accurate is approximately (17.37%, 27.83%).
To know more about confidence interval click here :
https://brainly.com/question/32546207
#SPJ4
Can someone help me with this. Need answer and explanation/work. Thank you. Will Mark brainliest.
Answer:
The hikers are 5 miles apart.
Step-by-step explanation:
East + West = 3 miles apart (x-axis)
North + South = 4 miles apart (y-axis)
Then use the pythagorean theorem to find the distance between them.
sqrt(distance) = sqrt(3^2+4^2)
distance = sqrt(25)
distance = 5 miles
use base conversion method, convert the decimal expansion (25679),, to an Octal expansion.
The decimal number (25679)₁₀ is equivalent to the octal number (62117)₈. The base conversion method, also known as the radix conversion method, is a systematic approach to converting numbers from one base to another.
To convert the decimal expansion (25679)₁₀ to an octal expansion, we can use the base conversion method.
Step 1: Divide the decimal number by 8 and keep track of the remainders.
25679 ÷ 8 = 3209 remainder 7
3209 ÷ 8 = 401 remainder 1
401 ÷ 8 = 50 remainder 1
50 ÷ 8 = 6 remainder 2
6 ÷ 8 = 0 remainder 6
Step 2: The remainders from bottom to top form the octal expansion.
Therefore, (25679)₁₀ = (62117)₈.
Hence, the decimal number (25679)₁₀ is equivalent to the octal number (62117)₈.
The question should be:
Use base conversion method, convert the decimal expansion (25679)₁₀ to an Octal expansion.
To learn more about octal expansion: https://brainly.com/question/31655449
#SPJ11
Using Substitution, what is the point of intersection of the following
systems? *
3x – ly = 14
y = - 2x + 16
1) (6,4)
2) (-6,-4)
3) (-6, 4)
4) (6,-4)
Answer:
A
Step-by-step explanation:
(6,4)
3x-1y=14
-y= 3x-14
y=-2x+16
sub in first equation
3x-14 =-2x+16
3x+2x= 16 +14
5x = 30
x = 6
plug in x
y=-2x+16
y = -2(6)+16
y = 4
(6,4)
Which expression is equivalent to 3t - 5 + 8t + 3 ?
Answer:
11t -2
Step-by-step explanation:
3t - 5 + 8t + 3
Combine like terms
3t +8t- 5 + 3
11t -2
Start by changing the problem to 3t + -5 + 8t + 3.
Now combine like terms.
Combine like terms → your numbers
and your "t" terms.
So 3t + 8t is 11t and -5 + 3 is -2.
So the answer is 11t - 2.
Jo records the number of text messages she receives each day she uses this information to draw this bar chart write 3 mistakes she has made
Answer:
X axis labels aren't evenly spaces
Y axis has no origin
Missing label
Step-by-step explanation:
Scale of a graph is important when displaying numerical data on a plot.
Based on the bar chart given, it could be seen that the x axis which is labeled days of the week is not adequately spaced. Data on both axis should he a recognizable.
2.)
Taking a look at the graph, it has no origin, the numbering of the vertical axis, number of text messages should start from 0
3.) Also, the x and y axis aren't labeled Hence charts should be well labeled to include x - axis and y-axis.
Answer:
X axis labels aren't evenly spaces
Missing label
there us no scale written starting at 0
Step-by-step explanation:
this will give u 3/3
P and Q are points on the line 4x+2y=8
b) Draw the line 4x+2y=8 for values of x from -2 to 3.
WINNER WILL GET BRAINLIEST
Please help me.
There is no picture but it would be great if you could help me.
Answer:
[tex]4 \sqrt{2 - 3 = 1[/tex]
Answer:
(-2,8), (-1,6), (0,4), (1,2), (2,0), (3,-2)
Step-by-step explanation:
Insert these points in graph and draw a line. You will get the answer. ^_^
sorry had to edit because of a blunder
please help asap
which inequality is represented by this graph
Answer:
W is either less than or( less than or equal to)
Step-by-step explanation:
I do not know what shows if something is equal to so the best answer I can think if is less than -2 as it looks like W is everything lower or equal to -2
Find the volume of compostie figure
Step-by-step explanation:
The first composite shape is a combination of a rectangular prism and a pyramid. To find the volume of the entire shape you find the volume of each individual shape and add them together. The second figure consists of a cylinder and a hemisphere.
Hope that helps :)
Nicole wants to rent a boat and spend less than $33. The boat costs $6 per hour , and Nicole has a discount coupon for $9 off. What is the answer in inequality
Answer: Nicole can spend up to 7 hours in the boat.
Step-by-step explanation:
Based on the information given in the question, the possible number of hours that can be used will be calculated as thus:
(6 × t) - 9 ≤ 33
6t - 9 ≤ 33
Collect like terms
6t ≤ 33 + 9
6t ≤ 42
Divide both side by the coefficient of t
6t/6 ≤ 42/6
t ≤ 7
Nicole can spend up to 7 hours in the boat.
A certain college graduate borrows $6600 to buy a car. The lender charges interest at an annual rate of 10%. Assuming that interest is compounded continuously and that the borrower makes payments continuously at a constant annual rate k dollars per year, determine the payment rate k that is required to pay off the loan in 5 years. (Round your answer to two decimal places.) k = $ per yr
The borrower would need to make payments of approximately $943.57 per year to pay off the loan in 5 years.
