z simple JJ r dzdrdo 6. ㅋ Using cylindrical coordinates, find the mass of the solid with density P(x, y, z) = 4 – z that is bounded by the cone z = Vx² + y2 and the plane z=4. (14 points) ? 4 니
Answers
Using cylindrical coordinates, the mass of the solid bounded by the cone z = sqrt(x^2 + y^2) and the plane z=4, with density rho(x,y,z) = 4 - z, is (704π/15).
We can use cylindrical coordinates to describe the region and then set up a triple integral to calculate the mass.
In cylindrical coordinates, the region is described by
0 ≤ r ≤ 4sin(θ)
0 ≤ θ ≤ 2π
0 ≤ z ≤ 4
To see why, note that the cone z = sqrt(x^2 + y^2) can be written in cylindrical coordinates as z = rcos(θ), and this is equal to 4 at z = 4. So the cone intersects the plane z = 4 at r = 4sin(θ). The limits for r and θ are straightforward, as they cover the full range of the cylindrical coordinates. The limit for z is simply the height of the region, which is 4.
The mass of the solid can be calculated using the triple integral
M = ∭ ρ(x,y,z) dV
where dV is the volume element in cylindrical coordinates
dV = r dz dr dθ
Substituting ρ(x,y,z) = 4 - z, we get
M = ∫₀²π ∫₀⁴sin(θ) ∫₀⁴ (4 - z) r dz dr dθ
Evaluating the z integral, we get:
M = ∫₀²π ∫₀⁴sin(θ) (4r - 2r^2) dr dθ
Evaluating the r integral, we get
M = ∫₀²π [(2r^3 - (4/3)r^4)]|₀⁴sin(θ) dθ
M = ∫₀²π [(2(4sin(θ))^3 - (4/3)(4sin(θ))^4)] dθ
M = ∫₀²π [(128sin^3(θ) - (256/3)sin^4(θ))] dθ
Evaluating this integral, we get
M = (320π/3) - (256π/15) = (704π/15)
Therefore, the mass of the solid is (704π/15).
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--The given question is incomplete, the complete question is given
" Using cylindrical coordinates, find the mass of the solid with density rho(x, y, z) = 4 – z that is bounded by the cone z = squareroot(x² + y2) and the plane z=4. ? "--
Related Questions
A company claims that its tablet computers have an average recharge time of 3 hours. In a random sample of these computers, the average recharge time is 2.5 hours. You suspect that the average recharge time might be less than what the company claims. Let µ represent the average time, in hours, needed to recharge the company's tablet computers.
What is the alternative hypothesis for this situation?
DONE | Second option
Answers
The alternative hypothesis in this situation is An hypothesis is u < 3.
What is the alternative hyothesis?An hypothesis is a temporary explanation to a phenomena. The explanation is either disproved by carrying out tests. Alternative hypothesis states that there is a relationship between the population parameters.
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Answer:
U=3
Step-by-step explanation:
next - U<3
next - alternative
sugmah
Which quadratic equation is equivalent to (x + 2)^2 + 5(x + 2) – 6 = 0? A. (u + 2)^2 + 5(u + 2) – 6 = 0 where u = (x – 2) B. u^2 + 4 + 5u – 6 = 0 where u = (x – 2) C. u^2 + 5u – 6 = 0 where u = (x + 2) D. u^2 + u – 6 = 0 where u = (x + 2) (This is a question from Edg by the way)
Answers
Answer:
C. u^2 + 5u – 6 = 0 where u = (x + 2)
Step-by-step explanation:
(x + 2)^2 + 5(x + 2) – 6 = 0
Let u = x+2
(u)^2 + 5(u) – 6 = 0
Answer:
C.u^2+5u-6=0
Step-by-step explanation:
By comparing (x+2)^2+5(x+2)-6=0 to answer C,that is u^2+5u-6=0,u=(x+2).
By sustituting (x+2)into answer C,we get;
(x+2)^2+5(x+2)-6=0 which is the same as the quadriatic equation given in the question.
Tasha has foam blocks stored in a box that measures 214 ft long by 2 ft wide by 2 ft tall.
Each foam block is a cube with 12ft edge length.
How many blocks can fit into the box?
Answers
help me pls
Find the value of x.
Answers
Answer:
33
Step-by-step explanation:
The bottom angle is a completely straight line, and that means the angle is 180 degrees.
180 - 81 = 99
So, this means 3x = 99. We need to isolate the variable, so we have to divide everything by 3.
x = 33
Answer:
waaait i know how to do this lol ( i feel like this is correct)
x = 33
Step-by-step explanation:
so a line is 180 right?
so make the equation like this
180 = 81 + 3x
now solve for x by doing algebra
(minus both sides by 81)
3x = 99
x = 33
A line is parallel to y = 5x + 3 and
intersects the point (3, 9).
What is the equation of this
parallel line?
y = 5x + [?]
Answers
Answer:
-6
Step-by-step explanation:
9=5(3)+[?] means that [?] = -6
Answer:
y = 5x - 6
Step-by-step explanation:
Slope of the parallel lines are same
So, m= 5
(3,9)
Equation: y - y1 = m(x -x1)
y - 9 = 5(x - 3)
y - 9 = 5x - 3*5
y -9 = 5x -15 {add 9 to both sides}
y - 9 + 9 = 5x - 15 + 9
y = 5x - 6
You are holding a balloon and have let out 24 feet of string. If the angle of elevation to the balloon is 32 degrees and you are 5 feet tall. How high is the balloon above the ground
Answers
The balloon is above 17.7180 the ground
What is the trigonometry ?
A branch of mathematics called trigonometry looks at how triangle side lengths and angles relate to one another. Applications of geometry to astronomical studies led to the development of the field in the Hellenistic world during the third century BC.
Given
The angle Ф is 32°
The hypotenuse becomes 24 feet
Let AB be the opposite side
Using trigonometric function of sinФ
ie sinФ = Opposite / hypotenuse
sin Ф = AB / 24
AB = sin Ф * 24
AB = sin 32° * 24
AB = 12.7180
As that person is 5 feet tall we have to add 5 to the value
ie
12.7180 + 5
= 17.7180
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The factors of the polynomial 3x3 - 75x do NOT include which of the
following:
Ox+5
O x-5
O 3x
O3x+25
Answers
Answer:
3x + 25 is not a factor
Step-by-step explanation:
3x³ - 75x ← factor out common factor of 3x from each term
= 3x(x² - 25) ← x² - 25 is a difference of squares
= 3x(x - 5)(x + 5) ← in factored form
thus 3x + 25 is not a factor of the polynomial
HURRY PLEASE!!!
Solve the compound inequality:
3x + 1 <-5 OR 2x -5> 7
Answers
Answer:
x < -2
x > 6
Step-by-step explanation:
use a number line if u need a visual
How do i get my grade up in algebra 1 honors? i am in middle school taking the class early and i dont wanna fail
Answers
Answer:
just do the assignments get help when neccesary ask the teacers if they have any extra credit materials
Step-by-step explanation:
A homeowner bought a dryer from a discount appliance store for $698.27 and makes 12 monthly payments of $63.29 with a credit card. The store charges $1.25 for every purchase made with a credit card. The homeowner also had to pay late fees in the amount of $35 four different times. What is the total cost of the dryer?
$713.27
$809.48
$900.73
$914.48
Answers
If the homeowner also had to pay late fees in the amount of $35 four different times, the total cost of the dryer is $809.48. So, correct option is A.
To calculate the total cost of the dryer, we need to add the initial cost of the dryer, the monthly payments, the credit card fees, and the late fees.
The total cost of the dryer can be calculated as follows:
Cost of dryer = $698.27
Total credit card charges = 12 x $1.25 = $15
Total late fees = 4 x $35 = $140
Total cost of the dryer = Cost of dryer + Total credit card charges + Total late fees
= $698.27 + $15 + $140
= $809.27
Therefore, the total cost of the dryer is $809.48, which is the closest option to the calculated answer.
So, correct option is A.
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10. A furniture company allows customers to purchase household furnishings with an in-store loan,
pay with cash or a credit card, or Rent-To-Own with a lease agreement.
A customer chooses furniture worth $3,225.00 including tax and chooses to Rent-To-Own.
Rent to Own Furniture Warehouse
• No down payment is required.
• The monthly lease payment is $156.99 for 2 years.
a. Calculate the total cost to own the furniture using the Rent-To-Own option.
b. What the amount of the finance charge on this purchase?
c. What simple interest percentage rate is this finance charge? Recall: = �
Answers
Answer:
a) Cost of rent to own option is = ($156.99/month) ( 2 yrs)( 12 month/yr) = $3767.76
b) The amount of the finance charge is = $3767.76 - $3225.00 = $542.76
c) the simple interest rate can be calculated by this formula
I = Prt, where
I = total interest value = $542.76
P = is the present worth or original cost including taxes = $3225.00
t = time in yrs = 2
r = Yearly interest rate, By rearranging the formula:
r = I /Pt, r = ( $542.76 / $3225.00 . 2) ( 100) = 8.415%
Step-by-step explanation:
Plot the points (-3,-4) and (6,-4) on the coordinate plane below.
What is the distance between these two points?
units
y
9-
8
7
6-
4-
3-
2-
11
H
{}
-9-8-7-6-5-4-3-2
1 2 3 4 5 6 7 8 9
-34
14
-5-
-6-
-7-
18
Answers
Answer:
d = 9
Step-by-step explanation:
Distance formula:
d=√((x_2-x_1)²+(y_2-y_1)²)
Your ordered pairs (-3, -4) and (6, -4)
d=√((6-(-3))²+(-4-(-4))²)
d=√((6+3))²+(-4+4))²)
d=√((9)²+(0)²)
d = √81
d = 9
The economy is in a recession. Real GDP is well below potential GDP. If the government wants to increase real GDP so that it is closer to potential GDP, it could ____. (Select all that apply.) Group of answer choices -increase government spending -decrease government spending -decrease taxes -increase taxes
Answers
To increase real GDP and bring it closer to potential GDP during a recession, the government could increase government spending and/or decrease taxes.
During a recession, when real GDP is below potential GDP, the government can use fiscal policy tools to stimulate economic growth and close the GDP gap. The two options that can be effective in this situation are increasing government spending and decreasing taxes.
Increase government spending: By increasing spending on infrastructure projects, education, healthcare, or other sectors, the government can create demand in the economy, which leads to increased production and employment, ultimately raising real GDP.
Decrease taxes: Reducing taxes can provide individuals and businesses with more disposable income, encouraging consumption and investment. This increased spending and investment can boost aggregate demand, leading to higher production levels and closing the GDP gap.
Decreasing government spending and increasing taxes, on the other hand, would have contractionary effects, potentially exacerbating the recessionary conditions by reducing overall demand in the economy. Therefore, these options are not suitable for increasing real GDP during a recession.
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increase £130 by 15%
Answers
Answer:
£149.5
Step-by-step explanation:
130/100=1.3
1.3*15=19.5
130+19.5=149.5
23 - C<6
I cannot find the answer can someone help me?
Answers
Answer:
C > 17
Step-by-step explanation:
23 - C < 6
-23 -23
-----------------
-C < -17
multiply both sides by -1
(-c) (-1) > (-17) (-1)
C > 17
Solve the system by using matrices.
X = 4
X + y = -6
4x - 3y + 2z = 26
Answers
Answer:
x=4, y=-10, z=-10
Step-by-step explanation:
question 8in all segments, how many orders were placed in one quarter of the year but shipped in the next quarter (for example, an order in which order date = qtr1 2009 and ship date = qtr2 2009)?
Answers
The number of orders placed in one quarter of the year and shipped in the next quarter will vary depending on the segment. To determine the exact number, you would need to analyze the data from each segment separately.
