Answer:
[tex]\frac{56}{15}[/tex]
Step-by-step explanation:
Given that [tex]\vec F(x, y, z) = x^2y \hat i + xy^2 \hat j + 3xyz \hat k[/tex]
F(x, y, z) = x^2y \hat i + xy^2 \hat j + 3xyz \hat k
The flux of \vec F across the surface S is given by
[tex]\int \int _s \vec F \cdot dS[/tex]
Where the survare S is the surface of the tetrahedron bounded by the planes x = 0, y = 0, z = 0, and x + 4y + z = 4.
Now, by using the Gauss Divergence theorem:
[tex]\int \int _s \vec{F} \cdot dS=\int \int \int _v \bigtriangledown \cdot \vec F dV[/tex]...(i)
where V is the volume enclosed by the surface S and [tex]dV=dxdydz[/tex]
\bigtriangledown \cdot \vec F = \hat i \frac {\partial \vec F}{\partial x}+\hat j \frac {\partial \vec F}{\partial y}+\hat k \frac {\partial \vec F}{\partial z}
=2xy+2xy+3xy=7xy
Putting this value in equation (i), we have
\int \int \int _v \bigtriangledown \cdot \vec F dV = \int \int \int _v (7xy)dxdydz
= [tex]7\int_{y=0}^{y=1} \int_{x=0}^{x=4-4y} \left( \int_{z=0}^{z=4-x-4y}xy\;dz\right)dxdy[/tex]
[tex]=7\int_{y=0}^{y=1} \int_{x=0}^{x=4-4y} xy(4-x-4y-0)dxdy \\\\=7\int_{y=0}^{y=1} \int_{x=0}^{x=4-4y}(4xy-x^2y-4xy^2)dxdy \\\\=7\int_{y=0}^{y=1} (2x^2y-\frac 1 3 x^3y-2 x^2y^2)|_{x=0}^{x=4-4y}dy \\\\[/tex]
[tex]=7\int_{y=0}^{y=1} (2(4-4y)^2y-\frac 1 3 (4-4y)^3y-2 (4-4y)^2y^2)dy[/tex]
[tex]=7\int_{y=0}^{y=1} (32(1-y)^2y-\frac {64}{3} (1-y)^3y-32(1-y)^2y^2)dy[/tex]
[tex]=7\int_{y=0}^{y=1} (32(1-2y+y^2)y-\frac {64}{3} (1-y^3-3y+3y^2)y-32(1-2y+y^2)y^2)dy[/tex]
[tex]=7\int_{y=0}^{y=1} \{32(y-2y^2+y^3)-\frac {64}{3} (y-y^4-3y^2+3y^3)-32(y^2-2y^3+y^4)\}dy[/tex]
[tex]=7 \{32(\frac 1 2 y^2- \frac 2 3 y^3+\frac 1 4 y^3)-\frac {64}{3} (\frac 1 2 y^2-\frac 1 5 y^5-y^3+\frac 3 4 y^4)-32(\frac 1 3 y^3-\frac 1 2 y^4+\frac 1 5 y^5)\} |_{y=0}^{y=1}[/tex]
[tex]=7 \{32(\frac 1 2 - \frac 2 3 +\frac 1 4 )-\frac {64}{3} (\frac 1 2 -\frac 1 5 -1+\frac 3 4 )-32(\frac 1 3 -\frac 1 2 +\frac 1 5 )\}[/tex]
[tex]=7\times \frac {8}{15} \\\\=\frac{56}{15}[/tex]
Hence, the flux of F across S is [tex]\frac{56}{15}[/tex].
11. In a swimming race, Yvonne swam 0.18 mile.
David swam 4 times as far as Yvonne. How far
did David swim?
(A) 2.2 miles
B
0.22 mile
C.7.2 miles
D
0.72 mile
Answer: D= 0.72
Step-by-step explanation: Because 0.18 times 4 is 0.72 miles.
Answer:
D. 0.72 miles
Step-by-step explanation:
Since David swam 4 times as far is Yvonne, he swam 4 times more than 0.18. 0.18 times 4 is 0.72. If you want/need to do it in your head, just imagine 0.18 as 18, and that multiplied by 4 is 72. then move the decimal point back over before the 7, to get your answer.
Two of the other choices are clearly wrong because the actual answer is way less than the other choices (except for B). One way to quickly figure out which two (or sometimes three) are wrong is by rounding 0.18 up to 0.2. You can try this quickly because 0.2 is barely bigger than 0.18, and 0.2 is easy to multiply by 4. The answer you would get from multiplying 0.2 is not exactly correct, but gives you a general idea.
The height h, in feet of a model rocket t seconds after launch is given
by the equation h= 245t - 16t?. As the rocket descends, it deploys
a recovery parachute when it reaches 325 feet above the ground.
Express your final answer to the nearest tenth place.
What is the maximum height of the rocket?
Answer:
h_max = 324.09 ft
Step-by-step explanation:
The correct equation is;
h = 245t - 16t²
We are told that as the rocket descends, it deploys
a recovery parachute when it reaches 325 feet above the ground.
