I need this practice problem answered Here are the answer options:The eccentricity of the ellipse is approximatelyA. 0.71B. 0.91C. 1.10This value indicates that the ellipse is moreA. Circular then elongated B. Elongated than circular
Answers
SOLUTION
The eccentricity is the measure of how much the ellipse deviates from a circle.
The eccentricity of an ellipse which is not a circle is greater than zero but less than 1.
For an ellipse, the eccentricity is giving as
\(\frac{\sqrt[]{a^2-b^2}}{a}\)where
\(\begin{gathered} a^2=50,a=\sqrt[]{50}=5\sqrt[]{2} \\ b^2=9,b=\sqrt[]{9}=3 \end{gathered}\)Substitute the value into the formula we have
\(\begin{gathered} \frac{\sqrt[]{50-9}}{5\sqrt[]{2}} \\ \text{Then } \\ \frac{\sqrt[]{41}}{5\sqrt[]{2}} \end{gathered}\)Then rationalize the expression in the last line
\(\frac{\sqrt[]{41}\times\sqrt[]{2}}{5\sqrt[]{2}\times\sqrt[]{2}}=\frac{\sqrt[]{82}}{10}=0.9055\)Hence the eccentricity of the ellipse is approximately 0.91
Since the value of a is much larger than b, then it indicates that the ellipse is
More Elongated than circular.
Related Questions
Complete the function digits(n) that returns how many digits the number has. For example: 25 has 2 digits and 144 has 3 digits
Answers
Answer:
Step-by-step explanation:
We can get this done by using the code
def digits(n):
count = 0
if n == 0:
return 1
while (n > 0):
count += 1
n= n//10
return count
Also, another way of putting it is by saying
def digits(n):
return len(str(n))
------------------------------------------
print(digits(25)) # Should print 2
print(digits(144)) # Should print 3
print(digits(1000)) # Should print 4
print(digits(0)) # Should print 1
Doing this way, we've told the system to count the number of figures that exist in the number. If it's 1000 to 9999, then it records it as 4 digits. If it's 100 - 999, then it records it as 3 digits. If it's 10 - 99, it records as 2 digits. If it's 0 - 9, then it has to record it as a single digit.
Thanks
Following are the digits function that calculte the digits:
Program Explanation:
In this question, we define two in which one use predefine methods and one is used for calculate value by logics, which can be defined as follows: Defining a method "digits" that takes "n" variable inside the parameter.Inside the method "x"variable that converts parameter value into string and counts its length value and use return keyword that return the length of x.Outside the method, a variable n is define that inputs value, and call the method and print its return value.Program:
def digits(n):#defining a method digits that takes n variable in the parameter
x=len(str(n))#defining a variable x that converts parameter value into string and counts its length value
return x#using return keyword that return the length of x
n=int(input("Ennter number: "))#defining a variable n that inputs value
print(n, "has", digits(n) ,"digits") #using print method that calls the digits method and print its value
OR
def digits(n):#defining a method digits that takes n variable in the parameter
x = 0#defining an integer variable x
if n == 0:#defining an if block that checks n value equal to 0
return 1#return value 1
while (n > 0):#defining a while loop that check n value grater than 0
x += 1#incrementing the value of x
n =n//10#calculating the digits
return x#return digits value
n=int(input("Ennter number: "))#defining a variable n that inputs value
print(n, "has", digits(n) ,"digits") #using print method that calls the digits method and print its value
Output:
Please find the attached file.
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Antonio is in a bowling league. His goal is to score an average of at least 100 points per game. His scores so far are 105,95,97,82, and 110. How many points can Antonio score in his next game to reach his goal? Show your work.
Please show work I need it so please have step by step I will give brainly thanks!
Answers
Antonio needs to score at least 111 points in his next game to reach his goal of an average of at least 100 points per game.
What are basic arithmetic operations?
Basic arithmetic operations are fundamental mathematical calculations that involve manipulating numerical values using a set of basic operations.
