The value of the given triple integral is \(539\pi\).
The triple integral is a mathematical tool used to compute the volume of a solid region in three-dimensional space. It is a generalization of the concept of the double integral in two-dimensional space. To evaluate the triple integral \($\iiint\limits_E (11 - 22z) r dV$\) over the region E given by \($1\leq z\leq 4$\), \($x^2+y^2\leq 49$\), and \($-5\leq y\leq -2$\) in cylindrical coordinates, we have:
\(\begin\iiint\limits_E (11 - 22z) r , dV &= \int_{\theta=0}^{2\pi}\int_{r=0}^{7}\int_{z=1}^{4} (11-22z) r\cdot z , dz, dr, d\theta\qquad (\because \text{cylindrical coordinates})\\\&=\int_{\theta=0}^{2\pi}\int_{r=0}^{7}\left(\int_{z=1}^{4} (11-22z) r\cdot z , dz\right), dr, d\theta\\end\)
\(&=\int_{\theta=0}^{2\pi}\int_{r=0}^{7} \left[\dfrac{11}{2}z^2 - 11z^3\right]{z=1}^{z=4} \cdot r dr d\theta\\\&=\int{\theta=0}^{2\pi}\int_{r=0}^{7} (22r) dr d\theta\\\&=\int_{\theta=0}^{2\pi} \left[\dfrac{11}{2}r^2\right]_{r=0}^{r=7} d\theta\\\&=\int_{\theta=0}^{2\pi} \dfrac{539}{2} d\theta\\\)
Therefore, the value of the given triple integral is \(539\pi\).
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--The complete question is, Evaluate the triple integral ∫∫∫ (11 - 22z) r dV over the region E given by 1 ≤ z ≤ 4, x^2 + y^2 ≤ 49, and -5 ≤ y ≤ -2 in cylindrical coordinates. The integrand is multiplied by the z-component of the standard unit vector SIS_ in cylindrical coordinates.--
PLz help
how would you represent this situation( Write the equation or inequality.)
On a carnival ride you must be at least 42 inches tall to ride
Answer:
x≥k y for you y≥42 inches tall
Step-by-step explanation:
can i have brainliest if right
(7xy-8yz+3x)-(4x-8yz)
Answer:
7xy-8yz+3x-4x+8yz
7xy-8yz+8yz+3x-4x
7xy-x
Step-by-step explanation:
The quastion is on graph theory, matching.
Let A and B each be sets of N labeled vertices, and consider bipartite graphs between A and B.
Consider taking |E| =aN, i.e., the total number of edges is proportional to the number of vertices. This is a relatively sparse number of edges, given the total number of edges that can exist between A and B.
6) Show that taking |E| = 3/N, the expected number of matchings goes to 0 as N › [infinity]. (5 points)
7) Show that taking |E| = 4.V, the expected number of matchings goes to infinity as N › [infinity]. (5 points)
The expected number of matchings goes to infinity as N › [infinity].
Matching in Graph Theory:A matching in Graph Theory is a set of edges of a graph where no two edges share a common vertex. In other words, a matching is a set of independent edges of a graph. A perfect matching in a Graph Theory is a matching of size equal to half the number of vertices in a graph.The expected number of matchings goes to 0 as N › [infinity]:The expected number of matchings goes to zero as N › [infinity] when |E| = 3/N. It is because 3/N is a relatively dense number of edges that are independent of the number of vertices that can exist between A and B. The expected number of matchings is thus very small in comparison to the total number of matchings possible as N › [infinity].The expected number of matchings goes to infinity as N › [infinity]:The expected number of matchings goes to infinity as N › [infinity] when |E| = 4.V. It is because 4.V is a relatively large number of edges that are independent of the number of vertices that can exist between A and B. The expected number of matchings is thus very large in comparison to the total number of matchings possible as N › [infinity]. Hence the expected number of matchings goes to infinity as N › [infinity].
