PLEASE HELP ASAP!!! CORRECT ANSWER ONLY PLEASE!!!

Evaluate.

To evaluate the surface integral [tex]\( \iint_S xy \, dS \)[/tex] over the triangular region with vertices[tex]\((1,0,0)\), \((0,8,0)\), and \((0,0,8)\):[/tex]

1. **Equation of the plane**:

  8x + y + z = 8.

2. **Parametrize the surface**:

 [tex]\[   \mathbf{r}(x, y) = (x, y, 8 - 8x - y).   \][/tex]

3. **Normal vector**:

  [tex]\[   \mathbf{N} = (8, 8, 1), \quad |\mathbf{N}| = \sqrt{129}.   \][/tex]

4. **Surface integral setup**:

  [tex]\[   \iint_D xy \sqrt{129} \, dA, \quad \text{with} \quad D: \int_0^1 \int_0^{8(1-x)} xy \, dy \, dx.   \][/tex]

5. **Evaluate the integral**:

[tex]\[   \sqrt{129} \int_0^1 32x (1-x)^2 \, dx = \frac{8 \sqrt{129}}{3}.   \][/tex]

Thus, the value of the surface integral [tex]\( \iint_S xy \, dS \) is \( \frac{8 \sqrt{129}}{3} \).[/tex]

To evaluate the surface integral [tex]\( \iint_S xy , dS )[/tex], where ( S ) is the triangular region with vertices (1, 0, 0) ,  (0, 8, 0) , and  (0, 0, 8) , we can follow these steps:

1. Determine the equation of the plane containing the triangle:

  The vertices of the triangle are (1, 0, 0), (0, 8, 0), and (0, 0, 8). The equation of the plane can be found using these points.

  The general form of a plane equation is (Ax + By + Cz = D).

  Substituting the points:

[tex]- For \((1, 0, 0)\): \(A(1) + B(0) + C(0) = D \rightarrow A = D\).[/tex]

 [tex]- For \((0, 8, 0)\): \(A(0) + B(8) + C(0) = D \rightarrow 8B = D \rightarrow B = \frac{D}{8}\).[/tex]

[tex]- For \((0, 0, 8)\): \(A(0) + B(0) + C(8) = D \rightarrow 8C = D \rightarrow C = \frac{D}{8}\).[/tex]

  So, (D = A), [tex]\(B = \frac{A}{8}\), and \(C = \frac{A}{8}\).[/tex]

  Using (A = 8) (chosen for simplicity):

  - (A = 8),

  - (B = 1),

  - (C = 1),

  - (D = 8).

  Thus, the plane equation is (8x + y + z = 8).

2. Parametrize the surface:

  We can use (x) and (y) as parameters. From the plane equation, we get (z = 8 - 8x - y).

  Let ( (x, y) ) be the parameters. The surface can be parametrized as:

 [tex]\[ \mathbf{r}(x, y) = (x, y, 8 - 8x - y). \][/tex]

3. Find the normal vector and its magnitude:

  The normal vector [tex]\( \mathbf{N} \)[/tex] can be found from the cross product of the partial derivatives of [tex]\(\mathbf{r}\)[/tex] with respect to (x) and (y).

[tex]\[ \mathbf{r}_x = \frac{\partial \mathbf{r}}{\partial x} = (1, 0, -8), \][/tex]

 [tex]\[ \mathbf{r}_y = \frac{\partial \mathbf{r}}{\partial y} = (0, 1, -1). \][/tex]

 [tex]\[ \mathbf{N} = \mathbf{r}_x \times \mathbf{r}_y = \begin{vmatrix} \mathbf{i} & \mathbf{j} & \mathbf{k} \\ 1 & 0 & -8 \\ 0 & 1 & -1 \\ \end{vmatrix} = (8, 8, 1). \][/tex]

  The magnitude of [tex]\( \mathbf{N} \)[/tex] is:

[tex]\[ |\mathbf{N}| = \sqrt{8^2 + 8^2 + 1^2} = \sqrt{64 + 64 + 1} = \sqrt{129}. \][/tex]

4. Surface integral:

  The surface integral is given by:

[tex]\[ \iint_S xy \, dS = \iint_D xy |\mathbf{N}| \, dA, \][/tex]

  where (D) is the projection of (S) on the (xy)-plane.