To find out how many points Antonio needs to score in his next game to reach an average of at least 100 points per game, we can use the following formula:
Total points needed = (number of games + 1) × average score goal - total points scored so far
In this case, Antonio has played 5 games, so the number of games he will have played after his next game is 6. His goal is an average of 100 points per game, so his average score goal is 100. The total points he has scored so far is:
105 + 95 + 97 + 82 + 110 = 489
Substituting these values into the formula, we get:
Total points needed = (6) × (100) - 489
Total points needed = 600 - 489
Total points needed = 111
Hence, Antonio needs to score at least 111 points in his next game to reach his goal of an average of at least 100 points per game.
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91 pointSimplify the following function4.222-25 12-36O4(x+6(22-25)(4x+6)+ +5,0(x+5)(8-5) 2 + +6, +5,0O4(x+6)(3-5)(x+5)*7 +5, +6,0(2+5)27-5,0O
Answers
ANSWER
\(\begin{gathered} -\frac{4(x+6)}{(x-5)(x+5)} \\ x\ne\pm5,\pm6,0 \end{gathered}\)EXPLANATION
We want to simplify the expression:
\(-\frac{4x}{x^2-25}\div\frac{(x^2-6x)}{x^2-36}\)To do this, first change the sign to a multiplication sign and flip the fraction on the right:
\(-\frac{4x}{x^2-25}\cdot\frac{x^2-36}{(x^2-6x)}\)Now, simplify the expression by applying the difference of two squares and factorization:
\(\begin{gathered} -\frac{4x}{(x-5)(x+5)}\cdot\frac{(x-6)(x+6)}{x(x-6)} \\ \Rightarrow-\frac{4}{(x-5)(x+5)}\cdot\frac{(x+6)}{1} \\ \Rightarrow-\frac{4(x+6)}{(x-5)(x+5)} \end{gathered}\)The expression will be invalid when x is:
\(\pm5,\pm6,0\)Therefore, the answer is option C.
Help with math problems
Answers
The vertex form of the quadratic equations in standard form are, respectively:
Case 9: y = 2 · (x + 2)² - 12
Case 10: y = - (1 / 2) · (x + 3 / 4)² + 33 / 32
Case 11: y = 3 · (x - 4 / 3)² - 16 / 3
Case 12: y = - 3 · (x - 3)²
Case 13: y = (x - 4)² + 3
Case 14: y = (x - 1)² - 7
Case 15: y = (x + 3 / 2)² - 9 / 4
Case 16: 2 · (x + 1 / 4)² - 1 / 8
Case 17: y = 2 · (x - 3)² - 7
Case 18: y = - 2 · (x + 1)² + 10
How to derive the vertex form of a quadratic equationIn this problem we find ten cases of quadratic equation in standard form, whose vertex form can be found by a combination of algebra properties known as completing the square. Completing the square consists in simplifying a part of the quadratic equation into a power of a binomial.
The two forms are introduced below:
Standard form
y = a · x² + b · x + c
Where a, b, c are real coefficients.