Thus;
245t - 16t² = 325
Thus;
16t² - 245t + 325 = 0
Using quadratic formula, we have the roots as;
t = 1.47s or 13.85s
We will pick the higher value.
Thus;
Maximum height will occur at t = 13.85 s
Thus, plugging in 13.85 for t into h = 245t - 16t², we have;
h_max = 245(13.85) - 16(13.85)²
h_max = 324.09 ft
is the square root of 10 greater less than or equal to 5
Answer: it is less then 5
Step-by-step explanation:
Because 10 lies between two consecutive perfect squares (in increasing order) 10 is located between the square roots of these two numbers. This means that 10 is located between 10 is less than 5.
Answer:
less than
Step-by-step explanation:
finding the square root of 10 is a bit complicated because the number 10 is not a perfect square which has a number 0 at it's unit Place. Finding the square root of a number is the reverse process of squaring the number. we can find the square root of 10 using two methods one method is to find the root value using unit places and another method is with the help of long division method.
The decay of 277 mg of an isotope is described by the function A(t)= 277e^0.019t , where t is time in years. Find the amount left after 64 years. Round your answer to the nearest mg. Show all of your work for full credit.
The decay of 277 mg of an isotope is described by the function
A(t)= 277e-0.019t,
where t is time in years.
To find the amount left after 64 years,
We substitute t = 64 in the expression.
A(t=64)= 277e-0.019(64)
or A(t=64) = 277 * e-1.216
= 277 * 0.29
= 82 mg
What is the value of the expression when a = 5, b = 4 , and c = 6?
4a/2b−c
2
5
9
10
Answer:
10...............................
Which of the following polynomials is in standard form?
z10-5z-6z2+z3
-4+z15+z5-z3
z5-2z4+z2-4z
z5+z15-z3-4
Answer:
running a two year contract is the best i have to do with my life in this world and it has a great way to go through the
Answer:
The 2nd one
Step-by-step explanation:
Luther starts jogging 8minutes on the first day and then increases his time by 4 minutes each day. How many minutes will he jog the fifth day?
Answer:
80?
Step-by-step explanation:
Answer:
(8+4)x5
Step-by-step explanation:
If the measure of angle 5 is (11 x minus 14) degrees and x = 6, which expression could represent the measure of angle 2?
Step-by-step explanation:
what are the expressions?
Jorge is running a race. In 23 of an hour he ran 225 miles. At this rate, what distance will Jorge run in one hour?
Answer:
9.7
Step-by-step explanation:
225 divided by 23 equals 9.7
What is the value of the following expression: 3.25 x 4
Answer:
13
Step-by-step explanation:
Demi has 221 songs on her phone. The songs take up 884 megabytes of storage. Each song takes up the same amount of space. How many megabytes do 135 of these songs take up?
What is the average time in seconds between 2.15 2.05 2.02
Answer:
[tex]Average = 2.073[/tex]
Step-by-step explanation:
Given:
Time: 2.15, 2.05, 2.02
Required
Determine the average
Average is calculated as thus:
[tex]Average = \frac{\sum x}{n}[/tex]
In this case:
[tex]\sum x = 2.15+2.05+2.02[/tex]
and
[tex]n = 3[/tex]
[tex]Average = \frac{\sum x}{n}[/tex] becomes
[tex]Average = \frac{2.15+2.05+2.02}{3}[/tex]
[tex]Average = \frac{6.22}{3}[/tex]
[tex]Average = 2.073[/tex]
Answer:
2.07
Step-by-step explanation:
I took the Lab and got it right
the answer for the next two questions are
The average time to the first quarter checkpoint is
2.07
seconds.
The average time to the second quarter checkpoint is
3.16
seconds.
The average time to the third quarter checkpoint is
4.11
seconds.
The average time to the finish line is
4.92
seconds.
Have a good day and good luck with the rest of your school :D
2 quarters and 2 dimes is what percent of 1 dollar?
Answer: 70%
Step-by-step explanation:
2 quarters and 2 dimes is 70 cents. 100 cents total in a dollar so no need for further calculation. 70%
you are being deal one card from a standard 52 card deck. what is the probability that you will be dealt a card other than an ace?
The probability of you getting in Ace is 4/52
Pls help I just need the answer
p(0)
17. If p (m) = 4m3 + 3, the value of
p(1)-P(-1)
divides it int
Answer:
[tex]p(1) - p(-1) =8[/tex]
Step-by-step explanation:
Given
[tex]p(m) = 4m^3 + 3[/tex]
Required
[tex]p(1) - p(-1)[/tex]
First, we calculate p(1)
Substitute 1 for m in [tex]p(m) = 4m^3 + 3[/tex]
[tex]p(1) = 4(1)^3 + 3[/tex]
[tex]p(1) = 4*1 + 3[/tex]
[tex]p(1) = 4 + 3[/tex]
[tex]p(1) = 7[/tex]
Next, we calculate p(-1)
Substitute -1 for m in [tex]p(m) = 4m^3 + 3[/tex]
[tex]p(-1) = 4(-1)^3 + 3[/tex]
[tex]p(-1) = 4*-1 + 3[/tex]
[tex]p(-1) = -4 + 3[/tex]
[tex]p(-1) = -1[/tex]
[tex]p(1) - p(-1)[/tex] is then calculated as:
[tex]p(1) - p(-1) = 7 - (-1)[/tex]
[tex]p(1) - p(-1) = 7+1[/tex]
[tex]p(1) - p(-1) =8[/tex]
if the temperature drops 7f to -17f how much did the temperature decrease
Answer:
The answer is that it decreased 24f.
