The triple integral using these bounds ∫₀^(π/2) ∫₀^(√(9 - z)) ∫₀^(9 - r^2) (r cosθ + r sinθ + z) r dz dr dθ.
To evaluate the triple integral ∭E (x + y + z) dV in cylindrical coordinates, we first need to express the bounds of the integral and the differential volume element in cylindrical form.
The paraboloid z = 9 - x^2 - y^2 can be rewritten as z = 9 - r^2, where r is the radial distance from the z-axis. In cylindrical coordinates, the solid E in the first octant is defined by the conditions 0 ≤ r ≤ √(9 - z) and 0 ≤ θ ≤ π/2, where θ is the angle measured from the positive x-axis.
Now, let's express the differential volume element dV in cylindrical form. In Cartesian coordinates, dV = dx dy dz, but in cylindrical coordinates, we have dV = r dr dθ dz.
Now we can rewrite the triple integral using cylindrical coordinates:
∭E (x + y + z) dV = ∫∫∫E (r cosθ + r sinθ + z) r dr dθ dz.
The bounds of integration are as follows:
For z: 0 ≤ z ≤ 9 - r^2 (from the equation of the paraboloid)
For r: 0 ≤ r ≤ √(9 - z) (within the first octant)
For θ: 0 ≤ θ ≤ π/2 (within the first octant)
We can now evaluate the triple integral using these bounds:
∫∫∫E (r cosθ + r sinθ + z) r dr dθ dz
= ∫₀^(π/2) ∫₀^(√(9 - z)) ∫₀^(9 - r^2) (r cosθ + r sinθ + z) r dz dr dθ.
Performing the integration in the specified order, we can find the numerical value of the triple integral.
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You are a researcher studying the lifespan of a certain species of bacteria. A preliminary sample of 35 bacteria reveals a sample mean of = 66 hours with a standard deviation of 8 = 6.2 hours You would like to estimate the mean lifespan for this species of bacteria to within a margin of error of 0.5 hours at a 98% level of confidence. What sample size should you gather to achieve a 0.5 hour margin of error? Round your answer up to the nearest whole number. n= bacteria
You should gather a sample of at least 29 bacteria to estimate the mean lifespan for this species of bacteria with a margin of error of 0.5 hours at a 98% level of confidence.
We are given a preliminary sample of 35 bacteria with a sample mean of 66 hours and a standard deviation of 6.2 hours. We need to calculate the sample size required to achieve the desired margin of error.
To calculate the sample size, we can use the formula:
n = (Z * σ / E)²
Where:
n is the required sample size
Z is the z-score corresponding to the desired confidence level (98% confidence corresponds to a z-score of 2.33)
σ is the standard deviation of the population
E is the desired margin of error
Plugging in the values, we have:
n = (2.33 * 6.2 / 0.5)²
Calculating the expression within parentheses:
2.33 * 6.2 / 0.5 ≈ 28.84
Rounding up to the nearest whole number, the required sample size is 29 bacteria.
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Sue is 15 years older than Mike. in 5 years mikes’s age will be ½ sue’s age. What is the present age of each?
Show work!!!!
Answer:
5
Step-by-step explanation:
Sue in 5 years would 20, meaning Mike would be 10. Subtract 5 from Mike to get their current age.
Answer:
Mike= 10 years old
Sue= 25 years old
Step-by-step explanation:
Let the present age of Sue be s years old, while that of Mike be m years old.
Present
s= m +15 -----(1)
In 5 years
Sue's age= s +5
Mike's age= m +5
Given that Mike would be ½ of Sue's age in 5 years,
m +5= ½(s +5)
Multiply both sides by 2:
2(m +5)= s +5
Expand:
2m +10= s +5
2m +10 -5= s
s= 2m +5 -----(2)
Substitute (1) into (2):
m +15= 2m +5
2m -m= 15 -5
m= 10
Substitute m= 10 into (1):
s= 10 +15
s= 25
Thus, the present age of Mike is 10 years old and the present age of Sue is 25 years old.
El auto que se va a comprar Pablo necesita que un cambio de aceite cada 60.000km y de neumáticos cada 90.000km. ¿En cuántos kilómetros coincidirá por primera vez el cambio de aceite y de neumáticos?
Answer:
El cambio de aceite y de neumáticos coincidirá por primera vez en 180.000 km.
