A ≈ 2π√(1 + e²) ∫[0,6] et dt ≈ 2π√(1 + (2.71828)²) ∫[0,6] et dt surface area
To find the area of the surface obtained by rotating the curve x = t + e, y = et (where t ranges from 0 to 6) about the x-axis, we can use the formula for the surface area of revolution.
The formula for the surface area of revolution is given by:
A = ∫[a,b] 2πy√(1 + (dy/dx)²) dx
In this case, we need to express y and dy/dx in terms of t. Let's start by finding dy/dx.
Given:
x = t + e
y = et
Differentiating y with respect to x:
dy/dx = dy/dt ÷ dx/dt
dy/dt = e (differentiation of et with respect to t)
dx/dt = 1 (differentiation of t + e with respect to t)
So, dy/dx = e/1 = e.
Now, we can rewrite the integral using the parameter t:
A = ∫[a,b] 2πy√(1 + (dy/dx)²) dx
A = ∫[0,6] 2π(et)√(1 + e²) dt
A = 2π√(1 + e²) ∫[0,6] et dt
To evaluate the integral, we can use a calculator or computer. Substituting the values a = 0, b = 6, and e ≈ 2.71828 (the base of natural logarithm), we can calculate the surface area:
A ≈ 2π√(1 + e²) ∫[0,6] et dt ≈ 2π√(1 + (2.71828)²) ∫[0,6] et dt
Evaluating this integral using a calculator or computer will yield the surface area of the rotated curve around the x-axis, correct to four decimal places.
learn more about "surface area":- https://brainly.com/question/16519513
#SPJ11
Please Help
How is an object's acceleration affected by its mass and the forces acting on it?
Answer:
Step-by-step explanation:
The acceleration of an object increases with increased forced and decreases with increased mass which is in the same direction as the force.
Which of the following activities is not associated with the purchase and payments business process? Select one: a. Buying products and services O b. Receiving goods O c. Recording payments to vendors d. Selling products and services
The activity that is not associated with the purchase and payments business process is Selling products and services.
therefore d. Selling products and services is correct.
Business process is a set of activities carried out in a systematic manner, aimed at achieving specific results.
The purchase and payment process are important in businesses as it involves the payment of vendors for goods and services bought.
The activities associated with the purchase and payment business process includes buying products and services, receiving goods, recording payments to vendors, and verifying and approving invoices.
The sales of goods and services, on the other hand, are part of the sales process, not the purchase and payment process.
for such more question on business process
https://brainly.com/question/28436755
#SPJ11
using statistics helps us make decisions based on what kind of evidence?
Using statistics helps us make decisions based on empirical evidence, which is obtained through data analysis and inference.
Statistics provides us with a set of tools and methods to collect, analyze, and interpret data. By applying statistical techniques, we can make decisions based on evidence derived from empirical observations and measurements.
Statistics allows us to summarize and describe data, identify patterns and relationships, and draw conclusions from samples or populations. It helps us quantify uncertainty and assess the strength of evidence supporting different claims or hypotheses.
Decision-making based on statistics involves making inferences about a larger population based on the information available from a sample. By using probability theory and statistical models, we can estimate population parameters, test hypotheses, and make predictions about future events or outcomes.
Statistics provides a systematic and rigorous framework for evaluating evidence and reducing bias in decision-making. It allows us to objectively assess the reliability and validity of information, making decisions that are informed by data-driven analysis rather than intuition or anecdotal evidence.
In summary, statistics helps us make decisions based on evidence obtained through data analysis, enabling us to draw reliable conclusions, quantify uncertainty, and make informed choices in various fields such as business, medicine, social sciences, and more.
Learn more about parameters here:
https://brainly.com/question/29911057
#SPJ11
Sally has 14 diamonds and she puts 6 in the ground how many more diamonds does sally have?
Answer:
Sally would have 8 diamonds left
Need help on both pleaseeee then I will be finished and need the someone to explain what the words define
Answer:
Linear pair angles
Step-by-step explanation:
Angle 5 and six are linear because they are both on the same line.
HI
I WANT AN ANSWER THAT
HOW WILL I MAKE r the subject of the formula
A= ½πr2,
Answer:
r = √(A/π)
Step-by-step explanation:
HI
I WANT AN ANSWER THAT
HOW WILL I MAKE r the subject of the formula
A= ½πr²,
inverse formula
r = √(A/π)
6g + 1, for g = 0 i need it in a sentence
Answer:
6*0 +1 = 1
Step-by-step explanation:
if g equals 0 the answer is 1
An isosceles triangle has a perimeter of 46 inches. The base is 6 less than twice each of the congruent legs. What is the sum of the lengths of the two congruent legs?
