Parameterize S by
[tex]\vec r(s, t) = (1-s)(1-t)\,\vec\imath + 6s(1-t)\,\vec\jmath + 6t\,\vec k[/tex]
with 0 ≤ s ≤ 1 and 0 ≤ t ≤ 1.
Take the normal vector to S to be
[tex]\vec n = \dfrac{\partial\vec r}{\partial s}\times\dfrac{\partial\vec r}{\partial t} = (36-36t)\,\vec\imath+(6-6t)\,\vec\jmath+(6-6t)\,\vec k[/tex]
with magnitude
[tex]\|\vec n\| = 6\sqrt{38}(1-t)[/tex]
Then the surface integral is
[tex]\displaystyle \iint_S xy\,\mathrm dS = 6\sqrt{38} \int_0^1\int_0^1 (1-t)\,\mathrm dt\,\mathrm ds = \boxed{3\sqrt{\frac{19}2}}[/tex]
List all the elements of the following set. Use set notation and the listing method to describe the set. { 2,4,8,...,256}
All the elements of the given set {2,4,8,...,256} are - {2, 4, 8, 16, 32,64, 128, 256} that are total 8 in numbers.
The set is formed by the number of objects in a particular manner, these objects are called elements of the set. The elements of the set are written inside a curly bracket separated by a comma in a particular or specific order.
There are two methods to represent the set and its elements that are:
Set notation: define the elements and properties of sets using symbols that help in describing the relationship between elements in the set.in this case, {[tex]2^{1},2^{2},2^{3},2^{4},2^{5},2^{6},2^{7},2^8[/tex]} as we know,
so the set notation would be :
= {x:x = [tex]2^{n}[/tex], n∈N and 1 ≤ n ≤ 8}
listing method: simple method that include the members or elements of the set are written as a list, separated by the comma and enclosed within the curly braces.The listing method: {2, 4, 8, 16, 32,64, 128, 256}\
Thus, the above mention set is all the elements of the set.
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Suppose vectors v1 ,... vp span Rn, and let T: Rn -> Rn be a linear transformation. Suppose T(vi) = 0 for i =1, ..., p. Show that T is a zero transformation. That is, show that if x is any vector in Rn, then T(x) = 0.
If the vectors [tex]\{\mathbf v_1,\mathbf v_2,\ldots,\mathbf v_p\}[/tex] span [tex]\mathbb R^n[/tex], then any vector [tex]\mathbf x\in\mathbb R^n[/tex] can be expressed as a linear combination of these vectors. This means there exist scalars [tex]\{c_1,c_2,\ldots,c_p\}[/tex] such that
[tex]\mathbf x = c_1\mathbf v_1 + c_2\mathbf v_2 + \cdots + c_p\mathbf v_p[/tex]
Since T is a linear transformation, we have for all x,
[tex]T(\mathbf x) = T(c_1\mathbf v_1 + c_2\mathbf v_2 + \cdots + c_p\mathbf v_p) \\\\ T(\mathbf x) = c_1T(\mathbf v_1) + c_2T(\mathbf v_2) + \cdots + c_pT(\mathbf v_p) \\\\ T(\mathbf x) = \mathbf 0 + \mathbf 0 + \cdots + \mathbf 0 = \mathbf 0[/tex]
» Jonah rides the train and the ferry to visit his uncle. The train ticket costs $45. The train ticket costs 5 times as much as the ferry ticket. How much does the ferry ticket cost?
The cost of Ferry ticket is $9.
What is an equation?In mathematics, an equation is a formula that expresses the equality of two expressions, by connecting them with the equals sign =.
Given that, the train ticket costs $45.
Let the cost of Ferry ticket be x.
The train ticket costs 5 times as much as the Ferry ticket.
Now, the cost of train ticket =5x
45=5x
x=$9
Therefore, the cost of Ferry ticket is $9.
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What is Histogram. Explain with an example? (Research work)
Answer: Hello There!................
A histogram is an approximate representation of the distribution of numerical data. It was first introduced by Karl Pearson.
Step-by-step explanation:
Mark me brainest please. Hope this helps. Anna ♥
Answer:
Hello! Your answer is BELOW!
Step-by-step explanation:
A histogram is an approximate representation of the distribution of numerical data. It was first introduced by Karl Pearson.
Hope I helped! Hope you make an 100%
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Which is not a rational number?
Answer:
Answer: A real number that is not rational is called irrational. Irrational numbers include √2, π, e, and φ. The decimal expansion of an irrational number continues without repeating.