Step-by-step explanation:
Como tenemos que encontrar cuándo se realizarán los dos cambios al mismo tiempo por primera vez, esto significa que tenemos que encontrar el mínimo común múltiplo de los dos números dado que este es el múltiplo más pequeño que tienen en común esos números y es donde coinciden por primera vez. Para encontrar el mínimo común múltiplo, puedes escribir los múltiplos de cada número y encontrar los que son comunes y seleccionar el más pequeño.
Múltiplos de 60.000= 60.000, 120.000, 180.000, 240.000, 300.000, 360.000, 420.000
Múltiplos de 90.000= 90.000, 180.000, 270.000, 360.000, 450.000, 540.000, 630.000
De acuerdo a esto, el mínimo común múltiplo es 180.000 dado que es el múltiplo más pequeño en el que coinciden y la respuesta es que el cambio de aceite y de neumáticos coincidirá por primera vez en 180.000 km.
The maximum weight of a shipping container is 125 pounds. What is the maximum weight in kilograms?
a. 56.7 kg
b. 62.5 kg
c. 75 kg
d. 100 kg
The maximum weight in kilograms is approximately 56.7 kg. Hence, the correct option is (a) 56.7 kg.
The maximum weight of a shipping container is 125 pounds.
We need to find out what is the maximum weight in kilograms.
Step 1: Find out 1 pound weight in kilograms We know that 1 pound = 0.45359237 kilograms (we already know that)
Step 2: Convert the maximum weight in pounds to kilograms
Maximum weight in pounds = 125 Maximum weight in kilograms
= 125 x 0.45359237
= 56.69904625≈ 56.7 kg
Therefore, the maximum weight in kilograms is approximately 56.7 kg.
Hence, the correct option is (a) 56.7 kg.
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Instructions: Write the equation of the line in Slope-Intercept Form given the information below.
Slope =
-7/4
Y-Intercept = 5
Slope-Intercept Form:
Answer:-8
Step-by-step explanation:
Answer:
y = -7/4x + 5
Step-by-step explanation:
y = mx + b
y = -7/4x + 5
Caleb has a guaranteed minimum salary of $1,200 per month, or 5.5% of his total monthly sales (as commission), whichever is higher. Last month, his total sales were $45,000. What was his gross pay?
Answer: $1,200 + 5.5% + $45,000= 46200.055 or 46200
Step-by-step explanation: All you have to do is just add because if you read the text it has a key word total.
Caleb has a guaranteed minimum salary of $1,200 per month, or 5.5% of his total monthly sales (as commission), whichever is higher. Last month, his total sales were $45,000. What was his gross pay?
f left parenthesis x right parenthesis equals 3 over 4 x squared .
Answer:
Step-by-step explanation: try your best
What is 14 + 6 =
+11
Since, 14 + 6 = 20
Therefore, 14 + 6 = 9 + 11
dont forget to like and mark me
Answer:
31
Step-by-step explanation:
How is 0.00400068 expressed in standard scientific notation?
Answer:
4.00068 × [tex]10^{-3}[/tex]
please and this quickly and no links please
Answer:
11 months
Step-by-step explanation:
Since he has already read 14 books subtract them from the 80 books. you'll end up with 66. then diviid by 6 and you'll get 11 months
What is the value of f(x) = 4x -9
Answer:
i believe its ()=4−9
Step-by-step explanation:
Answer:
f=4x-9
Step-by-step explanation:
f(x) = 4x-9
f(x)= 4x-9
x x
f=4x-9
|13 + 5| – |7 – 10|
PLEASE STEP BY STEP
Answer:
1
Step-by-step explanation:
|13 + 5| – |7 – 10| =1
Answer:
I18I-I-3I
18-3
15
Step-by-step explanation:
Simplify the expression 7 − 1x −1(−5x) − 10 + 4x
Answer: 3x-1(-5x)-3
Step-by-step explanation:
−3-x-1(-5x)+4x
-3+3x-1(-5x)
3x-1(-5x)-3
Let A and B be disjoint compact subspaces of a Hausdorff space X. Show that there exist disjoint open sets U and V, with A⊂U and B⊂V.
In Hausdorff-space "X", if A and B are disjoint "compact-subspaces", then there exist disjoint "open-sets" U and V such that A is contained in U and B is contained in V, because Hausdorff property ensures the existence of disjoint open neighborhoods for any two distinct points.
To prove existence of disjoint "open-sets" U and V with A⊂U and B⊂V, where A and B are "compact-subspaces" (disjoint) of "Hausdorff-space" X, we use the steps:
Step (1) : Since A and B are disjoint compact subspaces, we use the Hausdorff property to find open sets Uₐ and [tex]U_{b}[/tex] such that A⊂Uₐ and B⊂[tex]U_{b}[/tex], and Uₐ∩[tex]U_{b}[/tex] = ∅. This can be done for every pair of points in A and B, respectively, since X is Hausdorff.
Step (2) : Consider the set U = ⋃ Uₐ, where "union" is taken over all of Uₐ for each point in A. U is = union of "open-sets", hence open.
Step (3) : Consider the set V = ⋃ [tex]U_{b}[/tex], where union is taken over for all [tex]U_{b}[/tex] for "every-point" in B. V is also a union of open-sets and so, open.
Step (4) : We claim that U and V are disjoint. Suppose there exists a point x in U∩V. Then x must be in Uₐ for some point a in A and also in [tex]U_{b}[/tex] for some point b in B. Since A and B are disjoint, a and b are different points. However, this contradicts the fact that Uₐ and [tex]U_{b}[/tex] are disjoint open sets.
Therefore, U and V are disjoint open sets with A⊂U and B⊂V.
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you make a one time deposit of 2000 years that earn 5% simple interest. how much interest would you earn in 2 years ?
Answer:
$2205
Step-by-step explanation:
equation set up
2000 (1.05)^2
here is my question.
Answer:
the answer is 18
Step-by-step explanation:
9X6=54
54/3=18
Answer:
18
Step-by-step explanation:
If an argument has a self-contradictory statement as a premise, then the counterexample set of the argument is:
The counterexample set of an argument with a self-contradictory statement as a premise is empty, as there are no valid counterexamples that can be presented to contradict the argument.
If an argument has a self-contradictory statement as a premise, then the counterexample set of the argument is empty, meaning there are no counterexamples that can be provided to disprove the argument. A self-contradictory statement is one that inherently contradicts itself, containing both a proposition and its negation. Since a self-contradictory statement cannot be true, any argument that relies on such a premise is inherently flawed and cannot be logically valid.
In logic, a counterexample is a specific example or case that demonstrates the falsity or invalidity of a general statement or argument. However, when the premise itself is self-contradictory, it is impossible to find a counterexample that would refute the argument because the premise itself is contradictory.
Therefore, the counterexample set of an argument with a self-contradictory statement as a premise is empty, as there are no valid counterexamples that can be presented to contradict the argument.
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What is the area of a regular hexagon with an apothem of 28m in length
Step-by-step explanation:
can you check again the question , seems like something is missing.
How many solutions does the system of linear equations have? Use the drop-down menus to explain your answer.
y = 3/4x + 12
y = 4/3x
The system of linear equations will have
Choose...
no solution
exactly one solution
infanite many solutions
because the slopes of the equations are
Choose...
the same
different
, so the lines will
Choose...
not intersect at all
intercect at one point
both be the same line
Answer:
There is one equation, the slopes are different so they will intersect at one point
Step-by-step explanation:
What is the image of (-10,-8) after a dilation by a scale factor of 1/2 centered at the
origin?
Answer:
(-5, -4)
Step-by-step explanation:
A dilation at the origin would just result with you multiplying the coordinates by the scale factor.
-10 * 1/2 and -8 * 1/2
15 POINTS PLSS HELP THIS IS MY 3RD TIME POSTING THIS BC NO ONE WILL HELP ME PLSSS AND NO WRONG ANSWERS PLS I REALLY NEED HELPP
Answer:
to find the equation of the line you use y=mx+b
Step-by-step explanation:
m means the slope and the b is the y intercept of the line. so in this case the b is 5. the m is 6 so the answer is y=6x+5
How do you find the radius of a circle?
Answer:
Divide the diameter by two
example if the diameter is 25 you divide 25 by 2 to get 12.5 as your radius .
A portion of the Quadratic Formula proof is shown. Fill in the missing statement.
