Answer:
[tex]\dfrac{-8^3}{6}[/tex]
Step-by-step explanation:
According to the divergence theorem;
The flux through the surface S is given by the formula:
[tex]\iint _S F.dS = \iiint_E \ div (F) \ dV[/tex]
where the vector field is:
F = [tex]\langle y,z-y,x \rangle[/tex]
Then the divergence of the vector field is:
[tex]div (F) = \bigtriangledown.F = \Bigg [ \dfrac{\partial (y)}{\partial x} + \dfrac{\partial (z-y)}{\partial (y)}+ \dfrac{\partial (x)}{\partial (z)} \Bigg ][/tex]
= 0 - 1 + 0
= -1
Thus, the flux through the surface of the tetrahedron is:
[tex]\iint_S . FdS = \iiint _E(-1) \ dV \\ \\ = - \iiint_E \ dV[/tex]
To determine the volume of the tetrahedron with vertices O(0,0,0), A(8,0,0), B (0,8,0) & C(0,0,6)
The equation of the plane P moving through the vertices A, B and C is:
[tex]P = \dfrac{x}{8}+ \dfrac{y}{8}+ \dfrac{z}{8} = 1[/tex]
x + y + z = 8
Range:
For z: 0 ≤ z ≤ 8 - x - y
For y: 0 ≤ y ≤ 8 - x
For x; 0 ≤ x ≤ 8
Thus;
[tex]\iiint_E \ dV = \int ^8_0 \int ^{8-x}_{0} \int ^{8-x-y}_{0}[/tex]
[tex]\int ^8_0 \int ^{8-x}_{0} [z] ^{8-x-y}_{0} \ dydx = \int ^8_0 \int ^{8-x}_{0} \ (8 -x-y) \ dy dx[/tex]
[tex]\int ^8_0 [ (8-x)^2 - \dfrac{(8-x)^2}{2} ] dx = \dfrac{1}{2} \int ^8_0 (8-x)^2 \ dx[/tex]
i.e.
[tex]= \dfrac{1}{2} [ \dfrac{(8-x)^3}{(-1)^3}]^8_0[/tex]
[tex]= \dfrac{-1}{6}[(8-8)^3-(0-8)^3][/tex]
[tex]= \dfrac{-8^3}{6}[/tex]
This question is based on the Gauss Divergence theorem. Therefore, the surface integral [tex]\int\limits {F.dS}[/tex] is -85.33.
Given:
F(x, y, z) = y i + (z − y) j + x k S in outward orientation.
Tetrahedron with vertices (0, 0, 0), (8, 0, 0), (0, 8, 0), and (0, 0, 8).
We have to evaluate the surface integral [tex]\int\limits {F.dS}[/tex] .
According to the Gauss divergence theorem ,
The flux through the surface S is given by the formula:
[tex]\int\int _s F.dS = \int \int \int_e div (F)\; dV[/tex]
Where the vector field is:
F = ( y, z-y, x )
Therefore, the divergence of the vector field is:
[tex]div(F) = \bigtriangledown .F = ( \dfrac{\partial( y)}{\partial (x)} + \dfrac{\partial(z-y)}{\partial(y)} + \dfrac{\partial(x)}{\partial(z)} )\\\\div(F) = \bigtriangledown .F = 0-1+0=-1[/tex]
Thus, the flux through the surface of the tetrahedron is:
[tex]\int\int _s F.dS = \int \int \int_e (-1)\; dV = -\int \int \int_e \; dV[/tex]
Now, determine the volume of the tetrahedron with vertices O(0,0,0), A(8,0,0), B (0,8,0) & C(0,0,6).
The equation of the plane P moving through the vertices A, B and C is:
[tex]P = \dfrac{x}{8} +\dfrac{y}{8} +\dfrac{z}{8} = 1[/tex]
x + y + z = 8
Range:
For z: 0 ≤ z ≤ 8 - x - y
For y: 0 ≤ y ≤ 8 - x
For x; 0 ≤ x ≤ 8
Thus,
[tex]\int\int\int_e dV = \int\limits^8_0\int\limits^{8-x} _ 0 \int\limits^{8-x-y}_0 \; dzdxdy\\= \int\limits^8_0\int\limits^{8-x} _ 0 [z]\limits^{8-x-y}_0 dx \\= \int\limits^8_0\int\limits^{8-x} _ 0 (8-x-y) dy dx\\= \int\limits^8_0 [ 8y-xy-\dfrac{y^{2} }{2} ]\limits^{8-x}_ 0 dx\\= \int\limits^8_0 ([ 8-x]^{2} - \dfrac{ [ 8-x]^{2}}{2} ) dx\\= \dfrac{1}{2} [\dfrac{(8-x)^{3} }{(-1)^{3} } ] \limits^8_0\\=\dfrac{-8^{3} }{6} \\\\= -85.33[/tex]
Therefore, the surface integral [tex]\int\limits {F.dS}[/tex] is -85.33.
For further details, prefer this link:
https://brainly.com/question/3283106
pls help me I don't understand
Answer:
Domain (6, 9) Range (-5, 3)
Step-by-step explanation:
The domain is your x-values while your range is your y-values. For this particular relation your domain ranges from 6 to 9 given the fact that there are 3 numbers with x-values and your range is from -5 to 3 given the fact that there are 3 numbers with y-values.
Please welp more points!!!!
Nonrenewable energy resources include fossil fuels and nuclear power. What characteristics do all nonrenewable energy resources have in common?
I. They create some form of pollution as a byproduct.
II. They will eventually run out if they are continually used.
III. They formed from long-dead organisms.
IV. They can be used in most environments.
A. I, II, and IV only
B. I, II, III, and IV
C. II only
D. I and II only
Answer:
B) I, II, III, and IV
Step-by-step explanation:
Simplify the equation by combining like
terms.
2x + 2x – 4y- y = 4x + [? ]y
Answer:
4x+(-5y)
Step-by-step explanation:
Victor wants to purchase a perpetuity paying 100 per year with the first payment due at the end of year 11. He can purchase it by either: (i) paying 90 per year at the end of each year for 10 years; or i) payıng K per year at the end of each year for the years and nothing for the next 5 years. Calculate K
Answer:
K = 151.9422481
Step-by-step explanation:
At the end of year 10, your perpetuity is worth 100/i
(1) is worth 90×s_{10%i}
So if you set them equal you get 90*[(1+i)^10 - 1]/i = 100/i or [(1+i)^10 - 1] = 10/9 or (1+i)^10 = 19/9 or i = 0.077583937
So now the question compare (1) to (2), at t = 0
(1) is worth 90×a_{10%i} = 90(1 - 1/(1.077583937)^10)/0.077583937 = 610.5441743
(2) is worth K×a_{5%i} = 4.018264714×K
Therefore K = 151.9422481
Jason bought 7 new baseball trading cards to add to his collection. The next day half of his collection. There are now only 30 cards left.
Answer:
8 cards
Step-by-step explanation:
Work Backwards:
30/2 is 15
15-7 is 8.
Hope this helps :D
Answer:
Step-by-step explanation:
Let x be the number of cards Jason had initially in his collection.
"Jason bought 9 new baseball trading cards to add to his collection"
x
+
9
is the equation because
x
is the initial number of cards he has and he bought another 9
"His dog ate half of his collection"
1
2
(
x
+
9
)
because
x
+
9
is what he had before his dog ate his cards and since his dog ate half, there is a
1
2
added to the equation
"42 cards left"
1
2
(
x
+
9
)
=
42
Since his dog ate half, he is left with half of his initial card collection.
x
+
9
=
42
×
2
x
+
9
=
84
x
=
84
−
9
x
=
75
Triangle ABC contains side lengths b=3 inches and c= 5 inches in two or more sentences describe whether or not it is possible for mangle B =45 degrees
Answer:
Since sine of all angles are always less than one, this shows there is no possible way to have an angle C. Thus it is impossible to have a triangle ABC with the given properties of side lengths b=3 inches and c= 5 inches to have angle B =45 degrees.
Step-by-step explanation:
In the attached drawing, each of the tic-marks are equal and
represent 1 inch each. The angle B has measure 45. We can
see by the arc that the line AC, which equals 3 inches, is
not long enough to reach the slanted side of the 45 angle.
Therefore triangle ABC is not possible. We can also show
by the law of sines that no triangle ABC with the given
properties in possible.
Algebra 2
L.6 Evaluate polynomials using synthetic division CHC
If g(y) = 6y? + 8y - 9, use synthetic division to find g(1).
Submit
The price yesterday was $120 today it is $54 what is the percentage decrease.
