I need help finding the values of the last boxes shown in the image.
The region R is bounded by the x-axis, the straight line in the graph and the vertical line x+2.
Answers
The volume of the region R bounded by the x-axis is: [tex]\mathbf{\iint_R(x^2+y^2)dA = \int ^{tan^{-1}(4)}_{0} \int^{\frac{2}{cos \theta}}_{0} \ r^3 dr d\theta}[/tex]
What is the volume of the solid revolution on the X-axis?The volume of a solid is the degree of space occupied by a solid object. If the axis of revolution is the planar region's border and the cross-sections are parallel to the line of revolution, we may use the polar coordinate approach to calculate the volume of the solid.
In the graph, the given straight line passes through two points (0,0) and (2,8).
Therefore, the equation of the straight line becomes:
[tex]\mathbf{y-y_1 = \dfrac{y_2-y_1}{x_2-x_1}(x-x_1)}[/tex]
where:
(x₁, y₁) and (x₂, y₂) are two points on the straight lineThus, from the graph let assign (x₁, y₁) = (0, 0) and (x₂, y₂) = (2, 8), we have:
[tex]\mathbf{y-0 = \dfrac{8-0}{2-0}(x-0)}[/tex]
y = 4x
Now, our region bounded by the three lines are:
y = 0 x = 2y = 4xSimilarly, the change in polar coordinates is:
x = rcosθ, y = rsinθwhere;
x² + y² = r² and dA = rdrdθNow
rsinθ = 0 i.e. r = 0 or θ = 0rcosθ = 2 i.e. r = 2/cosθrsinθ = 4(rcosθ) ⇒ tan θ = 4; θ = tan⁻¹ (4)⇒ r = 0 to r = 2/cosθ θ = 0 to θ = tan⁻¹ (4)Then:
[tex]\mathbf{\iint_R(x^2+y^2)dA = \int ^{tan^{-1}(4)}_{0} \int^{\frac{2}{cos \theta}}_{0} \ r^2 (rdr d\theta )}[/tex]
[tex]\mathbf{\iint_R(x^2+y^2)dA = \int ^{tan^{-1}(4)}_{0} \int^{\frac{2}{cos \theta}}_{0} \ r^3 dr d\theta}[/tex]
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Related Questions
Connor leaves Omaha heading directly east at a rate of 32 miles per hour.
One hour later, Jason leaves from Omaha heading in the same direction at a rate of 50 miles per hour.
How long, in hours, after Jason leaves does Jason catch up with Connor?
Round your answer to the nearest hundredths place if necessary.
Answers
Answer:
1.02 miles
Step-by-step explanation:
What is 2/3 by 4/5 in fraction
Answers
Answer: If you mean to multiply, the answer is 8/15.
Step-by-step explanation:
Multiply numerator by numerator and denominator by denominator.
2 x 4 = 8
3 x 5 = 15
ANSWER: 8/15
Find the length of the following curve. If you have a grapher, you may want to graph the curve to see what it looks like.
y=1/27((9x^2)+(6))^3/2 ,from x=3 to x=6
Answers
The length of the curve [tex]y = \frac{1}{27}(9x^2 + 6)^\frac 32[/tex] from x = 3 to x = 6 is 192 units
How to determine the length of the curve?The curve is given as:
[tex]y = \frac{1}{27}(9x^2 + 6)^\frac 32[/tex] from x = 3 to x = 6
Start by differentiating the curve function
[tex]y' = \frac 32 * \frac{1}{27}(9x^2 + 6)^\frac 12 * 18x[/tex]
Evaluate
[tex]y' = x(9x^2 + 6)^\frac 12[/tex]
The length of the curve is calculated using:
[tex]L =\int\limits^a_b {\sqrt{1 + y'^2}} \, dx[/tex]
This gives
[tex]L =\int\limits^6_3 {\sqrt{1 + [x(9x^2 + 6)^\frac 12]^2}\ dx[/tex]
Expand
[tex]L =\int\limits^6_3 {\sqrt{1 + x^2(9x^2 + 6)}\ dx[/tex]
This gives
[tex]L =\int\limits^6_3 {\sqrt{9x^4 + 6x^2 + 1}\ dx[/tex]
Express as a perfect square
[tex]L =\int\limits^6_3 {\sqrt{(3x^2 + 1)^2}\ dx[/tex]
Evaluate the exponent
[tex]L =\int\limits^6_3 {3x^2 + 1} \ dx[/tex]
Differentiate
[tex]L = x^3 + x|\limits^6_3[/tex]
Expand
L = (6³ + 6) - (3³ + 3)
Evaluate
L = 192
Hence, the length of the curve is 192 units
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A polynomial function h(x) with integer coefficients has a leading coefficient of 20 and a constant term of 1. According to the Rational Root Theorem, which of the following are possible roots of h(x) ?