A. x plus b over 2 times a equals plus or minus the square root of b squared minus 4 times a times c, all over 2 times a
B. x plus b over 2 times a equals plus or minus the square root of b squared minus 4 times a times c, all over 4 times a
C. x plus b over 2 times a equals plus or minus the square root of b squared minus 4 times a times c, all over 2 times a squared
D. x plus b over 2 times a equals plus or minus the square root of b squared minus 4 times a times c, all over a
The missing statement in the Quadratic Formula proof is: A. x plus b over 2 times a equals plus or minus the square root of b squared minus 4 times a times c, all over 2 times a
This statement represents the quadratic formula, where x is the variable we are solving for in the quadratic equation ax^2 + bx + c = 0. The formula gives the solutions for x in terms of the coefficients a, b, and c of the quadratic equation.
The expression (b^2 - 4ac) represents the discriminant, which determines the nature of the solutions (real, imaginary, or equal). The square root of the discriminant is taken, and then the entire expression is divided by 2a to obtain the values of x. The "plus or minus" indicates that there are two possible solutions.
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In a standard deck of cards, what is the probability of drawing a face card followed by drawing a non-face card? Answer choices are in the form of a percentage, rounded to the nearest whole number.
a.) 45%
b.)27%
c.)4%
d.)18%
Reason:
The face cards are Jack, Queen, and King. There are 3 face cards per suit, and 4 suits, giving 3*4 = 12 face cards and 52-12 = 40 non-face cards in a standard deck.
12/52 = probability of getting a face card on 1st draw40/51 = probability of getting a non-face card on 2nd drawThe 52 dropped to 51 because we are not putting the 1st card back.
Multiply out those fractions:
(12/52)*(40/51) = 0.180995 approximately.
Move the decimal point two spots to the right to convert to a percentage.
0.180995 becomes 18.0995% and rounds to 18%
In a standard deck of cards, there are 12 face cards (4 kings, 4 queens, and 4 jacks) out of a total of 52 cards. The probability of drawing a face card followed by drawing a non-face card from a standard deck of cards is 18%.
To calculate the probability, we first determine the probability of drawing a face card on the first draw, which is 12/52 or 3/13. After drawing a face card, there are 51 cards remaining in the deck, of which 40 are non-face cards. Therefore, the probability of drawing a non-face card on the second draw, given that a face card was drawn on the first draw, is 40/51.
To find the overall probability of drawing a face card followed by a non-face card, we multiply the probabilities of the individual events. So the probability is (3/13) * (40/51) = 120/663, which is approximately 0.181 or 18%. Rounded to the nearest whole number, the probability is 18%.
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HURRY PLEASEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEE
Answer:
option 3
Step-by-step explanation:
Answer:
wouldn't it be one, someone lmk if I'm right
Step-by-step explanation:
48 is half of 96 and the ratio says there are less trucks. 36 is the closest to 48 but still less than it.
The index rises 4.9% over the course of the day. What is the value of the index at the end of the day? Round your answer to the nearest hundred.
Answer: $70400
Step-by-step explanation:
Attached is the question:
Based on the information given in the question:
Value of Stock X = 5000 × $4.30 = $21500
Value of Stock Y = 2000 × $3.20 = $6400
Value of Stock Z = 8000 × $4.90 = $39200
Total Stock Value = $67100.
Since there's a 4.9% increase in value of index, the value of the index at end of the day will be:
= $67100 × (100% + 4.9%)
= $67100 × 104.9%
= $67100 × 1.049 =
= $70388
= $70400 approximately
Answer:
$70,400
Explanation:
Ap3x
Which of the following is an example of a physical property?(55 points)
A. nail rusting
B. camp fire burning
C. Table salt melting
D. silver spoon tarnishing
Select the expression that is equivalent to (m2-16)
A
(m-4)2
B
(m+4)(m-4)
C
(m2+8m+16)
D
(m2-8m+16)
def:This is what we call the money you get back when you pay for something.
term:
Answer:
Change
Step-by-step explanation:
I call what I get back in return, change. The money we get back if you pay extra for something you buy.
Hope this helps!
The top of a tall building has four triangular faces that slope toward a single point. What shape best models the top
of the building?
А cube
c. triangular pyramid
B cone
Dsquare pyramid
Choose
Answer:
Option D, square pyramid
Step-by-step explanation:
The base of a square pyramid is a square of side of length "A"
and the height of the pyramid is "h"
From the four sides of base of pyramid, four surfaces arises that are slanting and meet at a point at the top at height "h"
Hence, option D is correct