Vertex form
y - k = C · (x - h)²
Where:
C - Vertex constant(h, k) - Vertex coordinates.Now we proceed to determine the vertex form of each quadratic equation:
Case 9
y = 2 · x² + 4 · x - 4
y = 2 · (x² + 2 · x - 2)
y = 2 · (x² + 2 · x + 4) - 12
y = 2 · (x + 2)² - 12
Case 10
y = - (1 / 2) · x² - 3 · x + 3
y = - (1 / 2) · [x² + (3 / 2) · x - 3 / 2]
y = - (1 / 2) · [x² + (3 / 2) · x + 9 / 16] + (1 / 2) · (33 / 16)
y = - (1 / 2) · (x + 3 / 4)² + 33 / 32
Case 11
y = 3 · x² - 8 · x
y = 3 · [x² - (8 / 3) · x]
y = 3 · [x² - (8 / 3) · x + 16 / 9] - 3 · (16 / 9)
y = 3 · (x - 4 / 3)² - 16 / 3
Case 12
y = - 3 · x² + 18 · x - 27
y = - 3 · (x² - 6 · x + 9)
y = - 3 · (x - 3)²
Case 13
y = x² - 8 · x + 19
y = (x² - 8 · x + 16) + 3
y = (x - 4)² + 3
Case 14
y = x² - 2 · x - 6
y = (x² - 2 · x + 1) - 7
y = (x - 1)² - 7
Case 15
y = x² + 3 · x
y = (x² + 3 · x + 9 / 4) - 9 / 4
y = (x + 3 / 2)² - 9 / 4
Case 16
y = 2 · x² + x
y = 2 · [x² + (1 / 2) · x]
y = 2 · [x² + (1 / 2) · x + 1 / 16] - 2 · (1 / 16)
y = 2 · (x + 1 / 4)² - 1 / 8
Case 17
y = 2 · x² - 12 · x + 11
y = 2 · (x² - 6 · x + 9) - 2 · (7 / 2)
y = 2 · (x - 3)² - 7
Case 18
y = - 2 · x² - 4 · x + 8
y = - 2 · (x² + 2 · x - 4)
y = - 2 · (x² + 2 · x + 1) + 2 · 5
y = - 2 · (x + 1)² + 10
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Find the number of years the annuity will last if it pays 300 per year.
Answers
The number of years the annuity will last if it pays $300 per year is 18 years.
What is an annuity?An annuity is an investment that pays the investor a fixed periodic amount for many years in the future.
The annuity payment may be monthly or yearly, as the case may be.
An online finance calculator can compute the annual payment (annuity).
I/Y (Interest per year) = 7%
PV (Present Value) = $3,000
PMT (Periodic Payment) = $-300
FV (Future Value) = $0
Results:
N = 17.795
Sum of all periodic payments = $-5,338.44
Total Interest $2,338.44
Thus, for an annuity with a present value of $3,000, earning 7% per annum and paying $300 per year will last almost 18 years.
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Question Completion:The present value of an annuity is $3,000 and earns 7% per annum.
Find the number of years the annuity will last if it pays $300 per year.
50 Points! Multiple choice algebra question. Photo attached. Thank you!
Answers
The exact value of cos theta if the terminal side of theta in standard position contains the point (6,-8) is, 3 / 5
We have to given that;
the terminal side of theta in standard position contains the point (6,-8)
Hence, For given condition we get;
The exact value of cos theta if the terminal side of theta in standard position contains the point (6,-8) is,
Here, x = 6, y = - 8
Hence, We get;
r = √x² + y²
r = √6² + 8²
r = √36 + 64
r = √100
r = 10
So, The exact value of cos theta if the terminal side of theta in standard position contains the point (6,-8) is,
cos θ = x / r
cos θ = 6 / 10
cos θ = 3 / 5
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Find the Central Angle
mXY = = 18 in
radius ZY = 7.64 in
Answers
The central angle is approximately 2.357 radians.
To find the central angle, we can use the formula:
Central angle (θ) = arc length ÷ radius
Given:
Arc length (mXY) = 18 in
Radius (ZY) = 7.64 in
Plugging in the values:
Central angle (θ) = 18 in ÷ 7.64 in
Calculating the division:
θ ≈ 2.357 radians
Therefore, the central angle is approximately 2.357 radians.
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explain why (a+b)^2 = a^2+b^2 if and only if a=0 or b=0
Answers
Hope this helps! Because when you would fill in the variables 0=0 which which make the expression too that they’d equal the same.
Please use the following for the next 6 questions. Suppose that the average weekly earnings for employees in general automotive repair shops is $450, and that the population standard deviation for the earnings for such employees is $50. A sample of 100 such employees is selected at random.
1) What is the probability distribution of the average weekly earnings for employees in general automotive repair shops?