Answers
Plus c
The graph shows China’s workforce from 2000 to 2019. A graph titled Percentage of Workers in Economic Sectors in China from 2000 to 2010 has year on the x-axis and percentage of workers on the y-axis, from 0 to 60 in increments of 10. Agriculture starts at 50 percent in 2000 and then decreases gradually to 37 percent in 2010. Industry starts at 23 percent and then slowly increases to 30 percent. Services starts at 29 percent and then slowly increases to 35 percent. Based on this graph, globalization has affected China’s workforce by creating a shift toward specialization in agriculture and away from services. services and away from agriculture. industry and away from services. agriculture, services, and industry.
Answers
Based on the graph, globalization affected China's workforce by creating a shift toward specialization in: B. services and away from agriculture.
What is globalization?Globalization is a strategic process that involves the integration of various markets across the world, in order to enhance and foster the continuous buying and selling of different goods and services between them.
This ultimately implies that, globalization helps in the creation of new forms of the following systems:
TransportationCommunicationTechnologyAgricultureBased on the given graph, we can logically deduce that globalization affected China's workforce by creating a shift toward specialization in services (increased from 29% to 35%) and away from agriculture (decreased from 50% to 37%).
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Answer:
B. services away from agriculture
Step-by-step explanation:
Which equation is quadratic in form?
Answers
A quadratic equation is written in the form [tex]ax^{2} + bx + c = 0[/tex]
Looking at the second, third, and fourth options, we see that the highest powers are greater than two, which automatically disqualifies them from being quadratics (since the highest power in a quadratic is 2).
This makes the first option the correct choice since the expansion of the equation gives [tex]2x^{2} + 28x + 61[/tex]
Answer:
a
Step-by-step explanation:
HELP QUICK!!!! NOW!!!!
Answers
Answer: B. 2,448π units³
Step-by-step explanation:
We will use the formula for the volume of a cylinder to solve.
(The formula, put simplify, finds the area of the base circle and multiples by the height.)
V = πr²h
V = π(12)²(17)
V = (144)(17)π
V = 2,448π
The volume is 2,448π units³ which is option B for your problem.
Solution :
We have been provided with the height and radius and we need to calculate the volume of cylinder. So we would be using it's formula :
V = πr²hHere,
r is radius h is heightWe have :
height (h) = 17 radius (r) = 12Substituting the value :
>> V = π (12)² (17)
>> V = π (12 × 12) (17)
>> V = π × 144 × 17
>> V = π × 2448
>> V = 2448 π
Therefore :
Option B is correct.2a - (a + 3) I need Answers
Answers
Answer:
a-3
Step-by-step explanation:
[tex]2a-(a+3)\\= 2a - a - 3\\= a - 3[/tex]
Answer:
a-3
Step-by-step explanation:
2a - (a+3)
removing bracket
2a -a-3
a-3
final answer
a-3How do you account for current liabilities and long-term debt?
Answers
The current portion of the long term liabilities are included in Current Liabilities.