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4. If you want to save your total contribution for all 4 years before you start attending college,
how much do you need to save each month if you have 4 years to accomplish your goal?
You need to save $62.06 each month for four years to achieve your total contribution goal before starting college.
First, 5% of the total cost for four years.
= 0.05 x ($14,895.00/yr x 4 years)
= 0.05 x $59,580.00
= $2,979.00
Second, Divide the total amount you need to pay over four years by the number of years.
= $2,979.00 / 4
= $744.75
Therefore, you need to pay $744.75 for each year of attending college.
Now, the total contribution goal.
= Amount to pay each year x 4 years
= $744.75 x 4
= $2,979.00
and, Monthly savings required
= Total contribution goal / 48 months
= $2,979.00 / 48
= $62.06
Therefore, you need to save $62.06 each month for four years to achieve your total contribution goal before starting college.
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find ta , the tension in string a. express the tension in string a in terms of g , m1 , l , d , m2 , and x .
The expression for tension in the string is T = [(L/2)×(m1×g) + (x)×(m2×g)]/d.
We are a diagram that shows two blocks with masses m1 and m2.There are two strings, A and B. Everything is in equilibrium. Equilibrium is a condition of rest or balance caused by opposing forces acting equally. We need to find the tension in string A. Let the tension in the strings A and B be denoted by the variables "Ta" and "Tb", respectively. The net torque at point B must be zero as everything is in equilibrium. The diagram is attached below.
Στ(B) = 0
τ(a) + τ(b) + τ(m1) + τ(m2) = 0
τ = r×F×sin(θ)
d×(Ta)×sin(90°) + 0 - (L/2)×(m1×g)×sin(90°) - (x)×(m2×g)×sin(90°) = 0
d×(Ta) - (L/2)×(m1×g) - (x)×(m2×g) = 0
Ta = [(L/2)×(m1×g) + (x)×(m2×g)]/d
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prove that if m n and n p are even integers, where m, n, and p are integers, then m p is even. what kind of proof did you use?
If m, n, and p are integers, and both m n and n p are even, then m p is even.
Does the product of two even integers result in an even integer?In order to prove the given statement, we need to show that if both m n and n p are even integers, then m p must also be even.
Let's assume that m, n, and p are integers, and m n and n p are both even. By definition, an even number can be expressed as 2k, where k is an integer.
Since m n is even, we can write it as 2a for some integer a. Similarly, n p can be expressed as 2b for some integer b.
Now, let's consider the product m p. We can express it as (2a)(2b), which simplifies to 4ab. Since 4 is divisible by 2, we can rewrite 4ab as 2(2ab), where 2ab is an integer.
Therefore, we have shown that m p can be expressed as 2 times an integer (2ab), which means m p is even.
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can anyone help me with this?
What is 11/2 divided by 3/4
Answer:
2 and 14/15
Step-by-step explanation:
4. (8 points) Use the Taylor series of cos (x) to find the following limit limx→0 2cosx−2+x^2/x^4 Do NOT use L'Hospital Rule
The limit is undefined or diverges to infinity.
To find the limit without using L'Hôpital's Rule, we can use the Taylor series expansion of cos(x) centered at x = 0. The Taylor series expansion of cos(x) is given by:
cos(x) = 1 - (x^2)/2 + (x^4)/24 - (x^6)/720 + ...
We can substitute this expansion into the given limit:
lim(x→0) [(2cos(x) - 2 + x^2) / x^4]
Using the Taylor series expansion of cos(x):
lim(x→0) [(2(1 - (x^2)/2 + (x^4)/24 - ...) - 2 + x^2) / x^4]
Simplifying:
lim(x→0) [(2 - x^2 + (x^4)/12 - ...) / x^4]
Taking the limit as x approaches 0:
lim(x→0) [(2 - 0^2 + (0^4)/12 - ...) / 0^4]
lim(x→0) [2 / 0^4]
As the denominator approaches 0, the limit tends to infinity. Therefore, the limit is undefined or diverges to infinity.