2) Find the probability that the average weekly earnings is less than $445.
3) Find the probability that the average weekly earnings is exactly equal to $445.
4) Find the probability that the average weekly earnings is between $445 and $455.
5) In answering the previous 3 questions, did you have to make any assumptions about the population distribution?
6) Now assume that the weekly earnings for employees in all general automotive repair shops is normally distributed, obtain the probability that a given employee will earn more than $480 in a given week.
Answers
1) The probability distribution of the average weekly earnings for employees in general automotive repair shops is the sampling distribution of the sample mean. According to the Central Limit Theorem, if the sample size is large enough, the sampling distribution of the sample mean is approximately normal, with a mean equal to the population mean and a standard deviation equal to the population standard deviation divided by the square root of the sample size.
2) To find the probability that the average weekly earnings is less than $445, we can standardize the sample mean and use a z-table. The z-score for $445 is calculated as follows: z = (445 - 450) / (50 / sqrt(100)) = -1. Using a z-table, we find that the probability that the average weekly earnings is less than $445 is approximately 0.1587.
3) Since we are dealing with a continuous distribution, the probability that the average weekly earnings is exactly equal to any specific value is zero.
4) To find the probability that the average weekly earnings is between $445 and $455, we can subtract the probability that it is less than $445 from the probability that it is less than $455. The z-score for $455 is calculated as follows: z = (455 - 450) / (50 / sqrt(100)) = 1. Using a z-table, we find that the probability that the average weekly earnings is less than $455 is approximately 0.8413. Therefore, the probability that it is between $445 and $455 is approximately 0.8413 - 0.1587 = 0.6826.
5) In answering questions 2-4, we made an assumption about the population distribution based on the Central Limit Theorem. We assumed that since our sample size was large enough (n=100), our sampling distribution would be approximately normal.
6) If we assume that weekly earnings for employees in all general automotive repair shops are normally distributed with a mean of $450 and a standard deviation of $50, then we can calculate the z-score for an employee earning more than $480 in a given week as follows: z = (480 - 450) / 50 = 0.6. Using a z-table, we find that the probability that an employee will earn more than $480 in a given week is approximately 1 - 0.7257 = 0.2743.
Naomi's dining room is 7 yards wide and 7 yards long. Naomi wants to install wooden trim around the top of the room. The trim costs $9.00 per yard. How much will it cost Naomi to buy enough trim?
Answers
Use the function f(x) to answer the questions:
f(x) = 2x2 − 5x + 3
Part A: What are the x-intercepts of the graph of f(x)? Show your work.
Part B: Is the vertex of the graph of f(x) going to be a maximum or a minimum? What are the coordinates of the vertex? Justify your answers and show your work.
Part C: What are the steps you would use to graph f(x)? Justify that you can use the answers obtained in Part A and Part B to draw the graph.
Answers
The x-intercepts of the graph of f(x) are x = 3/2 and x = 1,the Vertex of the graph of f(x) is (5/4, 3/8), and it is a minimum point, The vertex is at (5/4, 3/8). This is the minimum point of the graph.
Part A: To find the x-intercepts of the graph of f(x), we set f(x) equal to zero and solve for x.
2x^2 - 5x + 3 = 0
To factor this quadratic equation, we look for two numbers that multiply to give 3 (the coefficient of the constant term) and add up to -5 (the coefficient of the linear term). These numbers are -3 and -1.
2x^2 - 3x - 2x + 3 = 0
x(2x - 3) - 1(2x - 3) = 0
(2x - 3)(x - 1) = 0
Setting each factor equal to zero, we get:
2x - 3 = 0 --> x = 3/2
x - 1 = 0 --> x = 1
Therefore, the x-intercepts of the graph of f(x) are x = 3/2 and x = 1.
Part B: To determine whether the vertex of the graph of f(x) is a maximum or a minimum, we look at the coefficient of the x^2 term, which is positive (2 in this case). A positive coefficient indicates that the parabola opens upwards, so the vertex will be a minimum.