A pharmacy purchases 10,000 tablets of medication D for $27,000 and sells the 10,000 tablets for $34,380. The pharmacy has total monthly sales of $648,933, inventory purchases of $466,838, and overhead of $97,000.
• What is the gross margin on medication D?
• What is the gross income for the month?
• What is the net income for the month?
Answer:
nononoonoonononoononon
Step-by-step explanation:
In triangle ABC, angle BAC = 90
Work out the size of angle DAC AND DCA?
Quick plz:)
Answer:
Easy man it 9999
Step-by-step explanation:
Find the slope of the line that passes through the pair of points.
4. (1,6), (6,-1
7
b.
7
C
7
Answer:
-7/5
Step-by-step explanation:
Which of the following is true? (1 point)
Question 19 options:
1)
|–8| < 6
2)
|–6| < |–8|
3)
|8| < |–6|
4)
|–6| < –8
PLS GOD HELP ME
Find the slope between (-1, 7) and (-3, 1).
Answer:
[tex]m=3[/tex]
General Formulas and Concepts:
Pre-Algebra
Order of Operations: BPEMDAS
Brackets Parenthesis Exponents Multiplication Division Addition Subtraction Left to RightAlgebra I
Slope Formula: [tex]m=\frac{y_2-y_1}{x_2-x_1}[/tex]Step-by-step explanation:
Step 1: Define
Point (-1, 7)
Point (-3, 1)
Step 2: Solve for x
Substitute [SF]: [tex]m=\frac{1-7}{-3+1}[/tex]Subtract/Add: [tex]m=\frac{-6}{-2}[/tex]Divide: [tex]m=3[/tex]review the graph. a ship is traveling according to the vector shown. what is the ships directional bearing?
Answer:
D on edge i got it right
Step-by-step explanation:
By reviewing the graph, when the ship is traveling so here the ship's direction should be 60 degrees west.
What is a vector?In terms of mathematics, the vector means the quantity where it does contain both magnitude and direction but does not involved the position. It involved the examples like velocity and acceleration.
According to the given graph, the movement of the ship is in south west direction along with angle 60 degrees
So, here option d is correct.
Learn more about graph here: https://brainly.com/question/18265531
34
James was participating in a school readathon and his parents agreed to donate $ 2
plus an extra dollar for every book read. The dot plot below shows this:
Searned
10
3
20
340
If James reads more books, the next point marked on the plot will be:
5
Answer:
the next point will be 4, 6
Step-by-step explanation:
if you follow the dots in the line that they make, the next on will be 4, 6
Determine the product of 2.54 and 6.3
Answer:
2.54 x 6.3 = 16.00200
Step-by-step explanation:
hope this helped!
Answer:
i think the product (multiplication) of 2.54 and 6.3 is 16.002
PLS HELP I ONLY HAVE HR
Question 4 (4 points)
(04.02)
The graph shows the amount of money paid when purchasing bags of candy at the zoo:
A graph is shown. The x-axis is labeled from 0 to 9. The y-axis is labeled from 0 to 10. Four points are shown on the graph on ordered pairs 0, 0 and 1, 2 and 2, 4 and 3, 6. These points are joined by a line. The label on the x-axis is Bags of candy. The title on the y-axis is Total cost in dollars.
What is the cost of one bag of candy? (4 points)
a
$2
b
$4
c
$0
d
$6
Answer:
a $2
Step-by-step explanation:
One of the ordered pairs were (1, 2) which meant that at 1 bag of candy, the total cost in dollars is 2 based on the labelling of the x- and y-axis. Thus, the cost of one bag of candy is $2.
Convert the measurements below:
a. 8 millimeters = ____meters
Answer:
0.008 meters
Step-by-step explanation:
Answer:
0.008 meters
Step-by-step explanation:
Hope this helps! :3
plz mark as brainliest!
WHO WANTS BRAINLIST??
Answer:
Me please
Step-by-step explanation:
I like ice cream :D
Answer:
I do!!! Please may I get it? If someone else asked and you chose them that's fine!
Step-by-step explanation:
(The upcoming and this sentence is pre-written and copy and pasted in every brainly question or comment I write or answer.) If this answer helped you please consider giving it brainliest.
- •Trix•
( Yes I know my - •Trix• thingy is not my user but its what I would change it to if I could but I can't, please address me as Trix while commenting or talking to me here.)
please help solve this.
Please help, I only have 30 minutes left! );
Answer:
(3, -1)
Step-by-step explanation: