Find the volume V of the solid obtained by rotating the region bounded by the given curves about the specified line.y = 6/7 x2, y = 13/7 − x2; about the x-axis
Answers
The volume (V) of the solid obtained by rotating the region bounded by the curve y = (6/7)x^2 about the x-axis is V = π[((9/245)b^5) - ((9/245)a^5)].
the volume (V) of the solid obtained by rotating the region bounded by the curve y = (6/7)x^2 about the x-axis is (2/3)π[(13/7) * sqrt(13/7)] cubic units.
To find the volume (V) of the solid obtained by rotating the region bounded by the curve y = (6/7)x^2 about the x-axis, we can use the disk method. Here's a step-by-step explanation:
1. Identify the function: y = (6/7)x^2
2. Determine the limits of integration: Since we are not given specific bounds, let's assume the region is defined between x=a and x=b.
3. Set up the integral for the disk method: V = π∫[f(x)]^2 dx, where f(x) = (6/7)x^2.
4. Substitute the function and limits into the integral: V = π∫[a to b] [(6/7)x^2]^2 dx
5. Simplify the integral: V = π∫[a to b] (36/49)x^4 dx
6. Integrate to x: V = π[(9/245)x^5]∣[a to b]
7. Evaluate the definite integral: V = π[((9/245)b^5) - ((9/245)a^5)] So, the volume (V) of the solid obtained by rotating the region bounded by the curve y = (6/7)x^2 about the x-axis is V = π[((9/245)b^5) - ((9/245)a^5)].
To find the volume V of the solid obtained by rotating the region bounded by the curve y = 13/7 − x2 about the x-axis. Let us consider a region bounded by the curve y = 13/7 − x2 and the x-axis.Let us rotate this region about the x-axis to obtain a solid with a volume.The region bounded by the curve y = 13/7 − x2 and the x-axis is shown below:We need to integrate to find the volume V of the solid obtained by rotating the region bounded by the curve y = 13/7 − x2 about the x-axis. The volume of the solid is given by: V = ∫(π.y2)dx, where y = 13/7 − x2Integrating V, we get: V = π ∫ (13/7 − x2)2 dx Let us evaluate the integralπ ∫ (13/7 − x2)2 dx= π [(13/7) * x - (1/3) * x3] limits from -sqrt(13/7) to +sqrt(13/7))= π [(13/7) * sqrt(13/7) - (1/3) * (13/7)3/2] - π [-(13/7) * sqrt(13/7) - (1/3) * (13/7)3/2]= (2/3)π[(13/7) * sqrt(13/7)] cubic unitsTherefore, the volume of the solid is (2/3)π[(13/7) * sqrt(13/7)] cubic units.
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Related Questions
An author published a book which was being sold online. The first month the author sold 19000 books, but the sales were declining steadily at 7% each month. If this trend continues, how many total books would the author have sold over the first 12 months, to the nearest whole number?
Answers
If this trend continues, the total books the author would have sold over the first 12 months is 157,810 books.
How to calculate the total books sold over the first 12 months?In this scenario, we would calculate the total books sold by this author over the first 12 months as follows;
First month = 19,000 books.
Second month; 19,000 × (1 - 7)% = 19,000 × 93/100 = 17,670 books.
Third month; 17,670 × (1 - 7)% = 17,670 × 93/100 = 16,433 books.
Fourth month; 16,433 × (1 - 7)% = 16,433 × 93/100 = 15,283 books.
Fifth month; 15,283 × (1 - 7)% = 15,283 × 93/100 = 14,213 books.
Sixth month; 14,213 × (1 - 7)% = 14,213 × 93/100 = 13,218 books.
Seventh month; 13,218 × (1 - 7)% = 13,218 × 93/100 = 12,293 books.
Eigth month; 12,293 × (1 - 7)% = 12,293 × 93/100 = 11,432 books.
Ninth month; 11,432 × (1 - 7)% = 11,432 × 93/100 = 10,632 books.
Tenth month; 10,632 × (1 - 7)% = 13,218 × 93/100 = 9,888 books.
Eleventh month; 11,432 × (1 - 7)% = 11,432 × 93/100 = 9,196 books.
Twelveth month; 9,196 × (1 - 7)% = 9,196 × 93/100 = 8,552 books.