What are long term liabilities ?Long term liabilities are monetary obligations of a company that has to pay after an year.
Current Liabilities are those liabilities which have top be paid in the present financial year .
It includes the short term borrowings , accounts payable , expenses , notes payable etc.
The current portion of the long term liabilities are included in Current Liabilities.
Like the interest of a long term loan of this year is a long term liability in the current year.
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4. Give 5 possible solutions to the equation: y = -2x + 5
X
Y
Answers
Answer:
(0, 5), (1, 3), (2, 1), (3, -1), (4, -3)
Step-by-step explanation:
To find the possible solutions, we just plug in a random value for x and then solve for y. When x - 0, y = 5. When x = 1, y = 3. We just continue doing this until we have 5 different solutions.
BIY
74
6+
84
3
-2 -1
D'
B
1
Which rule represents the translation from the pre-
image, ABCD, to the image, A'B'C'D'?
T₁-2(x, y)
OT₁,2(x, y)
T-2, 1(x, y)
OT2 1(x, y)
Answers
Answer:d
Step-by-step explanation:
The translation from the pre-image, Parallelogram ABCD, to the image, Parallelogram A'B'C'D' is T2, 1(x, y)
What is Graph?Graph is a mathematical representation of a network and it describes the relationship between lines and points.
The parallelogram ABCD is shifted to the right by 2 units and shifted up by 1 unit to get parallelogram A'B'C'D'.
Graph transformation is the process by which a graph is modified to give a variation of the proceeding graph.
The graphs can be translated or moved about the xy-plane.
This transformation rule is represented as:
(x,y) -> (x + 2,y + 1)
This transformation rule can be rewritten as:
T2, 1(x, y)
Hence, the translation from the pre-image, Parallelogram ABCD, to the image, Parallelogram A'B'C'D' is T2, 1(x, y)
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ANSWER QUICK PLSSSS AND MAKE SURE YOUR ANSWER IS CORRECT!!
Which of the following algebraic expressions can be used to express the statement "three less than z squared?" (5 points)
z2 − 3
3 − z2
3 − 2z
2z − 3
Answers
f(x)= 3x + 4 + 2
g(x) = 4
Find (f + g)(x).
A. (f+g)(x) = |3x + 4| +6
B. (f+g)(x) = |3x + 6 + 4
O c. (f+g)(x) = |3x + 10||
D. (f+g)(x) = |3x| + 10
Answers
Answer:
3x + 4 + 2
7x + 2
9x
9x + 4
13x
Step-by-step explanation:
3x add 4 and 2
7x add 2
answer question below.
Answers
The speed of the Elvira is 6.545 miles per hour. Then the speed of the Altheia will be 0.545 miles per hour.
What is speed?The distance covered by the particle or the body in an hour is called speed. It is a scalar quantity. It is the ratio of distance to time.
We know that the speed formula
Speed = Distance/Time
Let the speed of the Elvira be x. Then the speed of the Altheia will be (x - 6).
Let the distance between the coffee shop and Elvira's house be d.
Then the distance between the coffee shop and Altheia's house will be (3.6 - d).
Then we have
x = d / 0.5 ...1
(x - 6) = (3.6 - d) / 0.6 ...2
In solving the equations 1 and 2, we have
x = 6.545 and d = 3.2725 miles
Then the speed of the Elvira is 6.545 miles per hour. Then the speed of the Altheia will be 0.545 miles per hour.
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Answer me pleaseeee..... prime numbers between 1 to 10 ?
Answers
Answer:
2, 3, 5, 7
Step-by-step explanation:
prime numbers between 1 to 10 are 2,3,5,7. it's very easy. 1 is not prime number because it behave as both prime and composite.
which situation representd 24÷6
Answers
Answer:
= 4
Step-by-step explanation:
24÷6
= 4
Admission to a baseball game is $3.00 for general admission and $5.50 for reserved seats. The receipts were $3277.50 for 845 paid admissions. How many of each ticket were sold?