To find the coordinates of the vertex, we can use the formula x = -b/2a. In the equation f(x) = 2x^2 - 5x + 3, the coefficient of the x term is -5, and the coefficient of the x^2 term is 2.
x = -(-5) / (2*2) = 5/4
Substituting this value of x back into the equation, we can find the y-coordinate:
f(5/4) = 2(5/4)^2 - 5(5/4) + 3 = 25/8 - 25/4 + 3 = 3/8
Therefore, the vertex of the graph of f(x) is (5/4, 3/8), and it is a minimum point.
Part C: To graph f(x), we can use the information obtained in Part A and Part B.
- The x-intercepts are x = 3/2 and x = 1. These are the points where the graph intersects the x-axis.
- The vertex is at (5/4, 3/8). This is the minimum point of the graph.
We can plot these points on a coordinate plane and draw a smooth curve passing through the x-intercepts and the vertex. Since the coefficient of the x^2 term is positive, the parabola opens upwards, and the graph will be concave up.
Additionally, we can consider the symmetry of the graph. Since the coefficient of the linear term is -5, the line of symmetry is given by x = -(-5) / (2*2) = 5/4, which is the x-coordinate of the vertex. The graph will be symmetric with respect to this line.
By connecting the plotted points and sketching the curve smoothly, we can accurately graph the function f(x).
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what is −2(x+6)=4x
x=
Answers
Answer:
x=-2
Step-by-step explanation:
Distribute, add 12 to both side, then simplify
Answer: -2
Let's solve your equation step-by-step.
−2(x+6)=4x:
Step 1: Simplify both sides of the equation.
−2(x + 6) = 4x
(−2)(x) + (−2)(6) = 4x (Distribute)
−2x + (−12) = 4x
−2x − 12 = 4x
Step 2: Subtract 4x from both sides.
−2x − 12 − 4x = 4x − 4x
−6x − 12 = 0
Step 3: Add 12 to both sides.
−6x − 12 + 12 = 0 + 12
−6x = 12
Step 4: Divide both sides by -6.
−6x/−6 = 12/−6
x = −2
solve the following system of equations graohically on the set of axes below.
Answers
To solve the system of equation graphically we need to plot each equation on the plane. First we notice that both equation are linear, which means that their graphs are lines; this also means that to graph them we just need two points for each equation. Let's graph the equations.
First equation: y=x-2
As we said we just need two points on the line, to get them we just need to give values to x (any values we want) and plug them in the equation to get y.
If x=0, then we have:
\(\begin{gathered} y=0-2 \\ y=-2 \end{gathered}\)hence the line passes through the point (0,-2)
If x=1, then we have:
\(\begin{gathered} y=1-2 \\ y=-1 \end{gathered}\)hence the line passes through the point (1,-1)
With this we conclude that the line passes through the points (0,-2) and (1,-1). Plotting this points on the plane and joining them with a straight line we have the graph of the first equation:
Second equation: y=-2x-5:
We follow the same procedure as with the first equation.
If x=0 we have:
\(\begin{gathered} y=-2(0)-5 \\ y=-5 \end{gathered}\)Hence the line passes through (0,-5)
If x=1 we have:
\(\begin{gathered} y=-2\left(1\right)-5 \\ y=-2-5 \\ y=-7 \end{gathered}\)Hence the line passes through (1,-7)
Plotting this points and joining then with a line we have the graph for the second equation:
Finally, we plot both lines in the same plane. The solution of the system will be the point of intersection of the lines. The graph of the system is shown below:
From it we notice that the lines intersect at (-1,-3).
Therefore, the solution of the system is the point (-1,-3) which means that x=-1 and y=-3.
Which of the following is an example of a proper fraction?
A.7/6
B.3/4
C.4/4
D.4/3
Answers
Answer: B
Step-by-step explanation:
A proper fraction is when a fraction has the numeration less than the denominator
Five companies have each sent one representative to a competition to pitch their newest business idea to a group of angel investors. The conference has 5 time slots designated for one representative to present their company's idea. How many different ways can the representatives be ordered to present their ideas?
Answers
Answer:
120 ways
Step-by-step explanation:
The number of different ways can the representatives be ordered to present their ideas is 120 ways.
Given that, 5 companies have each sent one representative to a competition to pitch their newest business idea to a group of angel investors.
What are Permutations?Permutations are different ways of arranging objects in a definite order. It can also be expressed as the rearrangement of items in a linear order of an already ordered set. The symbol nPr is used to denote the number of permutations of n distinct objects, taken r at a time.
Using nPr =n!(n-r)! we get
Here, n=5 and r=5
So, P(n, r) = P(5, 5) = 5!(5-5)!
= 5!/1
= 5×4×3×2×1
= 120 ways
Therefore, the number of different ways can the representatives be ordered to present their ideas is 120 ways.
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15)
136⁰
2
S
?
R
Find the measure of the arc or angle indicated
Answers
Answer:
224
Step-by-step explanation:
360.-136.
Perform the indicated operation by removing the parentheses and combining like terms.(-2x2 + 5) + (6x2 + 7)
Answers
Given the expression:
\(\mleft(-2x^2+5\mright)+(6x^2+7)\)Removing the parentheses and combining like terms.
\(\begin{gathered} =-2x^2+5+6x^2+7 \\ =-2x^2+6x^2+5+7 \\ \\ =4x^2+12 \end{gathered}\)so, the answer will be:
\(4x^2+12\)Answer 733
Step-by-step explanation:
find missing side length ? pls ty
Answers
Answer:
a
Step-by-step explanation:
because for a 45-degree right triangle the two legs are the same and because the legs are sqrt 3, it is sqrt 6
427 diveided by 3 do you have any aneswerers
Answers
Answer:
142.333....
Step-by-step explanation: just use a calculator
Answer:
142.34
Step-by-step explanation:
427 ÷ 3 = 142.34
good luck, i hope this helps :)
What is the slope of a line passing through (4,4) and (6,10)
Answers
Answer:
The slope of the line is;
\(3\)Explanation:
We want to find the slope of the line passing through the points;
\((4,4)\text{ and (6,10)}\)Recall that the slope m of a line can be calculated using the formula;
\(m=\frac{\Delta y}{\Delta x}=\frac{y_2-y_1}{x_2-x_1}\)substituting the given coordinates;
\(\begin{gathered} m=\frac{10-4}{6-4} \\ m=\frac{6}{2} \\ m=3 \end{gathered}\)Therefore, the slope of the line is;
\(3\)
PLEASE ANSWER ASAP!!!!!
Answers
Answer:
\(\huge\boxed{\sf r = 5}\)
Step-by-step explanation:
Given that,
7(q + 5) = (q + r)7Distribute7q + 35 = 7q + 7r
Subtract 7q from both sides7q - 7q + 35 = 7q - 7q + 7r
35 = 7r
Divide both sides by 735/7 = r
5 = r
OR
r = 5\(\rule[225]{225}{2}\)
Answer:
r = 5
Step-by-step explanation:
Given statement,
→ 7(q + 5) is equivalent to (q + r)7.
Forming the equation,
→ 7(q + 5) = 7(q + r)
Now we have to,
→ Find the required value of r.
Then the value of r will be,
→ 7(q + 5) = 7(q + r)
Applying Distributive property:
→ 7(q) + 7(5) = 7(q) + 7(r)
→ 7q + 35 = 7q + 7r
Cancelling 7q from both sides:
→ 35 = 7r
→ 7r = 35
Dividing the RHS with number 7:
→ r = 35/7
→ [ r = 5 ]
Therefore, the value of r is 5.