Next, we would add all of the books sold in each month together;
Total books sold = 19,000 + 17,670 + 16,433 + 15,283 + 14,213 + 13,218 + 12,293 + 11,432 + 10,632 + 9,888 + 9,196 + 8,552
Total books sold = 157,810 books.
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\text{The sum of 7 and the cube of a number.}
The sum of 7 and the cube of a number.
Answers
Answer:
Step-by-step explanation:
Lets call the number n.
So the cube of this number is \(n^3\) and the sum of 7 and the cube of this number is \(7+n^3\)
54. A bag contains 80 colored tokens. Of all
the tokens in the bag, 25 are black and
5
16 are red.
a. Find, in percent form, the
probability of choosing a black
token.
b. Find, in percent form, the
probability of choosing a red
token.
Answers
The probability of choosing a black token from the bag is 31.25% and the probability of choosing a red token from the bag is also 31.25%.
What is probability?Probability of an event is the ratio of number of favorable outcome to the total number of outcome of that event.
A bag contains 80 colored tokens. Of all the tokens in the bag, 25 are black and 5/16 are red.
a. In percent form, the probability of choosing a black token.There are total tokens are 80 in which black token are 25 black tokens. Thus, the probability of choosing black token is,
\(P=\dfrac{25}{80}\\P=0.3125\\P=31.25\%\)
b.In percent form, the probability of choosing a red token.There are total 5/16 tokens in bag. Thus, the number of red tokens in bag is,
\(n=\dfrac{5}{16}\times80\\n=25\)
Thus, the probability of choosing red token is,
\(P=\dfrac{25}{80}\\P=0.3125\\P=31.25\%\)
Thus, the probability of choosing a black token from the bag is 31.25% and the probability of choosing a red token from the bag is also 31.25%.
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write an equation
(X-P) (x-q)=0
Answers
Answer:
\(x^{2} -pqx+pq\)
Step-by-step explanation:
Ray purchased a jacket with 60% discount, for $240. how would you calculate price before a sale?
Answers
240/ 60% = A
Answer:
$400
Step-by-step explanation:
We will make this question into a function by setting 'p' as the initial price before sale and converting the percent to a decimal (60*0.01).
Because the final price was calculated by multiplying the initial price by 60%, we can represent that with the function:
0.6p=240
All we need to do now is isolate p by dividing out 0.6.
p=400
Giving us an answer of $400 (that's an expensive jacket )
What is the quotient of (x3 - 3x2 + 5x – 3) = (x - 1)?
x2 - 2x - 3
x2 + 2x + 7
x2-3x + 8
x2 - 2x + 3
Answers
Note: Consider "÷" sign instead of "=".
Given:
\((x^3-3x^2+5x-3)\div (x-1)\)
To find:
The quotient.
Solution:
We have,
\((x^3-3x^2+5x-3)\div (x-1)\)
It can be written as
\(=\dfrac{x^3-3x^2+5x-3}{x-1}\)
Splitting the middle terms, we get
\(=\dfrac{x^3-x^2-2x^2+2x+3x-3}{x-1}\)
\(=\dfrac{x^2(x-1)-2x(x-1)+3(x-1)}{x-1}\)
Taking out the common factor (x-1), we get
\(=\dfrac{(x-1)(x^2-2x+3)}{x-1}\)
Cancel the common factors.
\(=x^2-2x+3\)
The quotient is \(x^2-2x+3\).
Therefore, the correct option is D.
Answer:
D
Step-by-step explanation:
Does anyone know this?
Answers
Answer:
-6
Step-by-step explanation:
Hello!
Since we are finding f(-1) we put -1 in for x
2(-1)^2 + 8(-1)
Follow PEMDAS
2 * 1 + 8(-1)
2 * 1 + -8
2 + -8 = -6
The answer is -6
Hope this helps!
Please help giving 10 points!
Which statements about the graphs of the equations y = 2x + 4 and y = −x + 4 are true? Select all that apply.
A. The graphs intersect the x-axis at the same point.
B. The graphs intersect the y-axis at the same point.
C. The graphs have different slopes.
D. The graphs are parallel lines.
Answers
Answer:
The answer is B and c.
Step-by-step explanation:
first thing you need to do is look at slopes
the slopes are different then look at the y intersects there the same
and finally they both intersect at the same point.
the correct answer is B and C.
A fruit seller bought a crate of apples for $66.50.After selling each apple for 55 cents,he was able to cover his cost but did not make a profit of more than $20.How many apples could he have sold?
I have to solve this using simultaneous linear inequalities.
Answers
\(\large{\mathcal{ANSWER:}}\)
Let initially he had x No. of apples
ATQ :-
x-40% of x=420
x-2/5x=420
=> 3x=420×5
x= 700
\(\underline{\boxed{\purple{\tt{©⚘MissyRiel}}}}\)
Hope this helps!
Solve each proportion.
(z-1)/3 = 8/(z+1)
Answers
\(\dfrac{z-1}3 = \dfrac8{z+1}\)
Eliminate the denominators.
\(3(z+1)\cdot\dfrac{z-1}3 = 3(z+1)\cdot\dfrac8{z+1}\)
\(z^2 - 1 = 24\)
Solve for \(z\).
\(z^2 = 25\)
\(\boxed{z = \pm5}\)
19. Please help!!! Reporting all fake answers!:-(
Answers
my answer is (a) I think
a store sells 2 pounds of tomatoes for $7. Write an equation that represents the cost, c, for t pounds of tomatoes
Answers
Answer:
t pounds = 3.5 (or just t = 3.5c)
Step-by-step explanation:
2 pounds of tomatos for 7$ means that one pound of tomatos for 3.5$. Therefore, t pounds = 3.5 c
The equation which represents the sales of tomatoes will be ( t = 3.5c).
What is an expression?Expression in maths is defined as the collection of numbers variables and functions by using signs like addition, subtraction, multiplication, and division.
Numbers (constants), variables, operations, functions, brackets, punctuation, and grouping can all be represented by mathematical symbols, which can also be used to indicate the logical syntax's order of operations and other features.
2 pounds of tomatoes for 7$ means that one pound of tomatoes for 3.5$. Therefore, t pounds = 3.5 c
Let t represent tomatoes and c represents cost then the expression will be written as below:-
t = 3.5c
Therefore, the equation which represents the sales of tomatoes will be ( t = 3.5c).
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The average of six numbers is -3.65.If five numbers are each -3.20,what is the sixth number.
Answers
we know that the average for six numbers can be writen like:
\(A=\frac{x_1+x_2+x_3+x_4+x_5+x_6}{6}\)So if 5 of them are -3.20 and the average is -3.65 we can replace that values and find the missing one:
\(-3.65=\frac{5(-3.20)+x}{6}\)and we solve for x so:
\(\begin{gathered} -3.65\cdot6=-16+x \\ -22+16=x \\ -6=x \end{gathered}\)So the missing value is -6
–81, 108, –144, 192,. Which formula can be used to describe the sequence?.
Answers
The formula that can be used to describe the sequence is:\(a(n) = (-1)^(n+1) * 3^(n) * 4.\)
The given sequence is -81, 108, -144, 192.
The formula that can be used to describe the sequence is: \(a(n) = (-1)^(n+1) * 3^(n) * 4\), where n is the nth term in the sequence.
This formula is a geometric sequence formula that can be used to describe the given sequence.
The formula represents the nth term of the sequence as a function of the position of the term in the sequence.
Here, n represents the position of the term in the sequence
.For the given sequence, the first term is -81, which corresponds to the first position in the sequence (n = 1).
The second term is 108, which corresponds to the second position in the sequence (n = 2).
The third term is -144, which corresponds to the third position in the sequence (n = 3).
The fourth term is 192, which corresponds to the fourth position in the sequence (n = 4).
Therefore, the formula that can be used to describe the sequence is: \(a(n) = (-1)^(n+1) * 3^(n) * 4.\)
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Can someone tell me the answer to this please?????
Answers
Answer:
A
Step-by-step explanation:
The triangle NLM has corresponding angles with triangle LND
HELP WHOEVER IS GOOD AT ALGEBRA
Create a polynomial function that
- 6th, 7th, 8th, OR 9th-degree polynomial.
- It has at least two x-intercepts with different multiplicities.
- It has imaginary zeros.
- It has a negative y-intercept.
Answers
f(x)= x^3-6x^2-16x
=x(x-8) (x+2)
zeros : 0,8,-2
The graph of a quadratic function with vertex (1,-1) is shown in the figure below. Find the domain and the range. Write your answers as inequalities, using or as appropriate. Or, you may instead click on "Empty set" or "All reals" as the answer.
Answers
The domain of the function is all real numbers and range is y ≥ -1.
Since the vertex is at (1,-1), the axis of symmetry is x = 1.
This means that the domain of the function is all real numbers.
To find the range, we need to consider the y-values of the graph. Since the vertex is the lowest point of the graph, the range must be all y-values greater than or equal to -1.
However, since the parabola opens upwards, there is no upper bound on the y-values.
Therefore, the range is given by y ≥ -1.
Hence, the domain of the function is all real numbers and range is y ≥ -1.
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Which graph represents the system of inequalities?
y+2<5x
y+3x>4
y≥2x
Answers
Answer:
2nd graph above the one you chose
The Zearn Fair charges $1.75 for entrance and $1.05 for each ride. Mr. Sawicki brings $20 with him to the fair. What is the greatest number of rides Mr. Sawicki can go on if he uses $2.50 for food? How much money can Mr. Sawicki spend in total
Answers
Step-by-step explanation:
So
Total money = 20
Entrance fee = 1.75
Food = 2.50
Ride = 1.05
Amount spend = 1.75 + 2.05 = 3.8
Left for rides = 20 - 3.8 = 16.2
So rides = 16.2 ÷ 1.05 = 15
I think atleast 15 rides
Medical researchers have determined that for exercise to be beneficial, a person’s desirable heart rate, r, in beats per minute, can be approximated by the formulas r = 143 minus 0.65 a for women r = 165 minus 0.75 a for men, where a represents the person’s age. if the desirable heart rate for a man is 135 beats per minute, how old is he? a. 22.5 years old b. 40 years old c. 45 years old d. 42.5 years old
Answers
Age will be 40 years old.
R, in beats per minute, can be approximated by the formulas, where a represents the person's age.
where R= 143 - 0.65a for women.... (1)
and R= 165 - 0.75a for men,..... (2)
So by implementing these two equation we get a = 40
If the sum of ages is X and Y, and the ratio of their ages is p:q, then the age of Y can be calculated using the formula shown below: Y's age = Y's ratio/Sum of ratios x sum of ages The age dependency ratio is the ratio of dependents (people under the age of 15 or over the age of 64) to the working-age population (people between the ages of 15 and 64). The proportion of dependents per 100 working-age population is shown in the data.
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A car can travel 33 mi for each gallon of gasoline. The function d(x)=33x represents the distance d(x), in miles, that the car can travel with x gallons of gasoline. The car's fuel tank holds 17 gal
Answers
write the percent and the decimal shown by the model
percent: __ %
decimal: __
please please please help meee :>
Answers
The percentage represented is 72%, and the decimal is 0.72
How to write the percent and the decimal?
First lets find the decimal, it will be equal to the quotient between the total number of shaded squares and the total number of squares.
There are 200 squares in total, and of these 200, there are 144 shaded ones, then the decimal is:
d = 144/200 = 0.72
To find the percentage, you only need to multiply the decimal by 100%, we will get:
p = 100%*0.72 = 72%
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Mr. beasley 's science class wants to decorate one wall in the classroom like an underwater scene. They use sheets of blue poster board that are 2 feet long and 2 feet wide. How many sheets of blue poster board are used to cover the entire area of the wall? use math words and symbols to explain how you solve
Answers
Answer:
Area of the sheet = 2×2 = 4 feet2
Step-by-step explanation:
Factorise fully 18g - 15
Answers
Answer:
3(6g - 5)
Step-by-step explanation:
1. First, find the GCF of 15 and 18.
Factors of 15:
1, 3, 5, 15
Factors of 18:
1, 2, 3, 6, 9, 18
The GCF of 15 and 18 is 3.
2. Factorize
3(6g - 5)
3. Check you answer:
3(6g) + 3(-5)
18g - 15
Hope this helps!
what is the volume of a triangular pyramid that is 5 feet tall and has a base area of 9 square feet
Answers
The volume of the triangular prism as described is; 15 cubic foot.
What is the volume of the triangular pyramid?A triangular pyramid simply refers to any geometric solid with a triangular base, and all three lateral faces are also triangles with a common vertex
It follows from the formula for calculating the volume of a triangular prism that;
Volume = (1/3) × base area × height.
