Answers
There's nothing preventing us from computing one integral at a time:
[tex]\displaystyle \int_0^{2-x} xyz \,\mathrm dz = \frac12xyz^2\bigg|_{z=0}^{z=2-x} \\\\ = \frac12xy(2-x)^2[/tex]
[tex]\displaystyle \int_0^{1-x}\int_0^{2-x}xyz\,\mathrm dz\,\mathrm dy = \frac12\int_0^{1-x}xy(2-x)^2\,\mathrm dy \\\\ = \frac14xy^2(2-x)^2\bigg|_{y=0}^{y=1-x} \\\\= \frac14x(1-x)^2(2-x)^2[/tex]
[tex]\displaystyle\int_0^1\int_0^{1-x}\int_0^{2-x}xyz\,\mathrm dz\,\mathrm dy\,\mathrm dx = \frac14\int_0^1x(1-x)^2(2-x)^2\,\mathrm dx[/tex]
Expand the integrand completely:
[tex]x(1-x)^2(2-x)^2 = x^5-6x^4+13x^3-12x^2+4x[/tex]
Then
[tex]\displaystyle\frac14\int_0^1x(1-x)^2(2-x)^2\,\mathrm dx = \left(\frac16x^6-\frac65x^5+\frac{13}4x^4-4x^3+2x^2\right)\bigg|_{x=0}^{x=1} \\\\ = \boxed{\frac{13}{240}}[/tex]
Related Questions
twice the difference of a number and 8 is 6. use the variable x for the unknown number.
Answers
Answer:
11
Step-by-step explanation:
Unknown number = x
If twice the difference of x and 8 is 6:
2(x-8) = 6
2x-16 = 6
2x = 6 + 16
2x = 22
x = 22/2
x = 11
Answer from Gauthmath
Which of the following equations shows the linear relationship between the x and y variables shown in the table of ordered pairs? A. y = x + 5 B. y = 2x C. y = x + 6 D. y = x - 5
Answers
Answer:
The linear relationship will be B
Answer:
b
Step-by-step explanation:
Trong một lớp học có $35$ sinh viên nói được tiếng Anh, $25$ sinh viên nói được tiếng Nhật trong đó có $10$ sinh viên nói được cả tiếng Anh và tiếng Nhật. Mỗi sinh viên trong lớp nói được ít nhất một trong hai: tiếng Anh hoặc tiếng Nhật. Hỏi sỹ số của lớp là bao nhiêu
Answers
Answer:
please write this question in English then I give answer
Please I need help please!!!!
I need the answer ASAP…!!!!!!
If you know the answer please tell me
Answers
Answer:
x=−16/3 or x=2
Step-by-step explanation:
Step 1: Simplify both sides of the equation.
3x2+10x−8=24
Step 2: Subtract 24 from both sides.
3x2+10x−8−24=24−24
3x2+10x−32=0
Step 3: Factor left side of equation.
(3x+16)(x−2)=0
Step 4: Set factors equal to 0.
3x+16=0 or x−2=0
Help.. what does Y=
Answers
Answer:
The answer is B. 3
Step-by-step explanation:
The right angle points at side C which is the biggest side of a triangle and the smallest side is half of what side C is which is 3
Explanation: calculator.net, triangle calculator !
The Anthonys bought a home in January and borrowed $376000 to finance it. The mortgage interest and principal payment is $2011 per month. In the first year, they paid $22175 in interest, $7652 in principal, and $8312 in property taxes. They are in the 24% marginal tax bracket. Approximately, how much will they save in federal income taxes from home ownership the first year, if itemizing deductions?
Answers
Find the area of the circle. Use 3.14 for tt. d = 6 ft A = [?] ft2 A=Tr2
Answers
d=6ft
According to formula A=πr²
first we need 'r'
Hence,
as, r=d/2
r=6ft/2
r=3ft
A=πr²
A=3.14(3ft)²
A=3.14×9ft²
A=28.26ft²
a) Express the prime number 31 as the difference of two squares? 31 =
Answers
Answer:
31 = 16²-15²
Step-by-step explanation:
16² = 256
15² = 225
256 - 225 = 31
∠B=
Round to nearest hundredth
Hurry pls 50 points
I’ll mark brainliest if anyone answers in under 5 min
Answers
Answer:
Step-by-step explanation:
Calculate the sum and enter it below.
-4 + 16
Answer here
Answers
Adding a negative number to a positive number is like subtracting
Answer:
12
Step-by-step explanation:
because 16 + -4 is like 16-4 which is 12
Why school sucks: A makes you learn stuff you don’t care about and will never use B teachers suck and don’t teach property C they don’t teach you useful things like taxes bills ect D they overwork students E its not even about learning anymore all goals are is just good grades.
Why is our future determined on letters on a piece of paper? I’d rather die then be in this society
Answers
Answer:
I think answer is E
Step-by-step explanation:
write your answer as an integer or as a decimal rounded to the nearest tenth.
Answers
Answer:
6.43
Step-by-step explanation:
Cosine: cos(θ) = Adjacent / Hypotenuse
cosine of 39 degrees = 5/x
.77714596145 = 5/x
x = 5/.77714596145
x= 6.43379782952
A local cinema reduced its ticket prices by 15% which means a ticket now costs £10.88. how much was a ticket before the reduction?
Answers
What is the maximum of f(x)= sin(x)?
-2π
-1
1
2π
Answers
Answer:
1
Step-by-step explanation:
the maximum of f(X)=sin(X) is 1
(03.04) Use the graph below for this question: What is the average rate of change from x = −3 to x = 5? (1 point)
A.−1
B.0
C.1
D.8
Answers
Answer:
B. 0
Step-by-step explanation:
Rate of change from x = -3 to x = 5
Rate of change = [tex] \frac{f(b) - f(a)}{b - a} [/tex]
where, from the graph, we have:
a = -3, f(a) = -1,
b = 5, f(b) = -1,
Plug in the values
Rate of change = [tex] \frac{-1 -(-1)}{5 - (-3)} [/tex]
Rate of change = [tex] \frac{0}{8} [/tex]
Rate of change = 0
A student majoring in accounting is trying to decide on the number of firms to which he should apply. Given his work experience and grades, he can expect to receive a job offer from 70% of the firms to which he applies. The student decides to apply to only four firms.
(a) What is the probability that he receives no job offer?
(b) How many job offers he expects to get?
(c) What is the probability that more than half of the firms he applied do not make him any offer?
(d) What assumptions do you need to make to find the probabilities? To increase the chance of securing more job offers, the student decides to apply to as many companies as possible, he sent out 60 applications to all different accounting firms.
(e) What is the probability of him securing more than 3 offers?
Answers
Answer:
a) 0.0081 = 0.81% probability that he receives no job offer
b) He expects to get 2.8 job offers.
c) 0.0837 = 8.37% probability that more than half of the firms he applied do not make him any offer.
d) Each job must be independent of other jobs. Additionaly, if [tex]np \geq 10[/tex] and [tex]n(1-p) \geq 10[/tex], the normal approximation to the binomial distribution can be used.
e) 0.2401 = 24.01% probability of him securing more than 3 offers.
Step-by-step explanation:
For each application, there are only two possible outcomes. Either he gets an offer, or he does not. The probability of getting an offer for a job is independent of any other job, which means that the binomial probability distribution is used to solve this question.
Binomial probability distribution
The binomial probability is the probability of exactly x successes on n repeated trials, and X can only have two outcomes.
[tex]P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}[/tex]
In which [tex]C_{n,x}[/tex] is the number of different combinations of x objects from a set of n elements, given by the following formula.
[tex]C_{n,x} = \frac{n!}{x!(n-x)!}[/tex]
And p is the probability of X happening.
He can expect to receive a job offer from 70% of the firms to which he applies.
This means that [tex]p = 0.7[/tex]
The student decides to apply to only four firms.
This means that [tex]n = 4[/tex]
(a) What is the probability that he receives no job offer?
This is [tex]P(X = 0)[/tex]. So
[tex]P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}[/tex]
[tex]P(X = 0) = C_{4,0}.(0.7)^{0}.(0.3)^{4} = 0.0081[/tex]
0.0081 = 0.81% probability that he receives no job offer.
(b) How many job offers he expects to get?
The expected value of the binomial distribution is:
[tex]E(X) = np[/tex]
In this question:
[tex]E(X) = 4(0.7) = 2.8[/tex]
He expects to get 2.8 job offers.