The increase in a person’s body temperature T(t), above 98.6ºF, can be modeled by the function T (t) = StartFraction 4 t Over t squared + 1 EndFraction, where t represents time elapsed. What is the meaning of the horizontal asymptote for this function?
Answers
The horizontal asymptote of T(t)=0 means that the temperature will not increase above 98.6F as time elapses.
Given,\(T(t)=\frac{4t}{t^2+1}\\\)
where, t represents time elapse it means 't' reaches to infinity
In function \(\lim_{n \to \infty} f(n)\), f(n) is called as horizontal asymptote of the function.
then the above equation can be written as
\(T(t)=\lim_{t \to \infty}\frac{4t}{t^2+1}\\\\=\lim_{t \to \infty}\frac{4t}{t(t+\frac{1}{t})}\\\\=\lim_{t \to \infty}\frac{4}{(t+\frac{1}{t})}\\\\=\frac{4}{\infty +0}\\\\=0\)
Hence,the horizontal asymptote of T(t) is 0 it means there is no increase in the temperature above 98.6F.
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use the shell method to find the volume generated by revolving the shaded regions bounded by the curves and lines in exerciss 7-12about the y-axis
Answers
The answer is 1) V = \(2\pi\int\limits(2)+ {x} \, dx\); 2) V = \(2\pi \int\limits(1 - 2x) - 2x dx\); 3) V =\(2\pi \int\limits {\sqrt{2} } \, dx\) ; 4) V = \(2\pi\int\limits {\sqrt{(-2/2)(2-2)} \ dx\) .
1) The volume of the shell is then given by the product of the area of its curved surface and its height. The height is equal to 2 - (-2) = 4, and the radius is equal to the minimum of the distances from x = 2 to the two curves, which is x = 2 - () = 2 + . The volume of the solid is then given by the definite integral:
V = \(2\pi\int\limits(2)+ {x} \, dx\) = \(2\pi [(/3) + 2x]\) evaluated from 0 to 1 = (4/3)π.
2) The height of the region is equal to - (2x) = -2x, and the radius is equal to the minimum of the distances from x = 1 to the two curves, which is x = 1 - (2x) = 1 - 2x. The volume of the solid is then given by:
V = \(2\pi \int\limits(1 - 2x) - 2x dx\)=\(2\pi [/5 - 2/3 + /2]\) evaluated from 0 to 1 = (8π/15).
3) The height of the region is equal to (2-x) - = 2-x. The radius is equal to the minimum of the distances from x = 0 to the two curves, which is x = The volume of the solid is then given by:
V =\(2\pi \int\limits {\sqrt{2} } \, dx\) = \(2\pi [(x^4/4)]\) evaluated from 0 to √2 = (π/2).
4) The height of the region is equal to () - (2-) = 2 - 2. The radius is equal to the minimum of the distances from x = 0 to the two curves, which is x = √((2-)/2). The volume of the solid is then given by:
V = \(2\pi\int\limits {\sqrt{(-2/2)(2-2)} \ dx\) = \(4\pi [(2/3)\± (2\sqrt{2} /3)]\)
The complete Question is:
Use the shell method to find the volumes of the solids generated by revolving the regions bounded by the curves and lines in about the
1. y = x, y = -x/2, and x = 2
2. y = 2x, y = x/2, and x = 1
3. y = x/2, y = 2-x, and x = 0
4. y = 2-x/2, y = x/2, and x = 0
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What is the range of f(x) = -62*?
O A. y< 1
OB. y<0
O C. y> 0
O D. All real numbers
Answers
Answer:
D. all real numbers
Step-by-step explanation:
i think this is the answer sorry if you get it wrong.
A (non-zero) number multiplied by zero equals zero, whereas a non-zero number divided by zero is undefined.
a. True
b. False
Answers
Calvin wrote inequalities to compare the heights, in feet, of rivers above or below flood stage.
Select all of the inequalities that are correct.