Answers
Answer:
548, 297
Step-by-step explanation:
We can set this up as a system of equations. The first equation is for how many tickets were sold, which is x+y=845. The second equation is for the cost of the tickets, which is 3x+5.5y=3277.50. The best method for this problem (other than graphing) is elimination. First, we need to multiply one equation to get the opposite of one of the variables. The easiest one to do for this problem is x. The opposite of 3 is -3, so we have to multiply ALL of the first equation by -3. If you do this, then you get -3x-3y=-2535. Now, combine the equations:
3x + 5.5y = 3277.50
-3x -3y = -2535
________________
0x+2.5y=742.5
Now, isolate y by dividing both sides by 2.5. If you do this, you get y=297. Now, plug this in for the y in the first equation. Isolate x.
x+297=845
-297 -297
__________
0 548
x=548
Hope this helps!
Polygons: Mastery lest
?
What is the distance between C(4, 5) and
D(4,-5)?
5 units
08 units
O 10 units
Answers
Answer:
10 [units].
Step-by-step explanation:
1) the x-coordinates have the same value, then
2) the required distance can be calculated as distance between '-5' and '5':
5--5=10 [units].
Choose the words to finish the sentence. Euler’s Formula states that the of the number of faces and the number of in a polyhedron is equivalent to two more than the number of its .
Answers
Answer:
see explanation
Step-by-step explanation:
Euler's formula states that the sum of the number of faces (F) and the number of vertices (V) of a polyhedra is equivalent to two more than the number of its edges (E) , that is
F + V = E + 2
Kevin works at a restaurant. He stacks glasses as shown. Let x be the number of glasses and f(x) be the height of the stack. If 5.5 inch glasses with 1.2 inch lips are stacked vertically, which table correctly models this situation?
Answers
The table that correctly models the linear equation is table A.
Which table correctly models this situation?
The first glass added will have a height of 5.5 inches, and then for each glass that we add, we are adding a height of 1.2 inches.
This means that the first value on the table must be 5.5 in.The second value must be 5.5 in + 1.2in = 6.7 in.The third value must be: 6.7in + 1.2in = 7.9 inAnd so on, so we have the linear relation:
y = 5.5in + x*1.2in
Where x is the number of glasses in the tower.
Then the table that correctly models this situation is table A.
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Answer:
the one with 5.5, 6.7 etc
Step-by-step explanation:
no
find the radius of a circle whose arc length is 55 m and its central angle measure if 5 radians
Answers
Answer:
Step-by-step explanation:
To solve this question, we can use the formula [tex]S=\theta r[/tex], where [tex]S[/tex] is the arc length, [tex]\theta[/tex] is the central angle of the sector in radians, and [tex]r[/tex] is the radius.
In this situation, we know that [tex]S=55[/tex] and [tex]\theta=5[/tex]
This means that [tex]55=5r \longrightarrow \boxed{r=11}[/tex]
David has 30 sweets. He gives Sarah of his sweets and Joe 20% of his
sweets. How many sweets does David have left?
Answers
Answer:
24
Step-by-step explanation:
20 percent of 30 is 6
30-6=24
therefore david has 24 sweets left
8. What is the volume of the pyramid?
PLS GELP
Answers
Then 8*8 equals 64
The volume of the given pyramid is 64 cubic inches.
What is the volume of the pyramid?The volume of the pyramid is the product of one-third of the height and square of the base side length.
The volume of Pyramid A = (1/3)(side²)(height)
The volume of a square pyramid is equal to one-third of the product of the base’s area and the pyramid’s height. The formula is:
V = (1/3) × a² × h
where a is the length of the square base, and h is the height (or altitude).
We are given that;
h = 3 inch, a = 8 inch, and hypotenuse = 5 inch,
Now, we can plug in the values into the formula and get:
V = (1/3) × 8² × 3
V = (1/3) × 64 × 3
V= (64 x 3)/3
V = 64 inch³
Therefore, by the given data the volume of the pyramid will be 64 cubic inches.