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A researcher interviews 6 widows about their marriages and notices how many cats are wandering around. Is there a significant relationship between the number of times an old widow was married and the number of cats the old lady owns? ( You don't need to do the math to calculate it - the Pearson r is given).
Times Married: 1 1 2 2 3 3
Cats Owned: 3 2 4 5 5 6
Pearson r = +.91
Write up the conclusion for this study in APA format and be sure to include the r2.
There is a significant relationship between the number of cats she owns and the number of times an old widow was married (r = +0.91, p < 0.05, r² = 0.82).
Given, the Pearson correlation coefficient of +0.91,
There appears to be a strong +ve correlation between the number of cats she owns and the number of times an old widow was married.
It suggests that the more times a widow was married,the more cats she tends to own.
Approximately 82% of the variance in the number of cats owned can be explained by the number of times a widow was married is indicated by the coefficient of determination (r²).
Hence, we can say that there is a significant relationship between the number of cats she owns and the number of times an old widow was married (r = +0.91, p < 0.05, r² = 0.82).
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NEED HELP!! THX! please answer part b, I already have part a.
Answer:
See below ~
Step-by-step explanation:
3.25% is the interest rate, meaning it won't be constant, but a coefficient of the function$15,000 is a constant as the interest gets added to itThe function can be written as :
aₙ₊₁ = 0.325aₙ + 15000Help me with this assignment please I don’t understand it
Graph the exponential function.
g(x) = 4/3(2)^x
Find some points
x=0
y=4/3×2⁰y=4/3x=1
y=4/3(2¹)y=8/3x=2
y=4/3(2²)y=16/3Graph attached
Answer:
Given function:
\(g(x)=\dfrac{4}{3}(2)^x\)
To find the y-intercept, input x = 0:
\(\implies g(0)=\dfrac{4}{3}(2)^0\)
\(\implies g(0)=\dfrac{4}{3}\cdot 1\)
\(\implies g(0)=\dfrac{4}{3}\)
End behaviors:
\(\textsf{As }x \rightarrow \infty, g(x) \rightarrow \infty\)
\(\textsf{As } x \rightarrow -\infty, 2^x \rightarrow 0 \implies \textsf{As }x \rightarrow -\infty, g(x) \rightarrow 0\)
Therefore, y = 0 is an asymptote (the curve gets close to but never touches the x-axis).
To help graph accurately (rather than sketch), input other positive values of x as plot points for the curve:
\(\implies g(x)=\dfrac{4}{3}(2)^1=\dfrac{8}{3}\)
\(\implies g(x)=\dfrac{4}{3}(2)^2=\dfrac{16}{3}\)
\(\implies g(x)=\dfrac{4}{3}(2)^3=\dfrac{32}{3}\)
Solve for k.
8
12
7
k
A baby gains 11 pounds in its first year of life. The baby gained 4 and one-fourth pounds during the first four months and 3 and one-halfpounds in its second four months. How much did the baby gain in the last four months?
Answer:
18.75
Step-by-step explanation:
Answer:
The correct answer would be A.) 3 1/4 or 3.25.
Step-by-step explanation:
I just did the test on edge 2020
6.
12(30-12)
3
helpppp
Answer:
648 is your answer
Step-by-step explanation:
hope this helps!!
Answer:
216
Step-by-step explanation:30-12=18 so 18 x 12=216 hope that helped
I WILL GIVE 30 POINTS TO THOSE WHO ANSWER THIS QUESTION RIGHT
Which of the following is an example of dependent events?
tossing a coin twice
tossing a coin and spinning a spinner
drawing one card after the other
Answer:
drawing one card after other is your answer
how many days cut the Morales family rent a car for it if they choose this rental car company with her estimated budget
Answer:
4 days
Step-by-step explanation:
55d+15d=70d
70d+35=315
-35=-35
70d= 280
Divide by 70
X=4
Three friends are traveling to school. Let x represent the number of minutes traveled and y
represent the distance from the school in miles for each representation.
a. Who lives the closest to the school? Explain.
b. Who is traveling the fastest? Explain.
Answer:
christian closest-0.5 is the distance he traveled which is less than 8 and 6
Step-by-step explanation:
Freddie is the fastest because christian travles .1 miles every 2 minutes being the slowest and .8 is greater than .66666
Answer:
a. Christian
b. Freddie
Step-by-step explanation:
a.
y = mx + b
m is the slope. It represents the speed of walking.
b is the y-intercept. It represents the distance from the school at time 0. Time 0 is when a person leaves his home, so the higher b is the farther from the school the person lives.
Freddie: y = -0.8x + 8
b = 8
Freddie lives 8 miles from school.
Christian: (0, 0.5); b = 0.5
Christian lives 0.5 miles from school.
Trevor: (0, 6) from the graph. b = 6; Trevor lives 6 miles from school.
a. Answer: Christian
b.
Each slope is the speed.
Freddie: m = -0.8
Christian: m = (0.4 - 0.5)/(2 - 0) = -0.1/2 = -0.05
Trevor: m = rise/run = -2/3 = -0.666...
The fastest speed is the slope with the highest absolute value.
b. Answer: Freddie
Help me please I am having trouble figuring out the answer. Help me find the ratio.
Answer:
not equivalent to meteorologists ratio
Step-by-step explanation:
meteorologists ratio is
rainy days : sunny days = 2 : 5
last months weather is
rainy days : sunny days
= 10 : 20 ( divide both parts by LCM of 10 )
= 1 : 2 ← not equivalent to 2 : 5
1. What are the 3 conditions for a function to be continuous at xa? 2. the below. Discuss the continuity of function defined by graph 3. Does the functionf(x) = { ***
The three conditions for a function to be continuous at a point x=a are:
a) The function is defined at x=a.
b) The limit of the function as x approaches a exists.
c) The limit of the function as x approaches a is equal to the value of the function at x=a.
The continuity of a function can be analyzed by observing its graph. However, as the graph is not provided, a specific discussion about its continuity cannot be made without further information. It is necessary to examine the behavior of the function around the point in question and determine if the three conditions for continuity are satisfied.
The function f(x) = { *** is not defined in the question. In order to discuss its continuity, the function needs to be provided or described. Without the specific form of the function, it is impossible to analyze its continuity. Different functions can exhibit different behaviors with respect to continuity, so additional information is required to determine whether or not the function is continuous at a particular point or interval.
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∛a² does anyone know it
The equivalent expression of the rational exponent ∛a² is \((a)^{\frac{2}{3}\).
What is a rational exponent?Rational exponents are exponents that are fractions, where the numerator is a power and the denominator is a root.
So rational exponents (fractional exponents) are exponents that are fractions or rational expressions.
To determine the rational exponent equivalent to the expression given, we will apply the power rule of indices as shown below.
The given expression is ;
∛a²
The rational exponent is calculated as follows;
∛a² = \((a)^{\frac{2}{3}\)
Thus, based on exponent power rule, the given expression is equivalent to ∛a² = \((a)^{\frac{2}{3}\)
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The complete question is below:
Find the equivalent expression of the rational exponent ∛a². does anyone know it
Hashem puts boxes into small vans and into large vans.
He puts 5 boxes into each small van.
He puts 25 boxes into each large van.
Hashem puts a total of 400 boxes into the vans so that
number of boxes in small vans: number of boxes in large vans = 3:5
Hashem says that less than 30% of the vans filled with boxes are large vans.
Is Hashem correct?
You must show all your working.
Let's start by using algebra to solve for the number of boxes in small and large vans.