(c) What is the probability that more than half of the firms he applied do not make him any offer?
Less than 2 offers, which is:
[tex]P(X < 2) = P(X = 0) + P(X = 1)[/tex]
So
[tex]P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}[/tex]
[tex]P(X = 0) = C_{4,0}.(0.7)^{0}.(0.3)^{4} = 0.0081[/tex]
[tex]P(X = 1) = C_{4,1}.(0.7)^{1}.(0.3)^{3} = 0.0756[/tex]
Then
[tex]P(X < 2) = P(X = 0) + P(X = 1) = 0.0081 + 0.0756 = 0.0837[/tex]
0.0837 = 8.37% probability that more than half of the firms he applied do not make him any offer.
(d) What assumptions do you need to make to find the probabilities? To increase the chance of securing more job offers, the student decides to apply to as many companies as possible, he sent out 60 applications to all different accounting firms.
Each job must be independent of other jobs. Additionaly, if [tex]np \geq 10[/tex] and [tex]n(1-p) \geq 10[/tex], the normal approximation to the binomial distribution can be used.
(e) What is the probability of him securing more than 3 offers?
Between 4 and n, since n is 4, 4 offers, so:
[tex]P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}[/tex]
[tex]P(X = 4) = C_{4,4}.(0.7)^{4}.(0.3)^{0} = 0.2401[/tex]
0.2401 = 24.01% probability of him securing more than 3 offers.
Determine if the table below represents a linear function. If so, what's the rate of change?
A) No; it's a non-linear function.
B) Yes; rate of change = 4
C) Yes; rate of change = 2
D) Yes; rate of change = 3
Answers
Answer:
A
Step-by-step explanation:
Its not a linear function; there is no consistent rate of change between each of the points.
Please Help!
What is the locus of the midpoints of all chords that can be drawn from a given point on a circle with a radius of 6.
Answers
The locus of the midpoints of all chords that can be drawn from a given fixed point [tex](a,b)[/tex] on a circle with a radius of 6 units, is a circle of radius 3 units with center at a point whose x & y coordinates are shifted from the center of the given circle by [tex]\frac{a}{2}[/tex] and [tex]\frac{b}{2}[/tex] respectively.
Given: A circle of radius 6 units
To find: The locus of the midpoint of all chords that can be drawn from a given point on the circle.
To find the required locus, we need to know the following:
Locus of a moving point is the trajectory of that point. It is the geometrical figure represented by the equation which is satisfied by the coordinates of the moving point.A chord of a circle is a line segment joining any points of a circle.Equation of a circle with center at origin and radius of [tex]r[/tex] units is [tex]x^{2} +y^{2} =r^{2}[/tex] According to the midpoint formula, the coordinates of the midpoint of the line segment joining the points [tex](x_{1},y_{1})[/tex] and [tex](x_{2},y_{2})[/tex] is [tex](\frac{x_{1}+x_{2} }{2} ,\frac{y_{1}+y_{2} }{2} )[/tex]Let, without loss of generality, the given circle be centered at the origin. Even if it is not, we can shift the origin to the center of the given circle with coordinate transformation.
Then, the equation of the given circle is [tex]x^{2}+y^{2} =6^{2}[/tex], that is, [tex]x^{2}+y^{2} = 36[/tex]
Let the coordinates of the given fixed point be [tex](a,b)[/tex]
Let the coordinates of any point on the circle be [tex](p,q)[/tex] and let the coordinates of the midpoint of the chord joining the points [tex](a,b)[/tex] and [tex](p,q)[/tex] be [tex](h,k)[/tex]
We have to find the locus of [tex](h,k)[/tex]
Then, using the midpoint formula,
[tex](h,k)=(\frac{a+p}{2} ,\frac{b+q}{2})[/tex]
On solving, we get,
[tex]p=2h-a,q=2k-b[/tex]
Since [tex](a,b)[/tex] and [tex](p,q)[/tex] are both points on the given circle, they satisfy the equation of the circle, [tex]x^{2}+y^{2} = 36[/tex]
Then,
[tex]a^{2} +b^{2} =36[/tex]
[tex]p^{2} +q^{2} =36[/tex]
Substituting [tex]p=2h-a,q=2k-b[/tex] in [tex]p^{2} +q^{2} =36[/tex], we have,
[tex](2h-a)^{2} +(2k-b)^{2} =36[/tex]
[tex](2(h-\frac{a}{2}) )^{2} +(2(k-\frac{b}{2}))^{2} =36[/tex]
[tex]4(h-\frac{a}{2})^{2} +4(k-\frac{b}{2})^{2} =36[/tex]
[tex](h-\frac{a}{2})^{2} +(k-\frac{b}{2})^{2} =\frac{36}{4}[/tex]
[tex](h-\frac{a}{2})^{2} +(k-\frac{b}{2})^{2} =9[/tex]
[tex](h-\frac{a}{2})^{2} +(k-\frac{b}{2})^{2} =3^{2}[/tex]
This is the locus of the point [tex](h,k)[/tex]
Replace [tex](h,k)=(x,y)[/tex] to get,
[tex](x-\frac{a}{2})^{2} +(y-\frac{b}{2})^{2} =3^{2}[/tex]
This is the equation of a circle with center at [tex](\frac{a}{2} ,\frac{b}{2} )[/tex] and radius 3 units.
Thus, we can conclude that the locus of the midpoints of all chords that can be drawn from a given fixed point [tex](a,b)[/tex] on a circle with a radius of 6 units, is a circle of radius 3 units with center at a point whose x & y coordinates are shifted from the center of the given circle by [tex]\frac{a}{2}[/tex] and [tex]\frac{b}{2}[/tex] respectively.
Learn more about locus here:
https://brainly.com/question/23824483
What is the common ratio for this geometric sequence?
27, 9, 3, 1, ...
Answers
Answer:
a multiple of 3.
Step-by-step explanation:
1x3=3
3x3=9
9x3=27
d(1)=2
d(n)=d(n−1)⋅(−2)^n
What is the third term in the sequence?
Answers
Answer:
- 16
Step-by-step explanation:
The way this is given, you have to find the second term before you can fine the third.
a2 = d(n - 1) * (-2)^2
a2 = 2 * (-2)^2
a2 = 2 * 4
a2 = 8
a3 = d(3 - 1) * (-2)^3
a3 = 2 * (-2)^3
a3 = 2 * - 8
a3 = - 16
Find y' for the following.
Answers
Answer:
[tex]\displaystyle y' = \frac{5x - 2xy^2}{2y(x^2 - 3y)}[/tex]
General Formulas and Concepts:
Calculus
Differentiation
DerivativesDerivative NotationDerivative Property [Multiplied Constant]: [tex]\displaystyle \frac{d}{dx} [cf(x)] = c \cdot f'(x)[/tex]
Derivative Property [Addition/Subtraction]: [tex]\displaystyle \frac{d}{dx}[f(x) + g(x)] = \frac{d}{dx}[f(x)] + \frac{d}{dx}[g(x)][/tex]
Basic Power Rule:
f(x) = cxⁿf’(x) = c·nxⁿ⁻¹Derivative Rule [Product Rule]: [tex]\displaystyle \frac{d}{dx} [f(x)g(x)]=f'(x)g(x) + g'(x)f(x)[/tex]
Derivative Rule [Chain Rule]: [tex]\displaystyle \frac{d}{dx}[f(g(x))] =f'(g(x)) \cdot g'(x)[/tex]
Implicit Differentiation
Step-by-step explanation:
Step 1: Define
Identify
[tex]\displaystyle 5x^2 - 2x^2y^2 + 4y^3 - 7 = 0[/tex]
Step 2: Differentiate