  From the vertices, (D) is a triangular region with vertices (1,0), ((0,8), and (0,0).

5. Set up the integral in (xy) coordinates:

  We can describe (D) as:

[tex]\[ \iint_D xy \, \sqrt{129} \, dA. \][/tex]

  The bounds for (x) and (y) are:

[tex]\[ \int_0^1 \int_0^{8(1-x)} xy \, dy \, dx. \][/tex]

6. Evaluate the integral:

 [tex]\[ \sqrt{129} \int_0^1 \int_0^{8(1-x)} xy \, dy \, dx. \][/tex]

  Evaluate the inner integral with respect to (y):

[tex]\[ \int_0^{8(1-x)} xy \, dy = x \left[ \frac{y^2}{2} \right]_0^{8(1-x)} = x \left( \frac{(8(1-x))^2}{2} \right) = x \left( \frac{64(1-x)^2}{2} \right) = 32x (1-x)^2. \][/tex]

  So the integral becomes:

[tex]\[ \sqrt{129} \int_0^1 32x (1-x)^2 \, dx. \][/tex]

  Let ( u = 1-x ). Then ( du = -dx ), and the limits change from ( x = 0 ) to ( u = 1 ), and ( x = 1 ) to ( u = 0 ):

[tex]\[ \sqrt{129} \int_1^0 32(1-u) u^2 (-du) = \sqrt{129} \int_0^1 32(1-u) u^2 \, du. \][/tex]

  Expand and integrate:

 [tex]\[ \sqrt{129} \int_0^1 32 (u^2 - u^3) \, du = 32 \sqrt{129} \left[ \frac{u^3}{3} - \frac{u^4}{4} \right]_0^1 = 32 \sqrt{129} \left( \frac{1}{3} - \frac{1}{4} \right). \][/tex]

  Simplify:

 [tex]\[ 32 \sqrt{129} \left( \frac{4}{12} - \frac{3}{12} \right) = 32 \sqrt{129} \left( \frac{1}{12} \right) = \frac{32 \sqrt{129}}{12} = \frac{8 \sqrt{129}}{3}. \][/tex]

Thus, the value of the surface integral[tex]\( \iint_S xy \, dS \) is \( \frac{8 \sqrt{129}}{3} \).[/tex]

Answer:

Step-by-step explanation:

Essentially, what you have is a fraction divided by a fraction.  The rule there is to bring up the bottom fraction and then flip it to multiply.  That would look like this:

[tex]\frac{b^4}{2a^2}[/tex]×[tex]\frac{a}{b^3}[/tex]

Now you can do some canceling out of like terms.  There is a b^3 in the denominator and a b^4 in the numerator.  You can take 3 b's out of 4, so the b^3 cancels completely out with the b^4, leaving only one b behind.  The a in the numerator cancels with one of the a's in the a^2, leaving one behind.  So the answer to this is:

[tex]\frac{b}{2a}[/tex]

Answer:

  ∠FIG = (47/2)° = 23.5° . . . . . rounds to 24°

Step-by-step explanation:

The value of x can be found from ...

  72 = 3x+3 . . . . the central angle and the arc measure are the same

  24 = x+1 . . . . . divide by 3

  23 = x . . . . . . . .subtract 1

The measure of ∠FIG is half the difference of the arc measures FG and RZ, so is ...

  m∠FIG = (1/2)(3x+3 - (x+2)) = (1/2)(2x +1) = x +1/2

  m∠FIG = 23 1/2 . . . . degrees

_____

Perhaps you're supposed to round this to 24°.

i think its letter A. The outback seems very dry and desert like

Answer:

Dry desert

Step-by-step explanation:

did the quiz

The slope is 4/6 because its going up by 4 over by 6 .hope this helps

Answer:

slope = [tex]\frac{2}{3}[/tex]

Step-by-step explanation:

Calculate the slope m using the slope formula

m = (y₂ - y₁ ) / (x₂ - x₁ )

with (x₁, y₁ ) = (0, - 4) and (x₂, y₂ ) = (6, 0) ← 2 points on the line

m = [tex]\frac{0+4}{6-0}[/tex] = [tex]\frac{4}{6}[/tex] = [tex]\frac{2}{3}[/tex]

Answer:

-2

Step-by-step explanation:

5x+45=35

Next step--> subtract 45 from 35 to start to get x by itself

5x= -10

Next divide by 5 on both sides so x is by itself to get

x=.  -2

Answer:

x = - 2

Step-by-step explanation:

5x + 45 = 35

5x = 35 - 45

x = - 10

x = - 10 ÷ 5

x = - 2

Answer:

b

Step-by-step explanation:

(-2x³ - 4x²+ 9x² + 18x - 19x - 38 + 40)

÷ (x + 2)

[-2x²(x+2) + 9x(x+2) - 19(x+2) + 40]

÷ (x+2)

-2x² + 9x - 19 + 40/(x+2)

Answer:

i)

The confidence interval is at 90%

ii)

The margin of error is 5%

iii)

The 90% confidence interval is (70%, 80%)

iv)

We are 90% confident that the average score of seniors in the field test is between 70% and 80%.

Step-by-step explanation:

i)

The confidence interval is at 90%

We are informed that the exam creator claims that on this particular exam, nine times out of ten, seniors will have an average score within 5% of 75%. This implies that we are 9 times out of 10 confident that seniors will have an average score within 5% of 75%.

The level of confidence is thus;

(9/10)*100 = 90%

ii)

The margin of error is 5% or equivalently 0.05

We are informed that the exam creator claims that on the same exam, nine times out of ten, seniors will have an average score within 5% of 75%.

Since the average score is within 5%, the margin of error is 5%

iii)

A confidence interval is calculated using the formula;

point estimate ± margin of error

Our point estimate is 75%

Our margin of error is 5%

The 90% confidence interval is thus;

75% ± 5% = (70%, 80%)

iv)

The 90% confidence interval is interpreted as;

We are 90% confident that the average score of seniors in the field test is between 70% and 80%.

This is a confidence interval for the mean, the level of confidence is 90% and our confidence interval is (70%, 80%).

Answer:

False

Step-by-step explanation:

we know that

1 yard= 36 inches

To convert 360 inches to yards

Multiply

(360)*(1/36)=10 yards

therefore

You would use the ratio 1 yard over 36 inches

Answer:

false

Step-by-step explanation:

Step-by-step explanation:

There are five ways to find if two triangles are congruent: SSS, SAS, ASA, AAS and HL.

SSS (side, side, side) SSS stands for "side, side, side" and means that we have two triangles with all three sides equal. ...

SAS (side, angle, side) ...

ASA (angle, side, angle) ...

AAS (angle, angle, side) ...

HL (hypotenuse, leg)

Answer:

HL, ASA, SAS

Step-by-step explanation:

Hypotenuse Leg

Angle, side, angle

side, angle, side

Answer:

15%

Step-by-step explanation:

The population proportion can be estimated as the sample proportion.

6 / 40 = 0.15

Approximately 15% of the computers have viruses.

Answer: Hence, there are 15% of computers have viruses.

Step-by-step explanation:

Since we have given that

Total computers in an office = 500

Number of computers to be inspected = 40

Number of computers had viruses = 6

We need to find the percentage of the computers in the building that have viruses.

So, Percentage of computers in the buildings have viruses is given by

[tex]\dfrac{6}{40}\times 100\\\\=\dfrac{600}{40}\\\\=15\%[/tex]

Hence, there are 15% of computers have viruses.

Answer:

1/2

To simplify 12/24 you have to find a common multiple. a common multiple is 12. you see how many times 12 goes into each number. 12/12 is 1 and 24/12 is to. therefore 1/2 is the correct answer

The ratio of multiplication problems to division problems on the given math test is 1/2.

To answer the question, you need to set up a ratio between the number of multiplication problems and the number of division problems. In this case, you have 12 multiplication problems and 24 division problems.

The ratio would be set up as 12 (multiplication problems) to 24 (division problems), written as 12/24 in fractional form. However, we need to reduce this to its simplest form. Both 12 and 24 can be divided by 12, simplifying the ratio to its simplest form of 1/2.

Therefore, the ratio of multiplication problems to division problems on this math test is 1/2.

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The area of one face would he h^2.

There are 6 faces, so the total surface area would be h^2 x 6

Replace total surface area with 2.16, so you now have:

2.16 = h^2 x 6

Now we can solve for h.

Divide both sides by 6:

h^2 = 2.16/6

Take the square root of both sides:

h = √2.16/6

The answer is A.

Answer:

x=6

Step-by-step explanation:

Isolate the variable by dividing each side by factors that don't contain the variable.

Answer:

4x² + 22x − 1 = 0

Step-by-step explanation:

Start off with the standard formula to finding area with polynomials and quadratic functions.

(2x + 5)(2x + 6)

Work out like a normal binomial.

4 + 22x + 30 - 31

(You're subtracting 31 to take out the minimum of what the frame has to be)

4 + 22x - 1 = 0

Answer:

4x² + 22x − 1 = 0

Answer:

The correct option would be D, f(x)=2^x-3

Step-by-step explanation:

You can immediatly cross out options A and B because it cannot be negative. If it was negative, the graph would be going the opposite direction, it would curve closer to the negative numbers that the positive. We can cross out C because if it was -2, then it would cross the y-axis at -1 rather than -2.

hope this helps :)

Answer:

The system that models the situation is:

[tex]\left \{{{2x + y = 24} \atop {2x - y = 12}} \right.[/tex]

The solution is:

(9, 6)

Step-by-step explanation:

We must write the equations as indicated in the problem.

The sum of twice a number and another number is 24

a number:  x

other number:  y

Then

[tex]2x + y = 24[/tex]

The difference of twice the first number and the other number is 12

first number: x

other number:  y

Then:

[tex]2x - y = 12[/tex]

The system that models the situation is:

[tex]\left \{{{2x + y = 24} \atop {2x - y = 12}} \right.[/tex]

To solve the system we add both equations to find the value of x

[tex]2x + y = 24\\\\2x - y = 12[/tex]

---------------------

[tex]4x +0 = 36\\\\x=\frac{36}{4}\\\\x=9[/tex]

[tex]2(9) +y = 24\\\\y=24-18\\\\y=6[/tex]

The solution is:

(9, 6)

Answer:

  1/2

Step-by-step explanation:

cos(θ) = √(1 -sin(θ)²) = √(1 -3/4) = √(1/4)

cos(θ) = 1/2

Answer:

The answer is A I just looked it up on mathaway and it is never wrong

Step-by-step explanation:

Standard form always has the largest coefficients first

Answer:

A

Step-by-step explanation:

When putting polynomials into standard form, the highest degree goes first.

(for example 5x³ + x² + 8x + 9)

Answer:

D. Up

Step-by-step explanation:

When a parabola has the form  [tex]y=ax^2+bx+c[/tex] , It is vertical (opens up or down).

Because the variable "x" is squared.

If  "a" is positive, then the parabola opens up, but if it is negative, then the parabola opens down.

In this case you have the quadratic function:

[tex]f(x) = 2x^2+5x-4[/tex]

Which can be rewritten as:

 [tex]y = 2x^2+5x-4[/tex]

Therefore, it is vertical, because it has the form:  [tex]y=ax^2+bx+c[/tex]

You can observe that the value of "a" is:

[tex]a=2[/tex]

Then, since "a" is positive, the parabola opens up.

Answer:

Your answers are correct.

Step-by-step explanation:

The equality will be true for odd multiples of π/4, so the last two choices will not show the expression to be not an identity.

The mean is 7.7.

The range is 4.

The mode is 8.

The median is 8.

Mean is the average of a set of numbers. It is determined by adding the numbers together and dividing it by the total number

Mean = sum of the numbers / total number

(5 + 6 + 6 + 7 + 7 + 7 + 7 + 8 + 8 + 8 + 8 + 8 + 8 + 8 + 8 +  9 + 9 + 9 + 9 + 9) / 20

154 / 20 = 7.7

Mode is the number that occurs the most in the data set. The mode is 8.

Range is the difference between the highest number and the lowest number in the data set.

Range = 9 - 5 = 4

Median is the number at the center of the data set. The median is 8.

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Answer: The mean is 7.7.

The range is 4.

The mode is 8.

The median is 8.

Step-by-step explanation: I did the assignment.

Answer:

11. (r+9)(r+3)

12.(g-3)(g+3)

13.(p+3)(2p^2+3)

Answer:

The length of the longer side is 28 meters

Step-by-step explanation:

we know that

In a parallelogram,  the intersecting diagonals bisect each other;

The supplementary angle of 60° is 120°.

see the attached figure to better understand the problem

Let

a ----> the length of the longer side

b ----> the length of the shorter side.

Apply the Law of Cosines to the lower triangle.

[tex]a^2 = 20^2 + 12^2 - 2(20)(12) cos(120\°)[/tex]

[tex]a^2 = 784[/tex]

[tex]a=28\ m[/tex]

therefore

The length of the longer side is 28 meters

Answer:

-4

Explanation:

The slope of the line intersects points that are 4 points below and one point to the right of the previous point. (-4/1) = -4

Answer:

-4

Step-by-step explanation:

The line goes through the points (-1,3) and (0,-1)

We can find the slope by using the formula

m = (y2-y1)/(x2-x1)

   = (-1-3)/(0--1)

  = (-1-3)/(0+1)

   = -4/1

   = -4

منوال 60 is the answer you get ألب

Answer:

180

Step-by-step explanation:

Answer:

   5 inches wider

Step-by-step explanation:

The given area expression factors as ...

  x² +2x -15 = (x -3)(x +5)

Apparently, we're to assume that these factors represent length times width, and the factor x-3 corresponds to a length that is 3 inches shorter than the old length (x). Then the width is (x+5), which is 5 inches wider than the old length.

Answer:

5 in wider is right

Step-by-step explanation:

Answer:

[tex]\frac{1}{16}[/tex] Is the chance of the colours matching.

Step-by-step explanation:

The possibility of the spinner landing on an orange side is [tex]\frac{1}{4}[/tex]

and the possibility of the marble being orange is [tex]\frac{1}{4}[/tex] in this case you have to remember, in the fraction, you have 4 possibilities and 1 desirable outcome, when you have two dependant possibilities you have to multiply them:

[tex]\frac{1}{4} * \frac{1}{4}[/tex]

And the result of that multipliction is [tex]\frac{1}{16}[/tex] which is the probability of the marble and the spiner colours matching.

Answer:

Step-by-step explanation:

1/4

Answer:

A

Step-by-step explanation:

Opposite angles of a parallelogram are equal, so z = 96.

Alternate interior angles are congruent, so x = 31.

Angles of a triangle add up to 180, so y = 53.

Based on the parallelogram shown above, the values of the variables are: x = 31°, y = 53°, z = 96°.

In Mathematics, a parallelogram is a type of quadrilateral and two-dimensional geometrical figure that is composed of two equal and parallel opposite sides.

According to the opposite angles theorem, the opposite angles of a parallelogram are always congruent or equal and as such, we have the following:

m∠z = 96°

Based on the alternate interior angles theorem, angles on opposite of a line are congruent;

x = 31°.

Based on angle sum property, we have the following supplementary angles;

x + y + z = 180

31° + y + 96° = 180°

y = 180° - 127°

y = 53°.

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Answer:

The measure of angle DEF is ∠DEF=80°

Step-by-step explanation:

we know that

The incenter is constructed by taking the intersection of the angle bisectors of the three vertices of the triangle

The triangle DEF is an isosceles triangle

∠EDF=∠EFD

so

In the triangle DHF

∠HDF=∠HFD

∠HDF+∠DHF+∠HFD=180°

substitute the value

2∠HDF+130°=180°

∠HDF=25°

therefore

∠EDF=2*25°=50°

In the triangle DEF

∠EDF+∠DEF+∠EFD=180°

∠EDF=∠EFD=50°

substitute

50°+∠DEF+50°=180°

∠DEF=80°

Answer:

The answer would be 80?

That is correct!

Step-by-step explanation:

Once Im done with the question Ill come back and make sure its correct!