To determine the number of orders placed in one quarter of the year but shipped in the next quarter, you will need to analyze the data from each segment separately. Begin by extracting the data from the segment you are interested in and sorting it by order date and ship date. For example, if you are interested in orders placed in Q1 2009 and shipped in Q2 2009, you will need to identify all orders with an order date in Q1 2009 and a ship date in Q2 2009. Once you have identified these orders, you can count them up to determine the total number of orders in the segment that fit this criteria. You can then repeat this process for the other segments to determine the total number of orders placed in one quarter of the year but shipped in the next quarter across all segments.
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18) The degree of P(x) = (x-1)(x+2)(x+3)(2x-5) is
4
3
2
1
Answers
Answer:
degree 4
Step-by-step explanation:
The degree of a polynomial is determined by the term with the largest exponent for the polynomial in standard form
Given
P(x) = (x - 1)(x + 2)(x + 3)(2x - 5)
We need only consider the product of the leading terms in each factor, that is
x(x)(x)(2x) = 2\(x^{4}\) ← is the leading term in the expansion of the factors
with exponent 4
Thus polynomial is of degree 4
solve for variable its in pre algebra
Answers
Answer:
7
Step-by-step explanation:
7
If possible, find the area of the triangle defined by the following: b = 45, c = 20, a = 71°.405.2 square unitso189.1 square units465.4 square units425.5 square units
Answers
We will find the area of the triangle as follows:
\(A=(45)(20)\frac{\sin(71)}{2}\Rightarrow A=425.483359\ldots\)\(\Rightarrow A\approx425.5\)So, the area of the triangle is approximately 425.5 square units.
Find sin^2(pi/8) - cos^4(3pi/8)
Answers
Recall the following identities:
sin²(x) = (1 - cos(2x))/2
cos²(x) = (1 + cos(2x))/2
Then
sin²(π/8) = (1 - cos(π/4))/2 = (1 - 1/√2)/2
cos⁴(3π/8) = (cos²(3π/8))² = ((1 + cos(3π/4))/2)² = ((1 - 1/√2)/2)²
and so
sin²(π/8) - cos⁴(3π/8) = (1 - 1/√2)/2 - ((1 - 1/√2)/2)²
… = (1 - 1/√2)/2 • (1 - (1 - 1/√2)/2)
… = (2 - √2)/4 • (1 - (2 - √2)/4)
… = (2 - √2)/16 • (4 - 2 + √2)
… = (2 - √2)(2 + √2)/16
… = (4 - 2)/16
… = 1/8
PLS ANSWER THISHEHDNDJDJ
Answers
9514 1404 393
Answer:
1/12
Step-by-step explanation:
The slope of a ramp (or anything else) is the ratio of its "rise" to its "run."
The rise is the vertical change. Here, that is shown as 3 m.
The run is the horizontal change. Here, that is shown as 36 m.
Then the slope is ...
\(\text{slope }=\dfrac{\text{rise}}{\text{run}}=\dfrac{3\text{ m}}{36\text{ m}}=\boxed{\dfrac{1}{12}}\)
__
Additional comment
If this were a line on a graph, the slope would be calculated the same way. When the rise is positive to the right, the slope is positive. On a graph, if the rise is negative as you go to the right, the slope is negative.
Solve the equation.
Start Fraction b over negative 6 End Fraction = –3
Answers
Answer:
Step-by-step explanation:
b/-6=-3
b=18 (x -6 on both sides)
The circumference of a circle of diameter 10 cm is _____.
A
3.14 cm
B
0.314 cm
C
314 cm
D
31.4 cm
Answers
For a circle with a diameter of 10 cm, the circumference would be C = π(10) = 31.4 cm. The correct option is (D) 31.4 cm.
The circumference of a circle can be calculated using the formula C = πd, where C represents the circumference and d represents the diameter of the circle.
We have the diameter of the circle is 10 cm, we can substitute this value into the formula:
C = π * 10 cm
Calculating the circumference using an approximate value of π as 3.14:
C ≈ 3.14 * 10 cm
C ≈ 31.4 cm
Therefore, the circumference of a circle with a diameter of 10 cm is approximately 31.4 cm.