Implicit Differentiation: [tex]\displaystyle \frac{dy}{dx}[5x^2 - 2x^2y^2 + 4y^3 - 7] = \frac{dy}{dx}[0][/tex]Rewrite [Derivative Property - Addition/Subtraction]: [tex]\displaystyle \frac{dy}{dx}[5x^2] - \frac{dy}{dx}[2x^2y^2] + \frac{dy}{dx}[4y^3] - \frac{dy}{dx}[7] = \frac{dy}{dx}[0][/tex]Rewrite [Derivative Property - Multiplied Constant]: [tex]\displaystyle 5\frac{dy}{dx}[x^2] - 2\frac{dy}{dx}[x^2y^2] + 4\frac{dy}{dx}[y^3] - \frac{dy}{dx}[7] = \frac{dy}{dx}[0][/tex]Basic Power Rule [Product Rule, Chain Rule]: [tex]\displaystyle 10x - 2 \Big( \frac{d}{dx}[x^2]y^2 + x^2\frac{d}{dx}[y^2] \Big) + 12y^2y' - 0 = 0[/tex]Basic Power Rule [Chain Rule]: [tex]\displaystyle 10x - 2 \Big( 2xy^2 + x^22yy' \Big) + 12y^2y' - 0 = 0[/tex]Simplify: [tex]\displaystyle 10x - 4xy^2 - 4x^2yy' + 12y^2y' = 0[/tex]Isolate y' terms: [tex]\displaystyle -4x^2yy' + 12y^2y' = 4xy^2 - 10x[/tex]Factor: [tex]\displaystyle y'(-4x^2y + 12y^2) = 4xy^2 - 10x[/tex]Isolate y': [tex]\displaystyle y' = \frac{4xy^2 - 10x}{-4x^2y + 12y^2}[/tex]Simplify: [tex]\displaystyle y' = \frac{5x - 2xy^2}{2y(x^2 - 3y)}[/tex]Topic: AP Calculus AB/BC (Calculus I/I + II)
Unit: Differentiation
Book: College Calculus 10e
Transposition
make (m) the subject.
E = mc²
Answers
Answer:
m = [tex]\frac{E}{c^2}[/tex]
Step-by-step explanation:
Given
E = mc² ( isolate m by dividing both sides by c² )
[tex]\frac{E}{c^2}[/tex] = m
Answer:
m=E over c2
Step-by-step explanation:
u divide both sides by c2.then on the right side the c2 cancel each other .
then u will m=E over c2
7,25 x (y+5,6)=58 vậy y =
Answers
Answer:
y=2,4
Step-by-step explanation:
7,25x( y+5,6)=58
7,25y+ 40,6=58
7,25y=58-40,6
y=17,4:7,25
y=2,4
x
Drag the numbers to the boxes to order them from least to greatest value. Please answerr quick
Answers
Answer:
Please what is the first value there?
x is the same as 1x or 1
√5 = 2.2360679775
(2)1/2 is the same as 5/2 or 2.5
√7 = 2.64575131106
√11 = 3.31662479036
3.5
least to greatest:
x < √5 < (2)1/2 < √7 < √11 < 3.5
White colour is painted in 2 ft wide which lies inside from both sides in the basketball court of length 78 ft and breadth 46 ft . find the area of the painted part.
Answers
Answer:
L1=78
W1=46
L2=78+4=82
W2=46+4=50
Area=L2×W2-L1×W1
82×50-78×46
Ans- 512ft^2
Two angles of a triangle have the same measure.
If two sides have lengths 15 and 20, what is the
greatest possible value of the perimeter of the
triangle?
Answers
9514 1404 393
Answer:
55 units
Step-by-step explanation:
If two angles have the same measure, the triangle is isosceles. That means two sides have the same measure. Since the two given sides are different measures, the remaining side must be one of those. The perimeter will be greatest if the congruent sides are the longest. The greatest perimeter is ...
15 + 20 + 20 = 55 . . . units
Solve 3(5x + 7) = 9x + 39.
O A. X=-3
B. X= -10
O c. x = 10
O D. x= 3
Answers
Answer:
x=3
Step-by-step explanation:
3(5x + 7) = 9x + 39
15x + 21 = 9x + 39
15x - 9x = 39 - 21
6x = 18
x = 3
0.5 kilograms (kg) is equal to how many ounces? Round your answer to the
Answers
Answer:
17.637 ounces
Step-by-step explanation:
35.274 ounces is 1 kilogram so divide 35.274 by 2
A coffee pot holds 3 3/4 quarts of coffee. How much is this in cups.
Answers
Answer: 15 cups
Step-by-step explanation:
Oscar has 1/5 of a jar of mustard. He puts equal amounts of the mustard onto 7 sandwiches and uses all of the mustard. What fraction of a jar of mustard does each sandwich have?
Answers
Answer:
1/35 jar of mustard yuh yuh