Consequently,
volume of the prism is; = (1/3) ×9 × 5
Volume = 15 cubic foot
Therefore, volume of the triangular prism as described is; 15 cubic foot.
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Write each phrase or sentence as an algebraic expression or equation
6 more than y
3 times a number
5 less than the product of 10 and c
14 more than 6 times t
The sum of x and y is 18
A number minus 12 is y
Answers
6 more than y :
y + 63 times a number:
x ← a number
3x5 less than the product of 10 and c :
10c ← the product of 10 and c
10c - 514 more than 6 times t :
6t ← six times t
6t + 14The sum of x and y is 18:
x+y ← the sum of x and y
x + y = 18A number minus 12 is y:
x - a number
x - 12 = yfind the area of the shaded region!
please solve this with solutions !ASAP
Answers
the area of the shaded part is 30. 89 cm²
How to determine the area
We have the shape to be a rectangle
The area of the shaded part should be;
Area of rectangle - 2 ( area of a semi circle)
The formula for area of a rectangle
Area = length × width
Area = 12 × 12
Area = 144 cm²
Area of a semicircle = 1/2 πr²
Area = 1/ 2 × 3. 142 × 6²
Area = 56. 56 cm²
Area of shaded part = area of rectangle - 2( area of semicircle)
Area of shaded part = 144 - 2(56. 56)
Area of shaded part = 144 - 113. 11
Area of shaded part = 30. 89 cm²
Thus, the area of the shaded part is 30. 89 cm²
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CAN YOU GUYS PLEASE ANSWER THE QUESTION RIGHT FOR ONCE
Answers
Answer:
Step-by-step explanation:
1000*PI*4/3
4000/3*PI
1333.3 (3 REPEATING)*PI
4186.6 (6 REPEATING)
BRAINLIEST PLSSSSSSSSSSSSS
Answer:
4186.67
Step-by-step explanation:
volume of sphere = 4πr³/3
4 × 3.14 × 10 × 10 × 10 ÷ 3 = 4186.67cm³
O Assignment is
eBookwork
Consider the conjecture, "Any number divisible by 2 is also divisible by 4." Is each of the numbers 12, 19, 22, 28, and 30 a counterexample of the conjecture?
Complete the following table.
Answers
Please find attached a diagram with the completed table
In order to determine which number is a counterexample of the conjecture, we are to divide each number by 2 and 4. A counterexample of this conjecture would only be divisible by either 2 or 4 but not both of them
Dividing the numbers by 2
12 / 2 = 6
19 / 2 = 9.5
22 / 2 = 11
28 / 2 = 14
30 / 2 = 15
Dividing the numbers by 4
12 / 4 = 3
19 / 4 = 4.75
22 / 4 = 5.5
28 / 4 = 7
30 / 4 = 7.5
22 and 30 are counterexamples because they are divisible by 2 but not by 4
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If f(1) = 12, f ' is continuous, and 7 f '(x) dx 1 = 20, what is the value of f(7)? f(7) =
Answers
The value of function f(7) is approximately 14.857.
To find the value of f(7), we can use the information given about f(1), the continuity of f', and the definite integral involving f'.
Let's go step by step:
1. We are given that f(1) = 12. This means that the value of the function f(x) at x = 1 is 12.
2. We are also given that f' is continuous. This implies that f'(x) is continuous for all x in the domain of f'.
3. The definite integral 7 ∫ f'(x) dx from 1 to 7 is equal to 20. This means that the integral of f'(x) over the interval from x = 1 to x = 7 is equal to 20.
Using the Fundamental Theorem of Calculus, we can relate the definite integral to the original function f(x):
∫ f'(x) dx = f(x) + C,
where C is the constant of integration.
Substituting the given information into the equation, we have:
7 ∫ f'(x) dx = 20,
which can be rewritten as:
7 [f(x)] from 1 to 7 = 20.
Now, let's evaluate the definite integral:
7 [f(7) - f(1)] = 20.
Since we know f(1) = 12, we can substitute this value into the equation:
7 [f(7) - 12] = 20.
Expanding the equation:
7f(7) - 84 = 20.
Moving the constant term to the other side:
7f(7) = 20 + 84 = 104.
Finally, divide both sides of the equation by 7:
f(7) = 104/7 = 14.857 (approximately).
Therefore, f(7) has a value of around 14.857.
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