Answer: 26 inches
Step-by-step explanation:
An isosceles triangle has two congruent legs.
1) Set up the equations
P = b + 2L
b = 2L-6
2) Substitute for variables
46 = (2L - 6) + 2L
3) Solve the equation
46 = 4L - 6
52 = 4L
13 = L
4) Solve the problem
It asks for what is the sum of the two congruent legs
13 + 13 = Ans
26 = Ans
Can anyone help me on this math test real quick here is one of the questions!!
Answer:
D. 9/16
Step-by-step explanation:
3/4*3/4=9/16
Answer:
9/16
Hope this helped you!
V₁=13L
P₁ = 8 atm
V₂=7L
P₂= ?? atm
Answer:
14.85
Step-by-step explanation:
P₁V₁ = P₂V₂
13 x 8 = P₂ x 7
P₂ = (13 x 8)/7
= 104/7
P₂ = 14.85 atm
Find value of x and y
hi i need help on question 20! pls
Answer:
the answer is 3
Step-by-step explanation:
the formula gives the length of the side, s, of a cube with a surface area, sa. how much longer is the side of a cube with a surface area of 180 square meters than a cube with the surface area of 120 square meters?
As per the formula of surface area of cube, the length of the cube is 5.45 meters.
The general formula to calculate the surface area of the cube is calculated as,
=> SA = 6a²
here a represents the length of cube.
Here we know that the side of a cube with a surface area of 180 square meters than a cube with the surface area of 120 square meters.
When we apply the value on the formula, then we get the expression like the following,
=> 180 = 6a²
where a refers the length of the cube.
=> a² = 30
=> a = 5.45
To know more about Surface area here.
https://brainly.com/question/29298005
#SPJ4
Write an expression having only 2 terms that is equivalent to 2x - 3. Explain how you wrote the expression amd how you can check that it is equivalent.
Answer:
2x -3 =2x + 3
Step-by-step explanation:
Addition is commutative so as subtraction so 2x-3=2x+3
Given f (x)=9-14/x, find all c in the interval [2, 7] that satisfy the Mean Value Theorem
The value of c is √14 in the interval [2, 7], which satisfies the Mean Value Theorem.
By definition, the mean value theorem is
f'(c) = [f(b) - f(a)]/b - a
So, in this case, we know that a = 2 and b = 7.
Now, we need to find f(2) and f(7) by replacing those values with the given function
f(x) = 9 - 14/x
f(7) = 9 - 14/7 = 9 - 2 = 7
So, f(b) = f(7) = 7.
f(x) = 9 - 14/x
f(2) = 9 - 14/2 = 9 - 7 = 2
So, f(a) = f(2) = 2
Then, we replace all values,
f'(c) = [f(b) - f(a)]/b - a
= (7 - 2)/(7 - 2)
= 5/5
= 1
Now, calculate the derivative of the function, which has to be equal to 1,
f(x) = = 9 - 14/x
f'(x) = 14/x² = 1
Now, we solve the equation to calculate the value of c,
14/x² = 1
x² = 14
x = √14
Therefore, c = √14 is the value inside the given interval that satisfies the mean value theorem.
To know more about Mean Value Theorem, here
https://brainly.com/question/29107557
#SPJ4
Shade 3/4 on the grid
Help me thank you so much
\(\huge\text{Hey there!}\)
\(\maths{\sqrt{90}\)
\(\mathsf{{= \sqrt[3]{10}}}\)
\(\mathsf{= \sqrt{3^2\times10}}\)
\(\mathsf{= \sqrt{3\times 3 \times10}}\)
\(\mathsf{= \sqrt{9\times10}}\)
\(\mathsf{= \sqrt{90}}\)
\(\mathsf{= 9.48683298051}\)
\(\mathsf{\approx 9.48683298}\)
\(\mathsf{\approx 9.5}\)
\(\large\textsf{Thus, it is a little over 9 but not quite 10 yet..}\)
\(\huge\text{Therefore, your answer should be: \boxed{\mathsf{Option\ A. \ W}}}\huge\checkmark\)
\(\huge\text{Good luck on your assignment \& enjoy your day!}\)
Question 6
In the diagram of the flower bed below, are the triangles congruent by the AAS
Congruence Theorem?
yes
No
Yes, the flower bed below, are the triangles congruent by the AAS Congruence Theorem.
We have to given that,
In the diagram of the flower bed below are the triangles.
Now, By the given diagram,
Two triangle are shown.
Here, One side are common.
In both triangle, Measure of one angle is 90 degree
And , By definition of alternate angle one pair of angle is equal.
Hence, By ASA congruency theorem given triangles are congruent.
Learn more about the triangle visit;
brainly.com/question/1058720
#SPJ1
A cyclist rides a distance of 36 km at an average speed of 16 km/h.
