#9. Use the divergence theorem to find the flux of the vector field F = (4.x, x - 2y, y +52) outward through the surface of the box cut from the first quadrant by the planes x = 3, y = 4, z = 1. Include a sketch of the box.

Answer/Step-by-step explanation:

43 = (4 * 101) + (3 * 100)

43 = (4 * 10) + (3 * 1)

43 = 40 + 3

Answer:

B

Step-by-step explanation:

answer is B, 3,500. B 3500

Answer:

5

Step-by-step explanation:

Let x be that number.

(x^2) - 40 = 3x

x^2 - 40 = 3x

x*2-3x-40=0

(x-5)(x+8)=0

x=5

The equation of the parabola is:y = -13/36(x + 2)² + 5.

Equation is a mathematical statement that two expressions are equal. It is written as an expression that shows the equality of two values using mathematical symbols. Equations are used to solve problems by finding the unknown value. They are used in almost all branches of mathematics, and help to explain the behavior of physical and chemical systems.

The equation of a parabola with vertex (x_0,y_0) and that passes through (x_1,y_1) can be expressed as
y = a(x - x_0)² + y_0
where a is a constant.

In this case, the vertex of the parabola is (-2, 5) and it passes through (4, -8). We can substitute these values for x_0, y_0 and x_1, y_1 into the equation to get:

y = a(x - (-2))² + 5

We can solve for a by substituting the coordinates of the given point (4, -8) into the equation:

-8 = a(4 - (-2))² + 5

-8 = a(6)^2 + 5

-8 = 36a + 5

-13 = 36a

a = -13/36

Therefore, the equation of the parabola is:

y = -13/36(x + 2)²+ 5

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The required equation of the parabola is y = -13/36(x + 2)² + 5.

A parabola is a type of curve that is defined by a quadratic equation of the form y = ax² + bx + c.

In geometric terms, a parabola is the set of all points in a plane that are equidistant from a fixed point (called the focus) and a fixed line (called the directrix).

The equation of a parabola with vertex (x₁, y₁) that passes through
(x₂, y₂) can be expressed as

                        => y = a(x - x₁)² + y₁

Where a is a constant.

Here we have

The vertex of the parabola is (-2, 5) and it passes through (4, -8).

Substitute (-2, 5) in the formula y = a(x - x₁)² + y₁

=>  y = a(x - (-2))² + 5

Solve for a by substituting the coordinates of the given point (4, -8) into the equation:

=> -8 = a(4 - (-2))² + 5

=> -8 = a(6)² + 5

=> -8 = 36a + 5

=> -13 = 36a

=> a = -13/36

Therefore,

The required equation of the parabola is y = -13/36(x + 2)² + 5.

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The surface area of the region bounded by the function z=f(x,y) and the region R defined by (0,0), (0,4), (6,4), (6,0) can be found using a double integral.

To find the surface area, we need to integrate the magnitude of the partial derivatives of f with respect to x and y, and then multiply by the square root of 1 plus the sum of the squares of these derivatives. Mathematically, the surface area can be expressed as:

∬R √\((1+ (fx(x,y))^2 + (fy(x,y))^2)\) dA

where fx and fy represent the partial derivatives of f with respect to x and y, respectively, and dA is the area element in the xy-plane.

To evaluate this integral, we first need to determine the limits of integration. Since R is a rectangular region, we can set the limits of integration as: 0 ≤ x ≤ 6 and 0 ≤ y ≤ 4

We can then evaluate the partial derivatives of f and substitute them into the integral expression to obtain:

Surface area = ∫\(0^6\) ∫\(0^4\)\(\sqrt{(1+ 9x)}/(4\sqrt{x}) ^{2} +1\) dxdy

We can simplify this expression using algebraic manipulation and then evaluate the integral using appropriate integration techniques. The final result gives us the surface area of the region defined by z=f(x,y) and R.

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Answer:

The answer is option D.

Equation of a line is y = mx + c

m = slope

c = intercept on y axis

y-4= -2/3 (x-6)

y = -2/3x + 4 + 4

y = -2/3x + 8

From the above equation

m= -2/3

Since the lines are perpendicular the slope of the line is the negative inverse of the original line.

so m = 3/2

Equation of the line using point (-2 , -2) is

y + 2 = 3/2(x+2)

y = 3/2x + 3 - 2

y = 3/2x + 1

That's the last option

Hope this helps

The linear equation with the given characteristics is given by:

\(y = \frac{3}{2}x + 1\)

It is given by:

y = mx + b.

In which:

When two lines are perpendicular, the multiplication of their slopes is -1, hence:

\(-\frac{2}{3}m = -1\)

\(2m = 3\)

\(m = \frac{3}{2}\)

Then:

\(y = \frac{3}{2}x + b\)

It passes through the point (-2, -2), hence:

\(-2 = \frac{3}{2}(-2) + b\)

\(-3 + b = -2\)

\(b = 1\)

Hence, the equation is:

\(y = \frac{3}{2}x + 1\)

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Therefore, the answer of the given question of the equation maximum value is 41 .

What is equation?

The equal sign is used between numerical or changeable expressions to create an equation, such as 3x+5=11.

A number that can be entered as the variable's replacement in an equation serves as the solution.