5 3/4 + 3 1/2
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Answer:
37/4 is the answer
A researcher sends out a survey questionnaire to 200,000 people living in California, asking them to report how satisfied they are with their local political representatives. Of the 30,000 people who respond, 40% report being satisfied. Would it be appropriate to conclude that approximately 40% of the entire population of California is satisfied? Group of answer choices yes, as long as the 200,000 people were randomly sampled from the larger population of Californians Yes, regardless of sampling technique Probably not, people who respond to the survey may be different than people who do not respond to the survey
Answer:
I would say the last one.
Step-by-step explanation:
Political views are often reflected on every aspect of life, including whether or not the respond to a survey.
A national park has eighty thousand, nine-hundred twenty-three and eighty-six hundredths acres of land. Write in standard form
Hi :)
Eighty thousand nine hundred twenty three and eighty six hundredths
80,923.86
Please help! I can give brainliest also! Thank you!
9514 1404 393
Answer:
a) n(A∪B) = 20
b) n(A) = 31
Step-by-step explanation:
The relevant formula is ...
n(A∪B) = n(A) +n(B) -n(A∩B)
__
a) n(A∪B) = 5 +18 -3 = 20
b) 32 = n(A) +14 -13 ⇒ n(A) = 31
If you are dealt 4 cards from a deck 52 find the probability that 4 cards are clubs
Step-by-step explanation:
There are 13 clubs in the deck of 52 cards. That makes the probability of the first card being a club 13/52, which reduces to 1/4.
For the second card, there are 12 clubs in the 51 that remain, so the probability it's a club is 12/51, or 4/17.
There are now 11 clubs in the remaining 50, so the probability the third card is a club is 11/50.
Finally, you have 10 clubs out of 49 cards, making the probability that the 4th card is a club is 10/49.
To get the probability of this whole scenario, just multiply the four fractions (and simplify).
Answer:
Step-by-step explanation:
P(Clubs) = 13C4 // 52C4
The order doesn't matter in either case.
13 * 12 * 11 * 10
============
52 * 51 * 50 * 49
P(4 cards all clubs) = 11/4165
P(4 cards all clubs) = 0.002641
The quantity of a number plus 4, divided by 9
How many planes exist that pass through points A, B,
and C?
О
1
2
3
Rationalize the denominator.
Answer:
B. 27+3√5/76
Step-by-step explanation:
3/9-√5
~Multiply the conjugate to everything (9 + √5)
3(9+√5)/(9-√5)(9+√5)
~Simplify
27+3√5/76
Best of Luck!
3 2/3 x 5 please let me know the answers
Answer:
hi can u please add more to this question.. is it adding, multiplying, dividing ??
Step-by-step explanation:
I have the answers for all of them i just need someone to help me show work, please i’m really on cusp of flunking and need help
Answer:
Step-by-step explanation:
If p=(3,1) and Q=(-3,-7) find the distance PQ
Answer: The answer is 10.
standard notation 8.15×10^5
Answer:
8.15×10^5
Step-by-step explanation:
8.15×10^5
8.15×100000
815000
-3 + 8n = -5
A little help please?
Answer:
n = - 1
-------
4
Step-by-step explanation:
1.Add 3 t0 both sides of the equation.
● 8n-3= -5
● 8n-3+3= -5+3
2.Simplify.
● 8n= -5+34
● 8n= -2
3.divide both sides of the equation by same terms.
● 8n = -2
----- -----
8 8
4.simplify. divide the numbers.
n= -2
-----
8
n= -1
------
4
A tank is full of water. Find the work W required to pump the water out of the spout. (Use 9.8 m/s2 for g. Use 1000 kg/m3as the weight density of water.)
(A water tank shaped like a triangular prism is given. The base of the prism is at the top and a spout is located at the top of the tank. The dimensions of the tank are 9 meters long, 4 meters wide, and 4 meters deep. The spout is 3 meters long.)
Answer:
W = 1.06 MJ
Step-by-step explanation:
- We will use differential calculus to solve this problem.
- Make a differential volume of water in the tank with thickness dx. We see as we traverse up or down the differential volume of water the side length is always constant, hence, its always 8.
- As for the width of the part w we see that it varies as we move up and down the differential element. We will draw a rectangle whose base axis is x and vertical axis is y. we will find the equation of the slant line that comes out to be y = 0.5*x. And the width spans towards both of the sides its going to be 2*y = x.
Can someone please help
Answer:
3x - y = -6 is answerrrrrrrrrr
Write 2.06 X 1010 in standard form.
Answer:
20,600,000,000
Step-by-step explanation:
When writing a number in standard notation from scientific notation, counting decimal places is important. In this case, the exponent of 10 is 10. That means the decimal place must be moved 10 places; since it is positive the decimal place should be moved to the right. Finally, fill any empty spaces when moving the decimal point with zeros.
A rectangle has a height of 3 cm and width of 5cm. A proportional rectangle has a height of 12cm. What would be the width?
The ratio will be same
Let width be x[tex]\\ \sf\longmapsto \dfrac{3}{5}=\dfrac{12}{x}[/tex]
[tex]\\ \sf\longmapsto 3x=5(12)[/tex]
[tex]\\ \sf\longmapsto 3x=60[/tex]
[tex]\\ \sf\longmapsto x=\dfrac{60}{3}[/tex]
[tex]\\ \sf\longmapsto x=20cm[/tex]
Answer:
width=20 cm
Step-by-step explanation:
h=3 cm
w=5 cm
proportional rectangle:
height=12
Here height has become 12 by multiplying 3 by 4.Therefore to find the width do the same thing.width=5*4
=20 cm
Solve the equation.
5 = -2n
n =
Pls hurry 20 points
what is 10,000 written as a power with a base of 10
Answer:
10⁴ is 10,000 written as a power with a base of 10
Answer:
10^3
Step-by-step explanation:
10 has a decimal point at the end of it. You have to jump 3 places to get 10,000. So, the answer would be 10 to the third power, ,or 10^3
Which function is graphed?
Answer:
B
Step-by-step explanation:
Function B is graphed
Thank you
have a great day ❤️
Peace
the temperature in a room rises 1 F every 3 minutes. When the scientist enters the room, it is 50 F. a) write the equation b) what will be the temperature after 21 minutes? c) when will the temperature be 55 F ?
Answer:
equation is y= 50 + 3f
57F
15 Minutes
Step-by-step explanation:
a) the equation above because 50 is the starting temp and every 3 minutes is another degree F
b) if the temp rises 1 degree every 3 minutes, then 21/3 is 7 degrees hotter plus 50, which is 57 F.
c) if 50 plus 3f is the equation, then 3 times 5 will make 55 degrees. After 15 minutes, the temp will be 55 F.
I need help with this ASAP
Step-by-step explanation:
it's really simple.
g(f(x)) means that you use x to create f(x), and then you use this f(x) as argument in g(x).
with our functions here it means in general to use f(x) = 4 - x as argument (instead of purely x) in g(x).
g(f(x)) = 5×(4 - x) - 2 = 20 - 5x - 2 = 18 - 5x
that is the whole trick.
now, when we have a specific x value (x = 6 in our example here), it can be even simpler.
we need to "feed" 6 into f(x).
4 - x = 4 - 6 = -2
so, f(6) = -2
now this -2 becomes the argument for g(x).
5×(-2) - 2 = -10 - 2 = -12
so, g(f(6)) = -12
let's check for control and also use the functional definition of g(f(x)) we established above :
18 - 5×6 = 18 - 30 = -12
the same result, so all correct.
Exercise 1
The ratio of triangles to circles is 4 to 6.
Find 4 equivalent ratios.
4:6
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I need help pls need the answers by today
Answer:
71. 19 72. 100 73. 9 74.1 75. 90 76. 4
Step-by-step explanation:
#71.
Start with 2b-a
Plug in the given numbers where the variables are.
Now the equation is 2(12) - 5
Solve 2(12) - 5
2(12) = 24 24 - 5 = 19
#72.
Start with d(ab-c)
Plug in the given numbers where the variables are.
Now the equation is 2((5×12) - 10)
Solve in the parenthesis first.
5×12= 60 60-10=50 2(50)= 100
#73.
Start with 3+ [tex]\frac{b}{d}[/tex]
Plug in the given numbers where the variables are.
Now the equation is 3+ [tex]\frac{12}{2}[/tex]
Solve.
[tex]\frac{12}{2}[/tex] = 6 3+6 = 9
#74.
Start with [tex]\frac{4a}{b+4d}[/tex]
Plug in the given numbers where the variables are.
Now the equation is [tex]\frac{4(5)}{12+(4x2)}[/tex]
Solve.
4(5)= 20
(4×2)= 8 12+8= 20
Now the fraction is [tex]\frac{20}{20}[/tex] = 1
#75.
Start with 2a² - c
Plug in the given numbers where the variables are.
Now the equation is 2(5)² - 10
Solve 2(5) = 10 10² = 100 100-10= 90
#76.
Start with b - c + d
Plug in the given numbers where the variables are.
Now the equation is 12 - 10 + 2
Solve.
12 - 10 = 2 2 + 2 = 4
Need helppppppppppppppppp
Answer:
45.95% is the correct answer
Answer:
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