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Which quadratic function in vertex form has a vertex at (3, 4) and passes through the point (7,-4)
Answers
Answer:
First option
Step-by-step explanation:
Given the following question:
We are being asked to find the quadratic function that has a vertex of (3, 4) and passes through the point (7, -4). Remember that the vertex of any parabola is the point on the top of the parabola, directly in the middle of the top of the function.
First option:
[tex]y=-\frac{1}{2} (x-3)^2+4[/tex]
(see photo below)
As you can see the function has a vertex of (3, 4) which means the point on the top of the parabola is (3, 4) or the vertex. It also passes through the point (7, -4) meaning the first option is your answer.
Hope this helps.
twice a number added to 13 is equal to 27 what is the number
Answers
The number is 7. Let's represent the number as "x." According to the given information, "Twice a number added to 13 is equal to 27," which can be expressed as an equation.
2x + 13 = 27
Now, solve the equation for "x":
Subtract 13 from both sides:
2x = 27 - 13
2x = 14
Divide both sides by 2:
x = 14 / 2
x = 7
Therefore, the number is 7.
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a web adminitrator is interested in the average number of visitors per day that her website receives. Match the vocab word with its corresponding example'
Answers
The correct matching of the vocabulary words and the examples given of the web administrator's process are:
Population - All the days that the website has been in existence.Statistic - The average number of visitors per day for the 42 days that the administrator tracked.Sample - The 42 randomly selected days that the administrator tracked.Variable - The number of visitors that the website receives on a given day.Data - The list of visitor counts for the 42 days that were tracked. Parameter - The average number of visitors per day that have come to the website since it was created.What metrics are used by the website administrator?The entire population being looked at would best be all the days that the website has existed and the sample will be some selected days that have been tracked.
Parameters can be created such as the average number of visitors per say and then data would be derived on this. A statistic would simple show certain information such as the average visits in the days tracked.
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a) The scale of a map is 1:20 000. What distance in metres does 4cm on the map represent?
Answers
Answer:
80 000
Step-by-step explanation:
1 cm : 20 000 (The question does not state the unit of the other half)
So
4 cm : 4×20 000
4 cm : 80 000
I'm not sure about units but hope this helped and brainliest please
Answer:
80 000 meters
Step-by-step explanation:
In the map:
1 cm = 20000 m
4 cm = 4(20000) = 80 000 meters
4 cm on the map represents 80 km in reality.
Hope this helps
Chords AC and DB intersect at point E. Select all pairs of angles that must be congruent.
Answers
∠ADE and ∠ACB, ∠DEA and ∠CEB, ∠CAD and ∠CBD are pairs of angles that must be congruent.
What are congruent angles?Congruent angles are said to be angles that have equal measure.
From the figure, we can see that;
∠ADE and ∠ACB are congruent because they are corresponding angles, corresponding angles are equal.
∠DEA and ∠CEB are congruent because they are corresponding angles
∠CAD and ∠CBD are also congruent because they are corresponding angles
Therefore, ∠ADE and ∠ACB, ∠DEA and ∠CEB, ∠CAD and ∠CBD are pairs of angles that must be congruent.
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a)1 year into second
Answers
Answer:
31536000 seconds in a year
Step-by-step explanation:
there are 365 days in a year, 24 hours in a day, 60 minutes in an hour, and 60 seconds in each minute. you have to multiply all of them
find the product of
2a(a+b)
3xy(2x-3y)
Answers
Answer:
2a² + 2ab , 6x²y - 9xy²
Step-by-step explanation:
using the distributive property
a(b + c) = ab + ac
given
2a(a + b) ← multiply each term in the parenthesis by 2a
= 2a² + 2ab
given
3xy(2x - 3y) ← multiply each term in the parenthesis by 3xy
= 6x²y - 9xy²
Answer:
6x2-9x2
Step-by-step explanation:
because I don't know the explanation