A. -10 > -9
B. 1> -18
C. -25 > -30
D. 3 < -5
E. -10 < 3
Answers
Answer:
I'm not 100% sure but I think its B. 1> -18
Which value makes the number sentence true?
Answers
Answer:
D) 19
Step-by-step explanation:
-7 + 19 = 12
The General Social Survey (GSS) is a sociological survey used to collect data on demographic characteristics and attitudes of residents of the United States. In 2010, the survey collected responses from over a thousand US residents. The survey is conducted face-to-face with an in-person interview of a randomly-selected sample of adults. One of the questions on the survey is "For how many days during the past 30 days was your mental health, which includes stress, depression, and problems with emotions, not good?" Based on responses from 1,151 US residents, the survey reported a 95% confidence interval of 3.40 to 4.24 days in 2010. Given this information, which of the following statements would be most appropriate to make regarding the true average number of days of "not good" mental health in 2010 for US residents? 1 point For these 1,151 residents in 2010, we are 95% confident that the average number of days of "not good" mental health is between 3.40 and 4.24 days. There is not sufficient information to calculate the margin of error of this confidence interval. For all US residents in 2010, based on this 95% confidence interval, we would reject a null hypothesis stating that the true average number of days of "not good" mental health is 5 days.
Answers
The most appropriate statement is the one that correctly reflects the confidence interval obtained from the survey data, as stated above.
The most appropriate statement to make regarding the true average number of days of "not good" mental health in 2010 for US residents, based on the given information, is:
"For these 1,151 residents in 2010, we are 95% confident that the average number of days of 'not good' mental health is between 3.40 and 4.24 days."
The 95% confidence interval of 3.40 to 4.24 days is obtained from the survey data, and it provides an estimate of the range within which the true average number of days of "not good" mental health falls for the entire population of US residents.
Regarding the provided options:
There is not sufficient information to calculate the margin of error of this confidence interval: This statement is not accurate since the margin of error can be calculated using the formula Margin of Error = (Upper Limit - Lower Limit) / 2.
For all US residents in 2010, based on this 95% confidence interval, we would reject a null hypothesis stating that the true average number of days of "not good" mental health is 5 days: This statement is not supported by the given information. The confidence interval provides an estimate of the range within which the true average lies, but it does not involve a comparison to a specific value such as 5 days.
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Based on the provided information and the 95% confidence interval of 3.40 to 4.24 days for "not good" mental health in 2010,
The most appropriate statement to make regarding the true average number of days of "not good" mental health for US residents in 2010 is:
"For these 1,151 residents in 2010, we are 95% confident that the average number of days of 'not good' mental health is between 3.40 and 4.24 days."
This statement accurately represents the confidence interval obtained from the survey data.
It indicates that the true average number of "not good" mental health days for the entire US population in 2010 is likely to fall within this range with a 95% level of confidence.
It's important to note that this statement only applies to the specific sample of 1,151 US residents surveyed in 2010.
To make inferences about the true average number of "not good" mental health days for all US residents in 2010, a different sample with a larger representative size would be required.
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You leave a pile of sand in your backyard on a windy day. Every minute the wind blows away 10 percent of the remaining sand. You started with five cubic feet of sand. What equation models the amount of sand after minutes?
Answers
Answer:
10% of the remaining sand You had 5 ft of sand So y=5(.10(x))Answer:
the RIGHT answer is y = 5 x 0.90^x
Step-by-step explanation:
ten percent has already been blown away, so you only include the percentage of what hasn't been blown away in the equation. (also i just did the assignment and got 100% so you can trust this).
Milan made a shirt using 5/8 yards of yellow fabric and 1/4 yards of green fabric. How many more yards of yellow fabric did Milan use?
Answers
Answer: He used 3/8 more yards of yellow fabric.
Step-by-step explanation:
You are basically subtracting 1/4 from 5/8. So the equation is 5/8 - 1/4, when you find the common denominator it is 5/8 - 2/8 and this leaves us with 3/8