Answer:
66
Step-by-step explanation:
Answer:
55%
Step-by-step explanation:
120-54=66
This means that the price decreased by 66
66/120 = 0.55
This means that the percentage of decrease is 55%
Are the lines x− 2y= 4 and y= 2x − 2 parallel, perpendicular, or neither? Explain your answer. [ Select ] ; their [ Select ] [ Select ] the same and [ Select ] receiprocals.
Answer:
Neither.
Step-by-step explanation:
First we alter the first equation to match the second.
x - 2y = 4
2y = x - 4
y = x/2 - 2.
Next we compare the slopes
2x = 2
x/2 = 1/2
Their slopes are reciprocals, but they aren't opposites. Therefore they are neither parallel nor perpendicular.
Write -9/50 as a decimal number?
Answer: -0.18
Step-by-step explanation:
-9/50 is the same as -18/100. negative eighteen hundredths. so we write it as -0.18, because that fills into the hundredths place
Answer:
-0.18
Step-by-step explanation:
solve quadratic x^2+6x+1=0
Answer: x = 3 ± √ 10
Complete the following statement. Percent is a fraction where parts make one whole.
Answer:
Percent is a fraction where the denominator is represented by 100 or 100 parts make one whole.
Step-by-step explanation:
I hope this helped and if it did I would appreciate it if you marked me Brainliest. Thank you and have a nice day!
A percentage is a fraction whose denominator is 100, or how many parts make one whole.
What is percent?A number or ratio that can be expressed as a fraction of 100 is called a percentage. Divide the number by its whole number and multiply it by 100 if we have to figure out the percentage of that number. Consequently, the percentage represents one part per hundred. The word "per 100" means "per percent." The number "%" is used to symbolize it.
For given statement
A fraction with 100 as the denominator is called a percent.
Thus, a whole is made up of 100 parts. The percentage represents the number of relevant parts out of a total of one hundred.
For instance, 10% is represented by the decimal number 0.10 or the fraction 10/100.
Similarly, the decimal equivalent of 25% is 0.25, or the fraction 25/100.
Because 100/100 equals 1, 100% corresponds to the number 1.
Hence the statement is Percent is a fraction where the denominator is represented by 100 or 100 parts make one whole.
Learn more about percent;
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Mr. Richards garden is shaped like a rectangle. The length of garden is 10 meters more than twice the width. What expression represents the length in meters of a fence needed to fully surround garden
Answer:
The expression for length of fence in meters is: 6w+20 meters
Step-by-step explanation:
Let l be the length and w be the width of the given garden
Then according to given statements
[tex]l = 2w+10[/tex] Eqn 1
As we have to find the length of fence to fully surround garden that means the perimeter has to be found.
The formula for perimeter is given by:
[tex]P = 2(length+width)[/tex]
Putting the values
[tex]P = 2(2w+10+w)\\P = 2(3w+10)\\P = 6w+20[/tex]
Hence,
The expression for length of fence in meters is: 6w+20 meters
On April 15, 2015, Jorge buys 10 shares of Bling-Bling Inc. stock at a price of $450 per share. The share price of Bling-Bling increases to $600 on July 15, 2015. What is the percentage increase in the value of Jorge’s shares rounded to the nearest percent?
25%
33%
45%
67%
Answer:
33%
Step-by-step explanation:
Tell me if I'm wrong. :) And hope this helps.
Write a polynomial that represents the area of the square 7n-5, plz help, thank you!
Answer:
49n² - 70n + 25
Step-by-step explanation:
Area of a square = s²
Where,
s = side length = 7n - 5
Area of the square = (7n - 5)²
= (7n - 5)(7n - 5)
= 7n(7n - 5) -5(7n - 5)
= 49n² - 35n - 35n + 25 (distributive property of equality)
Add like terms
Area = 49n² - 70n + 25
Apply the distributive property to factor out the greatest common factor.
25p + 50q =
Answer:
25(p+2q)
Step-by-step explanation:
The GCF is 25, so factor out 25 and you have 25 (p + 2q)
select all the rational numbers
Answer:
B and D
Step-by-step explanation:
Answer:
B and d hope it helps
Step-by-step explanation:
hope it helps
Mel slides down waterslide A, and Victor slides down waterslide B. After 2 seconds, Mel was 50 feet in the air, and after 5 seconds, she was 35 feet in the air. After 1 second, Victor was 60 feet in the air, and after 4 seconds, he was 50 feet in the air. Who was descending at a faster rate?
Answer:
Mei descends faster
Mei's height decreases 5ft every second
Victor's height decreases 3.33 ft every second
Step-by-step explanation:
Given
Mel
[tex](x_1,y_1) = (2,50)[/tex]
[tex](x_2,y_2) = (5,35)[/tex]
Victor
[tex](x_1,y_1) = (1,60)[/tex]
[tex](x_2,y_2) = (4,50)[/tex]
Required
Who descend faster?
To do this, we simply calculate the slope/rate of both individuals
[tex]m = \frac{y_2 - y_1}{x_2 - x_1}[/tex]
For Mei:
[tex]m_1 = \frac{y_2 - y_1}{x_2 - x_1}[/tex]
[tex](x_1,y_1) = (2,50)[/tex]
[tex](x_2,y_2) = (5,35)[/tex]
[tex]m_1 = \frac{35 -50}{5 - 2}[/tex]
[tex]m_1 = \frac{-15}{3}[/tex]
[tex]m_1 = -5[/tex]
Mei descends at 5ft per second
For Victor:
[tex]m_2 = \frac{y_2 - y_1}{x_2 - x_1}[/tex]
[tex](x_1,y_1) = (1,60)[/tex]
[tex](x_2,y_2) = (4,50)[/tex]
[tex]m_2 = \frac{50-60}{4 - 1}[/tex]
[tex]m_2 = \frac{-10}{3}[/tex]
[tex]m_2 = -3.33[/tex]
Victor descends at 3.33ft per second
By comparison:
Mei descends faster
Answer:
Mel: -5, 5
Victor: -10/3, 10,3
Edge 2021
Whats type of account has a fixed interest rate, a term and a fixed date of
withdrawal? *
Answer:
A CD, or certificate of deposit, is a type of savings account with a fixed interest rate that's usually higher than a regular savings account, a fixed term length and a fixed date of withdrawal, known as the maturity date. You lock up funds in a CD for a term generally between three months and five years.
Step-by-step explanation:
What is the number that has a value 10 times the value of 0.009?
Answer:
0.09?
Step-by-step explanation:
0.009 x 10 is 0.09
Answer:
multiply 0.09 by 10 and that'd equal 0.09. A number 10 times greater then 0.009 is 0.09.
Step-by-step explanation:
Solve and check: ½ (c – 24) + 2/3c = 9
a) c = 18
b) c = 126
c) c = 1 1/6
d) c = 17
The closing stock prices of 35 U.S. semiconductor manufacturers are given as follows. 8.625; 30.25; 27.625; 46.75; 32.875; 18,25; 5; 0.125; 2.9375; 6.875; 28.25; 24.25; 21; 1,5; 30.25; 71; 43.5; 49.25; 2.5625; 31; 16.5; 9.5; 18.5; 18; 9; 10.5; 16.625; 1.25; 18; 12.87; 7; 12.875; 2.875; 60.25; 29.25
a. In words, X =
b.
i. X =
ii. Sx =
iii. n =
c. Construct a histogram of the distribution of the averages. Start at x = -0.0005. Use bar widths of ten.
d. In words, describe the distribution of stock prices.
e. Randomly average five stock prices together. (Use a random number generator.) Continue averaging five pieces together until you have ten averages. List those ten averages
f. Use the ten averages from part e to calculate the following.
i. x =
ii. Sx =
g. Construct a histogram of the distribution of the averages. Start at x = -0.0005. Use bar widths of ten.
h. Does this histogram look like the graph in part c?
i. In one or two complete sentences, explain why the graphs either look the same or look different?
j. Based upon the theory of the central limit theorem, X ~ ( , )
Answer:
The answer would be A.
Step-by-step explanation: In order to find the answer you would need A
I actually have no idea, I'm guessing- ;-;
Find the sum or difference
(4y+3)-(y-2) do help me pls i can't remember how to do these
Answer:
3y + 1
Step-by-step explanation:
(4y + 3) - (y - 2)
*subtract y from 4y because like terms must be combined*
3y + 3 - 2
*subtract 2 from 3*
3y + 1
Please answer pls and ty
Answer:
Width = 66 inches
Step-by-step explanation:
Zelda has 300 inch roll of binding for a quilt.
The length must be 84 inches
We need to find its width. Let it is b.
Let us assume that the quilt is in the shape of rectangle. The perimeter of the rectangle is given by :
P = 2(l+b)
300 = 2(84+b)
150 = 84+b
b = 150-84
b = 66 inches
So, the required width is 66 inches.
help now fast..................................
