Using polar/cylindrical coordinates, we take
x = r cos(t )
y = r sin(t )
z = z
so that
dV = dx dy dz = r dr dt dz
The solid is given by the set
D = {(x, y, z) : x ² + y ² ≤ 1 and 0 ≤ z ≤ 4 - 2x - y}
or in cylindrical coordinates,
D = {(r, t, z) : 0 ≤ r ≤ 1, 0 ≤ t ≤ 2π, and 0 ≤ z ≤ 4 - 2r cos(t ) - r sin(t )}
Then the volume of the solid is
[tex]\displaystyle \iiint_D \mathrm dV = \iiint_Dr\,\mathrm dr\,\mathrm dt\,\mathrm dz \\\\ = \int_0^{2\pi} \int_0^1 \int_0^{4-2r\cos(t)-r\sin(t)} r\,\mathrm dz\,\mathrm dr\,\mathrm d t \\\\ = \int_0^{2\pi}\int_0^1 (4r-2r^2\cos(t)-r^2\sin(t))\,\mathrm dr\,\mathrm dt \\\\ = \int_0^{2\pi} \left(2 - \frac23 \cos(t) - \frac13 \sin(t)\right) \,\mathrm dt \\\\ = \boxed{4\pi}[/tex]
The volume of the given solid below the plane 2x + y + z = 4 and above the disk x2 + y2 ≤ 1 is 4π.
What is the volume of the solid in polar coordinates?The volume of the solid in polar coordinates can be calculated by the double integral in polar coordinates.
[tex]V = \iint_R f(x,y) \,dA.\\[/tex]
Similarly, by polar coordinates,
x = r cost
y = r sint
z = z
we get, dV = dx dy dz = r dr dt dz
The solid is given
D = {(x, y, z) : x ² + y ² ≤ 1 and 0 ≤ z ≤ 4 - 2x - y}
or in polar coordinates,
D = {(r, t, z) : 0 ≤ r ≤ 1, 0 ≤ t ≤ 2π, and 0 ≤ z ≤ 4 - 2r cos(t ) - r sin(t )}
The volume of the solid is
[tex]\rm \int \int\int\ dV = \int \int\int\ rdr dt dz\\ \rm = \int\limits^{2\pi}_0\int\limits^1_0 \int\limits^{4-2rcost-rsint}_0 rdr dt dz\\\rm =\int\limits^{2\pi}_0\int\limits^1_0 {4r-2r^{2} cost-r^{2} sint} dr dt\\\rm =\int\limits^{2\pi}_0( 2-2/3cost-1/3sint) dt\\\rm =4\pi[/tex]
Hence, The volume of the given solid below the plane 2x + y + z = 4 and above the disk x2 + y2 ≤ 1 is 4π.
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Betsy's high school is putting on a production of a play as a fundraiser for the school's music programs. A local bank has agreed to
allow the school to use a line of credit from which they can withdraw money to pay for the play. Then, any deposits they make at the
bank will be applied to the negative balance of the credit account.
The play cost $2,500.00 to produce, and they intend to sell tickets for $7 each. After the play, Betsy will take the ticket proceeds and
deposit them with the bank. If 559 people attend the play's opening night, what will the balance of the bank account be?
5) True or False: Absolute Value can never be negative * O True False
Answer:
True
Step-by-step explanation:
Absolute value tells the distance a number is from 0.
[tex]|7|=7[/tex] because 7 is 7 units away from 0.
[tex]|-13|=13[/tex] because -13 is 13 units away from 0.
[tex]|0|=0[/tex] because 0 is 0 units away from 0
Absolute value always produces a number greater than or equal to 0, never negative.
Select all expressions that are equivalent to 7x + 4 - (2x - 5).
A: 7x + 4 - 2x -5
B: 7x + 4 - 2x + 5
C: 7x + 4 + (-2x) - (-5)
D: 9x + 9
E: 5x -1
F: 5x + 9
Answer:
B, C, F
Step-by-step explanation:
7x + 4 - (2x - 5) = 7x - 2x + 4 + 5 or 5x + 9
The solution is, B: 7x + 4 - 2x + 5, C: 7x + 4 + (-2x) - (-5), F: 5x + 9, are the expressions that are equivalent to 7x + 4 - (2x - 5).
What is simplification?Simplify simply means to make it simple. In mathematics, simply or simplification is reducing the expression/fraction/problem in a simpler form. It makes the problem easy with calculations and solving.
here, we have,
given that,
the expression is :
7x + 4 - (2x - 5)
now, we have to simplify this to get the equivalent expressions.
so, we have,
7x + 4 - (2x - 5)
= 7x + 4 - 2x + 5
(Removing the brackets)
=7x + 4+ (-2x) - (-5)
= 7x + (-2x) +4 - (-5)
=5x +4 + 5
= 5x + 9
so, the equivalent expressions are, B,C,F.
Hence, The solution is, B: 7x + 4 - 2x + 5, C: 7x + 4 + (-2x) - (-5), F: 5x + 9, are the expressions that are equivalent to 7x + 4 - (2x - 5).
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Subtract the following complex numbers:
(4 + 4i) - (13 + 17i)
If using the method of completing the square to solve the quadratic equation
x2 + 3x + 21 = 0, which number would have to be added to "complete the
square"?
Answer:
8
Step-by-step explanation:
Answer:-18.75
Step-by-step explanation:x^2+3x+21-18.75=x^2+3x+2.25=
(x+1.5)^2=-18.75
HELP ON BOTH HAVE 2 MINUTE'S LEFT. NO LINKS. I JUST NEED SIMPLE ANSWERS
Answer:
Q1: 48
Q2: 59
Step-by-step explanation:
Answer:
1. 48
2. 53
you can see that they are the same length as the one across from it so what the one across from it, is the answer
What is the value of g(0)
a. 1
b. 0
c. 8
d. 4
Answer:
c. 8
Step-by-step explanation:
1) [tex]g(x)=8(\frac{1}{2} )^{x}[/tex]
2) [tex]g(0)=8(\frac{1}{2} )^{0}[/tex]
3) [tex]g(0)=8*1[/tex]
4) [tex]g(0)=8[/tex]
Help pleaseeeeeeeeeee
Answer:
d
Step-by-step explanation:
Answer:
km/hr
Hope that helps! :)
Step-by-step explanation:
Select the expression that represents the following statement: 3 times one fourth the difference of 26 and 10. (4 points)
one fourth x (26 + 10) x 3
one fourth x (26 − 10) x 3
3 x one fourth x 26 − 10
3 x one fourth x 26 x 10
Drag each capacity to match it to an equivalent capacity.
24 cups
1 gallon
16 fluid ounces
6 pints
Capacity
Equivalent Capacity
2 cups
96 ounces
12 pints
4 quarts
HELP ME
Answer:
2 cups ⇔ 16 fluid ounces 96 ounces ⇔ 6 pints 12 pints ⇔ 24 cups 4 quarts ⇔ 1 gallonAlso see attached
Answer:
Solution:
2 cups=16 fluid ounches
96 ounces=6pints
12 pints=24cups
4 quarts=1 gallon
Find the area of each figure. Round to the nearest tenth if necessary
Answer:
c. 143.8 m³
Step-by-step explanation:
The figure can be decomposed into a semicircle and a trapezoid
Area = area of semicircle + area of trapezoid
= ½(πr²) + ½(a + b)h
Where,
r = ½(9) = 4.5 m
a = 9 m
b = 23 m
h = 7 m
Area of the figure = ½(π*4.5²) + ½(9 + 23)7
Area of the figure = 31.81 + 112
= 143.8 m³
can someone please explain how to do this?
Answer:
14)
tan θ = BC/AC = 9/13θ = arctan (9/13)θ = 34.7°15)
cos 45° = 14/xx = 14 / cos 45°x = 19.8What is the height, in yards, of a cylindrical water tank that holds 1,884 cubic yards of water and has a diameter of 120 feet? Be sure to convert so you are using like units.
Answer:
The height of the tank is 0.5 yards.
Step-by-step explanation:
To determine what is the height, in yards, of a cylindrical water tank that holds 1,884 cubic yards of water and has a diameter of 120 feet, knowing that the volume of a cylinder is equal to pi multiplied by the radius squared, multiplied by the height, the following calculation must be done:
1 foot = 0.3333 yards
R = Diameter / 2
R = 120/2 = 60
3.14 x 60 ^ 2 x H = 1,884
3.14 x 3,600 x H = 1,884
3.14 x 1,200 x H = 1,884
3.768 x H = 1.884
H = 1,884 / 3,768
H = 0.5
Therefore, the height of the tank is 0.5 yards.
Regina writes the expression y+9 ∙ 34. Which expression is equivalent to the one Regina writes?
None of these
(9 ∙ 3÷4)+y
(y+9)(3÷4)
9+y ∙(3÷4)
2/3 * n = 12
im not sure what this is please help
Answer:
n= 18
Step-by-step explanation:
:)
Answer:
18
Step-by-step explanation:
[tex]\frac{2}{3} *n=12\\\frac{2}{3} *n/\frac{2}{3} =12/\frac{2}{3} \\n=18[/tex]
I WILL MARK BRAINLIEST IF CORRECT! Look at the image below.
Answer:
C 1/10 × 33
D 0.1 × 33
Hope that helps
0=12X²-64X+20 quie me puede hacer el favor de realizarmelo
Answer:
x = 1/3 , 5
Step-by-step explanation:
Factoriza y establece cada factor igual a cero.
Point Z is the incenter of triangle RST. Point Z is the incenter of triangle S R T. Lines are drawn from the points of the triangle to point Z. Lines are drawn from point Z to the sides of the triangle to form right angles and line segments Z A, Z B, and Z C. Angle A S Z is (5 x minus 9) degrees and angle Z S B is 16 degrees. What is the value of x? x = 2 x = 3
9514 1404 393
Answer:
x = 5
Step-by-step explanation:
SZ is the angle bisector of angle S, so ...