Calculate the time taken to complete this ride. Give your answer in hours and minutes.
Please Help!
Answer:
2.25 hours, or 2 hours and 15 minutes.
Step-by-step explanation:
All we do is 36/16 which is 2.25. 0.25 or 1/4 of an hour is 15 minutes. So, your answer is 2 hours and 15 minutes.
It takes 2 hour and 12 minutes for the cyclist to complete the ride of 36km distance.
What is unitary method?
The unitary method is a technique for solving a problem by first finding the value of a single unit, and then finding the necessary value by multiplying the single unit value.
Total distance covered by cyclist= 36km
Average speed of the cyclist = 16km/hr
Therefore, using unitary method:
16 km distance takes time = 1hr
Therefore, 1 km distance takes time =(1/16)hr
Therefore, 36 km distance takes time = (1/16)×36 hr
=(1/4)×9 hr
=9/4 hr
=2.25 hr
=(2+0.25)hr
=2hr+0.25hr
=2hr+0.25×60minutes
=2hr and 15 minutes.
Hence, it takes 2hr and 15 minutes for the cyclist to complete 36 km rides.
To learn more about unitary method click here:
https://brainly.com/question/21179768
#SPJ3
7. Eight centimeters on the map represent two kilometers in reality. Determine the scale of this
Answer:
8 centimeters : 2 kilometers =
1 centimeter : 1/4 kilometer
A random sample of voters from three cities is asked to indicate political party affiliation. The results are given in the table. City Political Party Affiliation Democrat Independent Republican Miami 211 57 132 Austin 126 84 190 Detroit 158 96 146 To test whether the proportion of party affiliations for each city is the same, which inference procedure is appropriate to use?
The appropriate inference procedure to use when testing whether the proportion of party affiliations for each city is the same is the Chi-Square Test for Independence.
The Chi-Square Test for Independence is appropriate in this case because it allows you to test the relationship between two categorical variables (in this case, city and political party affiliation) using a contingency table (like the one provided). The test helps determine whether there is a significant association between the variables or if the observed frequencies are due to chance.
To perform the Chi-Square Test for Independence, follow these steps:
1. Create a contingency table with the observed frequencies of each combination of city and political party affiliation.
2. Calculate the expected frequencies for each cell of the table, assuming there is no association between the variables.
3. Calculate the chi-square test statistic, which is the sum of the squared differences between the observed and expected frequencies, divided by the expected frequencies.
4. Determine the degrees of freedom, which is equal to (number of rows - 1) * (number of columns - 1).
5. Compare the calculated test statistic to the critical value from a chi-square distribution with the determined degrees of freedom and an appropriate significance level (typically 0.05).
6. If the test statistic is greater than the critical value, reject the null hypothesis that there is no association between the variables, and conclude that the proportion of party affiliations for each city is not the same.
In your case, you would apply this procedure using the given data for the three cities and their political party affiliations.
Learn more about Chi-Square Test:
https://brainly.com/question/4543358
#SPJ11
List the coordinates of FOUR vertices that create the feasible region on the graph. Submit your answer in the form of FOUR ordered Pairs (x, y)
Answer:
see below
Step-by-step explanation:
The feasible region is the shaded area. We just need to find the coordinates of its vertices. These are (200, 200), (300, 0), (500,0) and (300, 200).
what is the next number in the sequence? 9….16….24….33…
The given sequence is 9, 16, 24, 33. To find the next number, let's look for a pattern in the differences between the terms.
The difference between 16 and 9 is 7, between 24 and 16 is 8, and between 33 and 24 is 9.
The pattern in the differences is that they are increasing by 1 each time. So, the next difference would be 10.
To find the next number, we add the next difference to the last term in the sequence. Adding 10 to 33 gives us 43.
Therefore, the next number in the sequence is 43.
To find the next number in the given sequence, we looked for a pattern in the differences between the terms. We observed that the differences were increasing by 1 each time. Using this pattern, we added the next difference to the last term in the sequence to find the next number.
The next number in the sequence 9, 16, 24, 33 is 43.
To know more about sequence visit
https://brainly.com/question/30262438
#SPJ11
MATH
Use the Law of Detachment to draw a conclusion from the two given statements.
If not possible, write not possible.
1) If a person went to the concert, then they had a ticket to get in to the show.
2) Nadia went to the concert.
Start
Rob has 40 coins, all dimes and quarters, worth $7.60. How many dimes
and how many quarters does he have?
... please solve this using if systems of equations
seen you with ur ex
Find the zeros for the polynomial function and give the multiplicity for each zero. State whether the graph crosses the x-axis or touches the x-axis and turns around, at each zero. f(x)=2(x 2
+3)(x+1) 2
−3, multiplicity 1 , crosses the x-axis; −1, multiplicity 2 , crosses the x-axis None −1, multiplicity 2 , touches the x-axis and turns around -3, multiplicity 1 , crosses the x-axis; −1, multiplicity 2 , touches the x-axis and turns around. −1, multiplicity 2 , crosses the x-axis
The polynomial function \(\(f(x) = 2(x^2+3)(x+1)^2\)\) has zeros at -3 with multiplicity 1, and -1 with multiplicity 2. The graph of the function crosses the x-axis at -3 and -1.
To find the zeros and their multiplicities, we set \(\(f(x)\)\) equal to zero and solve for \(\(x\).\)
Setting \(\(f(x) = 0\),\) we have:
\(\[2(x^2+3)(x+1)^2 = 0\]\)
Since the product of two factors is zero, at least one of the factors must be zero. Thus, we solve for \(\(x\)\) in each factor separately:
1. \(\(x^2 + 3 = 0\):\)
This equation does not have real solutions since the square of a real number is always non-negative. Therefore, this factor does not contribute any real zeros.
2. \(\(x + 1 = 0\):\)
Solving for \(\(x\), we find \(x = -1\).\) This gives us a zero at -1 with multiplicity 1.
Since the factor \(\((x+1)^2\)\) is squared, the zero -1 has a multiplicity of 2.
Therefore, the zeros for the polynomial function are -3 with multiplicity 1 and -1 with multiplicity 2. The graph of the function crosses the x-axis at both zeros.
To learn more about polynomial function click here: brainly.com/question/29054660
#SPJ11
What is the value of y=10x+2 when x=4
Answer:
y = 42
Step-by-step explanation:
Given
y = 10x + 2 ← substitute x = 4
y = 10(4) + 2 = 40 + 2 = 42
Answer:
=42
Step-by-step explanation:
y=10(4)+2
10 x 4 = 40
40 + 2 = 42
y=42
The measures of two angles are (4x + 39) and (16x - 12). What is the value of x that will make the two
angles congruent?
А
4.25
B
2.55
с
1.35
D
2.25
Answer:
A= 4.25
Step-by-step explanation:
4x+39−16x=16x−12−16x
−12x+39=−12
−12x+39−39=−12−39
−12x=−51
-12x/-12 = -51/-12
x=17/4
17/4= 4.25
The value of x that will make these two angles congruent is A. 4.25.
What is congruency?When angles are of equal measure we say that they are congruent to each other similar is for the sides of a figure when the corresponding sides of a similar figure are of the same length we say that the sides are congruent to each other.
We know two angles are congruent when they are of equal measure, Therefore we have to equate these two angles with each other.
So, (4x + 39) = (16x - 12).
4x + 39 = 16x - 12.
4x - 16x = -12 - 39.
-12x = -51.
12x = 51.
x = 51/12.
x = 4.25.
learn more about congruency here :
https://brainly.com/question/7888063
#SPJ5
Divide 500 among aryl,joy and kenneth such that arlyn's share is 2/3 of joy's share ang joy's share is 2/3 of Kenneth's share how much will each get?
The amount that each will get from the given fraction of amount is :
Kenneth's share = $236.842
Joy's share = 2/3 x = $157.895
Arlyn's share = 4/9 x = $105.263
Given that,
Total amount = 500
Let the fraction of amount of money Kenneth gets = x
The fraction of amount of money Joy gets = 2/3 of Kenneth's share
= 2/3 x
The fraction of amount of money Arlyn gets = 2/3 of joy's share
= 2/3 (2/3 x)
= 4/9 x
Now,
x + 2/3x + 4/9 x = 500
(9x + 6x + 4x) / 9 = 500
9x + 6x + 4x = 4500
19x = 4500
x = 236.842
Kenneth's share = $236.842
Joy's share = 2/3 x = $157.895
Arlyn's share = 4/9 x = $105.263
Hence each will get $236.842, $157.895 and $105.263.
Learn more about Fractions here :
https://brainly.com/question/30423291
#SPJ1
The volume of a cylinder, V, in terms of radius, r,
and height, h, is given by V = πr 2
h. If a cylinder has
a height of 6 meters, express the radius as a function
of V and find the radius of a cylinder with volume of
300 cubic meters.
Answer:
See explanation
Step-by-step explanation:
Volume of a cylinder = πr²h
Solve for r
V = π * r² * h
r² = V/πh
Find the square root of both sides
r = √V/πh
If height = 6 meters and volume = 300 cubic meters. Find r
r = √V/πh
= √(300/3.14*6)
= √(300/18.84)
= √15.923566878980
r = 3.9904344223381
Approximately,
r = 4 meters