Let x be the number of small vans and y be the number of large vans. Based on the ratio given, we know that:
- Number of boxes in small vans = 3/8 * Total number of boxes
- Number of boxes in large vans = 5/8 * Total number of boxes
Using the information provided, we can write an equation:
5x + 25y = 400
Simplifying, we get:
x + 5y = 80
Now let's use the inequality provided to determine if less than 30% of the vans filled with boxes are large vans. We know that:
- Total number of vans filled with boxes = x + y
- Less than 30% of these vans are large vans, so y/(x+y) < 0.3
Substituting x + 5y = 80, we can simplify the inequality:
y/(x+y) < 0.3
y/80 < 0.3
y < 24
So if y (the number of large vans) is less than 24, then less than 30% of the vans filled with boxes are large vans.
Now we can solve for x and y using substitution. From x + 5y = 80, we get x = 80 - 5y. Substituting into 5x + 25y = 400, we get:
5(80 - 5y) + 25y = 400
400 - 20y = 400
20y = 0
y = 0
This means that y cannot be less than 24, as y = 0 would result in no large vans at all. Therefore, Hashem's statement is incorrect, and the number of large vans must be equal to or greater than 24.
Which answers are equivalent to the ratio 13 to 25?
Select all that apply.
13:25
25/13
25:13
13/25
Please help I'm majorly confused!!
The ratio of 13 to 25 is 13/25 because 13 is a prime number
RatioThe ratio is defined as the comparison of two quantities of the same units that indicates how much of one quantity is present in the other quantity. Ratios can be classified into two types. One is part to part ratio and the other is part to whole ratio. The part-to-part ratio denotes how two distinct entities or groups are related. For example, the ratio of boys to girls in a class is 12: 15, whereas, the part-to-whole ratio denotes the relationship between a specific group to a whole. For example, out of every 10 people, 5 of them like to read books. Therefore, the part to the whole ratio is 5: 10, which means every 5 people from 10 people like to read books.
In this question, we have to find the ratio between 13 to 25
To do this, we simply divide 13 by 25
13÷25 = 13/25
This is so because the two numbers are not divisible as 13 is a prime number.
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what is an equation of the line that passes through the points (0, 7) and (5, 4)
Answer:
y=-3/5x+7
Step-by-step explanation:
m=(y2-y1)/(x2-x1)
m=(4-7)/(5-0)
m=-3/5
y-y1=m(x-x1)
y-7=-3/5(x-0)
y-7=-3/5(x)
y=-3/5x+7
If EF = x2, FG = 5x and EG = 14, find EF.
The drawing is not drawn to scale.
Answer: x2/e
Step-by-step explanation:
The value of a car that depreciates over time can be modeled by the function M(t)=10000(0.9)^3t+2. Write an equivalent function of the form M(t)=ab^t
The equivalent exponential decay function is given as m(t) = 10000\((0.729)^{t}\)
What is an exponential function?
Calculating the exponential growth or decay of a given collection of data is done using an exponential function, which is a mathematical function. Mathematical functions with exponents include exponential functions. f(x) = bx, where b > 0 and b 1, is a fundamental exponential function.
Here, we have
Given: The value of a car that depreciates over time can be modeled by the function M(t) = 10000\((0.9)^{3t}\)
An exponential function is in the form
y = abˣ
where y and x are variables, a is the initial value of y, and b is the multiplier.
Let m(t) represent the value of the car after t years, hence the exponential decay is given by:
m(t) = \(10000(0.9)^{3t}\)
m(t) = 10000\((0.9)^{3(t)}\)
m(t) = 10000\((0.729)^{t}\)
Hence, The equivalent exponential decay function is given as m(t) = 10000\((0.729)^{t}\)
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Given that YZ bisects VW, and VX = 46, find XW
Answer:
XW = 134
Step-by-step explanation:
The fact that YZ bisects VW means that the angles VX and XW are supplementary, that is, they add to 180º. So
VX + XW = 180
We have that VX = 46. So
46 + XW = 180
XW = 134
Which of the following inequalities defines the shaded region of the graph above