∠ASZ = ∠ZSB
5x -9 = 16
5x = 25 . . . . . . add 9
x = 5 . . . . . . . . .divide by 5
Answer:
C
Step-by-step explanation:
mhm
which exprssion can we use to convert 40 ounces to pouds
Answer:
2.5
Step-by-step explanation:
40 ounces = 2 12 pounds
So, 40 ounces = 4016 = 2 12 or 2.5 pounds.
Hope this helps and sorry if it doesn't
Can I get brainliest
Mrs.biillitti bought 3 pounds of red grapes and 2.5 all grapes cost $1.28 per pound how much money did she spend
Answer:
$9.60
Step-by-step explanation:
2.5 x 3=7.5
7.5 x 1.28=9.6
so the answer would be $9.60 I think.
Which table of values goes with the equation y = 3x ^2 + 1?
Answer:
the correct answer is table 2
express(16^5)^1/4 in simplest radical form.
Answer:
32
Step-by-step explanation:
Hello, in (16^5)^1/4, you would multiply the exponents together like this:
16^5 x 1/4= 16^5/4
The exponents multiplied make 5/4. Now you need to multiply 16 with 5/4 like this:
16 x 5/4= 80/4
80 divided by 4 is 32 so therefore, the answer is 32.
The first sequence rule is add 5 starting from 20. The second sequence rule is subtract 7 starting from 56. What is the first number that appears in both sequences?
25
28
42
35
Answer:
35
Step-by-step explanation:
its the 4th step your welcome
20-25-30-35
56-49-42-35
Answer: 35 I got it correct on the quiz
Step-by-step explanation:
FOR BRANLIEST PLEASE HELP!!
Answer:
55
Step-by-step explanation:
complementary angle means either of two angles whose sum is 90°.
we can use this to find that angle abc is 55 and since angle abc and ebf are opposite the measure the same
Criteria are the goals that a design must achieve. They are determined by what you want the cup to do. Criteria for the volume of the cup compartments have been decided for you. The volume is expressed in four different units: Volume cubic centimeters milliliters fluid ounces cups cold pack 150 150 5 0.6 drink compartment 600 600 20 2.5 total 750 750 25 3.1 Although the volume is set, the shape of the cup is up to you. There are no right or wrong answers. Do you want your cup to be tall and skinny or short and wide
Answer:
Criteria for my Cup:
I want my cup to be short and wide.
Step-by-step explanation:
a) By the way, a cup can be measured in volume. There are no tall and skinny cups. They are not attributes of a cup. However, a cup can be short (height). It can also be wide, usually measured in diameter and radius.
b) Data:
Volume cubic centimeters milliliters fluid ounces cups
cold pack 150 150 5 0.6
drink compartment 600 600 20 2.5
total 750 750 25 3.1
Pls help I will mark branliest
Answer:
Step-by-step explanation:
The question is on the ss btw
Answer:
The shop
Step-by-step explanation:
Given
Shop
[tex]Cost = E9[/tex]
[tex]Bag = 12.5kg[/tex]
Supermarket
[tex]Cost=E1.83[/tex]
[tex]Bag = 2.5kg[/tex]
Required
The better value
To do this, we simply calculate the unit price.
This is calculated as:
[tex]Unit = \frac{Price}{Bag}[/tex]
So, we have:
Shop
[tex]Unit = \frac{9}{12.5}[/tex]
[tex]Unit = 0.72[/tex]
Supermarket
[tex]Unit = \frac{1.83}{2.5}[/tex]
[tex]Unit = 0.732[/tex]
At the shop, the unit price is £0.72 per bag while at the supermarket, the unit price is £0.732
The best value is at the shop, because it is cheaper
i.e.
[tex]0.72 < 0.732[/tex]
A sociologist recorded the number of contacts entered in a cell phone and the number of texts sent in a week for 20 cell phone users. The resulting data were used to conduct a hypothesis test to investigate whether there is a linear relationship between the number of contacts and the number of texts sent. What are the correct hypotheses for the test?
a. H0:β1=0 Ha:β1≠0
b. H0:β1=0 Ha:β1>0
c. H0:β1=0 Ha:β1<0
d. H0:β1≠0 Ha:β1=0
e. H0:b1=0 Ha:b1≠0
The correct option for the hypotheses for the test is a. H0: β1 = 0 Ha: β1 ≠ 0
What is Statistic?The statistic is the study of mathematics that deals with relations between comprehensive data.
Here,
The correct hypotheses for testing the linear relationship between two variables can be stated as:
H0: β1 = 0 (there is no linear relationship between the number of contacts and the number of texts sent)
Ha: β1 ≠ 0 (there is a linear relationship between the number of contacts and the number of texts sent)
Therefore, the correct option for the hypotheses for the test is a. H0: β1 = 0 Ha: β1 ≠ 0
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Among all rectangles that have a perimeter of 202, find the dimensions of the one whose area is largest. Write your answers as fractions
reduced to lowest terms.
Answer:
How to write by fraction? 50 1/2 by 50 1/2
Step-by-step explanation:
the maximum area for a rectangle is a square.
To find a square with p = 202, divide it by 4,
202 / 4 = 50.5
ANSWER THIS PLEASE!!!!
Answer:
J
Step-by-step explanation:
Done.