To determine the payment rate required to pay off the loan in 5 years, we can use the continuous compound interest formula:
A = P * [tex]e^{(rt)[/tex],
where A is the final amount, P is the initial principal, e is the base of the natural logarithm (approximately 2.71828), r is the annual interest rate, and t is the time in years.
In this case, the initial principal is $6600, the annual interest rate is 10%, and the time is 5 years. We want to find the payment rate, so let's set A equal to zero, indicating that the loan is fully paid off:
0 = 6600 * [tex]e^{(0.10 * 5)[/tex]- k * 5,
Simplifying the equation, we have:
[tex]e^{(0.5)[/tex] = k / 6600.
Now, we can solve for k by multiplying both sides of the equation by 6600:
k = 6600 * [tex]e^{(0.5)[/tex],
Using a calculator or software, we find that k is approximately $943.57 per year.
To learn more about payment rate click on,
https://brainly.com/question/14806350
#SPJ4
The growth of an apple tree was measured. The tree grew 15 inches per year.
On average, how many millimeters did the tree grow per day?
Answer:
1.04 mill
Step-by-step explanation:
15 inches to mill = 381
[tex]365\sqrt{381}[/tex] = 1.04 ( rounded )
Raymond bought a car for $40,000. He took a 20,000 loan from a bank at an interest rate of 15% per year for a 5 - year period. What is the total amount ( interest and loan) that he would have to pay rhe bank at the end of 5 years
Answer:
$35,000
Step-by-step explanation:
The amount that would be repaid = amount borrowed + interest earned on loan
interest earned on deposit can be determined by determining the simple interest
Simple interest = principal x time x interest rate
principal = the amount deposited = 20,000
Time = the duration of the deposit =5
interest rate = the percentage on deposit that would be earned = 15
20,000 x 5 x 0.15 = $15,000
total = 20,000 + 15,000 = $35,000
What information is needed in order to apply the hypotenuse-leg (HL) theorem
Answer:
This theorem states that 'if the hypotenuse and one leg of a right triangle are congruent to the hypotenuse and one leg of another right triangle, then the triangles are congruent. ' This is kind of like the SAS, or side-angle-side postulate. But SAS requires you to know two sides and the included angle.
Step-by-step explanation:
Rachel makes $38.25 in 3 hours.
How much money did she make
per hour?
4
HELPPPPP 10 points
I NEED IT NOW
Answer:
1 hour: $12.75
Step-by-step explanation:
Easy divide 38.25 by 3 which is 12.75
This is my last question !
Answer:
x=50 degrees
Step-by-step explanation:
I'm not sure but hope this helps and have a wonderful day!!!!
Answer:
x = 48
Step-by-step explanation:
2x + 10 + x + 26 = 180
3x + 36 = 180
3x = 180 - 36
3x = 144
x = 48
(help asap) The steps to solving the expression the quantity of the sum of three squared plus four divided by the absolute value of negative 0.25 end quantity minus 10.4 ÷ 4 are listed below.
Part A: Explain what the missing expression should be in Step 3. (6 points)
Part B: Explain what the missing expression should be in Step 6. (6 points)
Step 1 the quantity of the sum of three squared plus four divided by the absolute value of negative 0.25 end quantity minus 10.4 ÷ 4
Step 2 the quantity of the sum of three squared plus four divided by 0.25 end quantity minus 10.4 ÷ 4
Step 3
Step 4 the quotient of quantity 13 divided by 0.25 end quantity minus 10.4 ÷ 4
Step 5 52 − 10.4 ÷ 4
Step 6
Step 7 49.4
The final result of the given expression is 49.4.
Part A: In the missing expression should be the result of squaring three and adding four.
This is because the expression in Step 2 states "the quantity of the sum of three squared plus four divided by 0.25.
" Therefore, to continue simplifying the expression, we need to evaluate the value of the sum of three squared plus four.
The quantity of [tex](3^2 + 4)[/tex] divided by 0.25
To solve Step 3, we first evaluate the expression inside the parentheses:
[tex]3^2 + 4 = 9 + 4 = 13[/tex]
So, Step 3 becomes:
The quantity of 13 divided by 0.25
Part B: In the missing expression should be the result of dividing 13 by 0.25.
This is because in Step 4, the expression is "the quotient of the quantity 13 divided by 0.25 end quantity minus 10.4 divided by 4."
To simplify further, we need to calculate the value of 13 divided by 0.25.
13 divided by 0.25
To solve Step 6, we perform the division:
13 ÷ 0.25 = 52
So, it becomes:
52 minus 10.4 ÷ 4
Following the remaining steps:
52 minus (10.4 ÷ 4) = 52 - 2.6 = 49.4
For similar question on expression.
https://brainly.com/question/945593
#SPJ8
HELP NQNSJNDNXJJXnwnfnf
Answer:
C. 14 is the answerStep-by-step explanation:
1. Write the question.
17 - 2x = -11
2. Subtract 17 from both sides
-17 -17
- 2x = -28
3. Negatives cancel
2x = 28
4. Divide both sides by 2
/2 /2
x = 14
5. Check the answer, write the equation.
17 - 2x = -11
6. Substitute x with the value
17 - 2(14) = -11
17 - 28 = -11
-11 = -11
The answer is correct!
So, 14 is the answerHope this helped,
Kavitha