The correct answer is D) 31.4 cm.
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A corner lot that originally was square lost 185 m² of area when one of the adjacent syreets what is wide by 3 m and the other was widnened by 5 m find the new dimensions of the lot
Answers
The new dimensions of the lot is length = 22 meters and width = 20 meters
The corner lot that originally was square
Consider the side of the lot = x
The area of the square = Length × length
Therefore,
x × x = \(x^2\)
one of the adjacent streets which is widened by 3 m and the other was widened by 5
Therefore
(x-3) × (x-5) = \(x^2\) - 185
open the brackets
\(x^2-5x-3x+15=x^2-185\)
The x square term will cancel each other
-5x-3x = -185-15
-8x = -200
x = 25 meter
The new length of the lot = x-3
= 25-3
= 22 meter
The new width of the lot = 25-5
= 20 meters
Hence, the new dimensions of the lot is length = 22 meters and width = 20 meters
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jonah bought 3 packs of hotdogs
Answers
Step-by-step explanation:
\( \sqrt{a {}^{2} } + 24 - 4 = a \)
-4x+ 7x + 3 ? Simplify algebraic expressions
Answers
Answer:
3x+3
Step-by-step explanation:
Add -4x + 7x.
81x^6-(y+1)^2 what are the U and V
Answers
The simplified form of the expression \(81x^6 - (y + 1)^2\) in terms of U and V is 729x^6 - V^2.
In this question, we are given specific values for U and V and asked to express the given expression in terms of those values.
To simplify the expression using the given values, we substitute \(U = 3x^3\)and V = y + 1 into the original expression:
\(81x^6 - (y + 1)^2\)
Replacing U and V:
\(81(3x^3)^2 - (V)^2\)
Simplifying:
\(81 \times 9x^6 - V^2\)
\(729x^6 - V^2\)
Therefore, the simplified form of the expression \(81x^6 - (y + 1)^2\) in terms of U and V is\(729x^6 - V^2.\)
In this way, we can represent the original expression in a simplified form using the assigned values for U and V.
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Consider the expression: \(81x^6 - (y + 1)^2\)
If\(U = 3x^3\) and V = y + 1, what is the simplified form of the expression in terms of U and V?
In this question, we are given specific values for U and V and asked to express the given expression in terms of those values.
A rectangular swimming pool is 28 feet wide. Jason drew the pool at the scale below. 1 inch : 4 feet How many inches wide is Jason's drawing?
F. 4 inches
G. 7 inches
H. 14 inches
J. 21 inches
Answers
Pizza Shop A pizza shop uses flour at a daily rate that is normally distributed with a mean of 15 pounds and a standard deviation of 6 pounds. When the pizza shop places an order for the flour it requires 4 days for the order to arrive. What is the reorder point if the pizza shop wants to limit the probability of a stockout to 7 percent? 63.10 pounds 60.00 pounds 75.04 pounds 62.16 pounds 77.76 pounds 71.40 pounds 107.76 pounds
Answers
The closest option to the reorder point is 71.40 pounds.
To determine the reorder point, we need to find the demand during the lead time and the safety stock.
First, let's calculate the demand during the lead time. The mean daily rate is 15 pounds, and it takes 4 days for the order to arrive. So, the mean demand during the lead time is 15 pounds/day * 4 days = 60 pounds.
Next, let's calculate the safety stock. The pizza shop wants to limit the probability of a stockout to 7 percent. We can find this value using the z-score table.
Looking up the z-score corresponding to a 7 percent probability, we find that it is approximately 1.89.
The standard deviation is given as 6 pounds.
So, the safety stock is calculated as 1.89 * 6 pounds = 11.34 pounds.
Finally, the reorder point is the sum of the mean demand during the lead time and the safety stock.
Reorder point = 60 pounds + 11.34 pounds = 71.34 pounds.
Therefore, the closest option to the reorder point is 71.40 pounds.
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