Answer:
C
Step-by-step explanation:
There are 6 units in the numberline, and 2 are shaded. So, 2/6 are shaded.
the question is in the photo
The rectangular front windshield of the bus has the length of 1.5√3 m and the width of 1.5 m . The wipers are attached to the bottom corners. If the length of each wiper is equal to the width of the windshield, find the percentage of the windshield that wipers can reach.
(Solve this task without using Trigonometry)
See the attached sketch. From their respective corners, each wiper sweeps out a portion of the total area of the windshield equal to the area of a quarter-circle with radius 1.5 m (shaded green), and they overlap in a half-lens-shaped region (shaded red). The area that the wipers together cover is equal to the sum of the green areas minus the area of the red overlap. It's easy to see that this red area is equal to the area of the highlighted circular segment (bordered in blue).
Not sure how exactly you can avoid finding the area of the segment without resorting to trigonometry, though... The radii AC and AD form an angle θ such that the segment has area
1/2 (1.5 m)² (θ - sin(θ))
but you can avoid mentioning the sine function by writing it as
1/2 (1.5 m)² (θ - √3/2)
which follows from
sin(θ) = 2 sin(θ/2) cos(θ/2) = 2 ((BD/2)/AB) ((AC/2)/AB)
and the fact that BD has length equal to the radii, since by the Pythagorean theorem
(AC/2)² + (BD/2)² = AB²
(whether this theorem falls under trigonometry is also up for debate)
You would need trig to find the measure of the angle θ as well, unless you just take for granted the fact that a triangle with side lengths 1.5√3/2, 1.5/2, and 1.5 (i.e. AC/2, BD/2, and AB), since they occur in a ratio of √3 : 1 : 2 is a 30°-60°-90° triangle, so that θ = 60° = π/3 rad.
At any rate, the percentage is about (2×(quarter-circle area) - (segment area))/(rectangle area) = 85.46%, since
• area of rectangle = (1.5 √3 m) • (1.5 m) ≈ 3.897 m²
• area of quarter-circle = π/4 (1.5 m)² ≈ 1.767 m²
• area of segment = 1/2 (1.5 m)² (π/3 - √3/2) ≈ 0.204 m²
Answer:
≈ 85.46%Step-by-step explanation:
Refer to attached
The area of coverage is the sum of two sectors of 60° and a triangle.
Find each area and calculate the percentage of covered region
Rectangle area:
A = 1.5*1.5√3 = 9√3/4 ≈ 3.8971Triangle height
h = √1.5² - (1/2*1.5√3)² = √1/4*1.5² = 1.5/2 = 3/4Since h is half of the hypotenuse, the opposite angle is 30°This leaves each sector 60°Triangle area
A = 1/2*1.5√3*3/4 = 9√3/16 ≈ 0.9742Sectors' area
A = 2*1/6*πr² = 1/3π(1.5)² = 3π/4 ≈ 2.3561Area covered by wipers
A = 0.9742 + 2.3561 = 3.3303Percentage of covered region:
3.3303/ 3.8971*100% ≈ 85.46%True or False: If f(x) = -3x^3 + 2(x + 2), then f(-2) = 24
Answer:
True
Step-by-step explanation:
When you plug in -2 for the x-values, it should be like this -3(-2)^3 + 2((-2)+2). When using the method of PEMDAS, you want to do the parentheses/exponents first since it is in order. -2 to the power of 3 is -8 for this case. Distribute 2 in -2 and 2 to get -4 + 4. Obviously. they will cancel in which you are left with -3(-8). Two negatives multiplied together equals a positive, so your final answer should be 24, in this case it is true.
NEED HELP PLEASE WITH THIS
Answer:
y = 28x
Step-by-step explanation:
if you work backwards you need to find miles per gallon which is 140/5 which is 28. x is gallons of gas used so if you multiply x by 28 will be y, the amount of miles driven.
During second period, Janet completed a grammar worksheet. She got 14 questions correct and 42 questions incorrect.
Part A: What percentage did Janet get correct
_________%
Part B: What percentage did Janet get incorrect?
A: 50%
B: 65%
C: 75%
D: 80%
Answer:
A=33.33
Step-by-step explanation:
Answer: Part A) 25%
Part B) 75%
Step-by-step explanation: Hope this helps.