According to the given question:

Correct option is D)

f(x)=  3+9x+17 /  3+9x+7

=> 3+9x+7+10 / 3+9x+7

=> 1 +  10 / 3+9x+7

f(x) = 0 for maximum value

f(x)= 10 (6x+9) / (3x2+9x+7)2

6x+9=0

X=-3/2

Given that x is real, the highest value of f(x) is => 1 +

=> 1 +

=> 1 + 40/1 = 41

Therefore, the answer of the given question of the equation is 41 .

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Answer:

-1/2 , -1, -3/2

Step-by-step explanation:

1.)log base 16 1/4

log base 16 \(4 ^{-1 }\) =x

\(16 ^{x} = 1/4\)

x = -1/2

2.)log base 7 ¹/7

log base 7  \(7^{-1}\) = x

7^x = 7^-1

x = -1

3.)log base 4 ⅛

4^x = 1/8

\(2^{2x} = 2^{-3}\)

2x = -3

x = -3/2

Answer:

Step-by-step explanation:

1. Let a = log16 0.25, then:

0.25 = 16 ^ a = 16^-0.5

So the answer is -0.5.

2. log7 1/7

1/7 = 7^-1

Answer is -1.

3.  log4 1/8

1/8 = 4^(-1.5)

Answer is -1.5

Answer:

wouldnt the answer be 9.9

Step-by-step explanation:

12.1-2.2=9.9

Answer:

Step-by-step explanation:

The elevation of Tammy's house is 3 1/2 times the elevation of Winston’s house which is 12.1 and that would give us 42.35 and then subtract the 2pm ocean elevation which is 2.2 and that would leave us with the answer of 42.15. so no the answer is not 9.9

Step-by-step explanation:

hope you can understand

Ok, so:

We know that the width of the confidence interval decreases as the sample size increases. And, the width increases as the standard deviation increases.

So, here we can analyze that the wifth of the confidence interval depends of the sample size and the standard deviation.

So, I would say that b and d aren't correct.

The width of the confidence interval also depends of the confidence level.

Here we got the situation.

As you can see, the confidence level affects the width.

The sample size, also affects the width.

And the standard deviation also affects it.

So, the correct answer could be A. The sample mean.

Answer:

88

Step-by-step explanation:

The area of a triangle is calculated using the following formula:

1/2*b*h (b: base, h: height)

The height here is 11 and the base is 16

1/2*16*11 = 88 units square

Answer:

x=8

Step-by-step explanation:

Hope this helps and have a wonderful day!!!

(a) The linear density (mass/length) rho has SI units of kg/m. Since rho = a + bx, the SI units of a must be kg/m and the SI units of b must be kg/m^2.
(b) To find the mass of the rod, we need to integrate the linear density function over the length of the rod:
m = ∫₀ᴸ ρ(x) dx
Substituting in ρ(x) = a + bx:
m = ∫₀ᴸ (a + bx) dx
m = [ax + (1/2)bx²] from 0 to L
m = aL + (1/2)bL²
Therefore, the mass of the rod in terms of a, b, and L is m = aL + (1/2)bL².

(a) In this problem, rho (ρ) represents linear density, which has units of mass per length. In SI units, mass is measured in kilograms (kg) and length in meters (m). Therefore, the units of linear density are kg/m. Since ρ = a + bx, the units of a and b must be consistent with this equation. The units of a are the same as those of ρ, so a has units of kg/m. For b, since it is multiplied by x (which has units of meters), b must have units of kg/m² to maintain consistency in the equation.

(b) To find the mass of the rod, we need to integrate the linear density function over the length of the rod (from x=0 to x=L). Let's set up the integral:

Mass (M) = ∫(a + bx) dx, with limits from 0 to L

Now, we can integrate:

M = [a * x + (b/2) * x²] evaluated from 0 to L

Substitute the limits:

M = a * L + (b/2) * L²

So, the mass of the rod in terms of a, b, and L is:

M = aL + (bL²)/2

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Step-by-step explanation:

From the image, let Angle 1 be x, and angle 2 be 16°

\({ \tt{x + 16 = 180}} \\ { \tt{x = 164 \degree}}\)

Answer:

B. a rectangle

Step-by-step explanation:

A cross section is the new face you see when you slice through a 3D figure. So if you slice a rectangular pyramid parallel to the base, you get a smaller rectangle as the cross section. Similarly, if you slice parallel to a triangular base then your cross section will be a triangle.

Hope this helps and God bless!

Step-by-step explanation:

I think Its D because In the rectangular base its not equal sides like a square so it would be more be like sides that are not perpendicular.

hope it helps

The function has an average rate of change of -1.

To find the average rate of change of a function, we can use the formula:

Average Rate of Change = (Change in y) / (Change in x)

Using the data provided in the table, we can calculate the average rate of change between each pair of consecutive points. Let's calculate it for each pair:

Between (-2, 7) and (-1, 6):

Change in y = 6 - 7 = -1

Change in x = -1 - (-2) = 1

Average Rate of Change = (-1) / (1) = -1

Between (-1, 6) and (0, 5):

Change in y = 5 - 6 = -1

Change in x = 0 - (-1) = 1

Average Rate of Change = (-1) / (1) = -1

Between (0, 5) and (1, 4):

Change in y = 4 - 5 = -1

Change in x = 1 - 0 = 1

Average Rate of Change = (-1) / (1) = -1

From the calculations, we can see that the function has a constant average rate of change of -1 between any two consecutive points in the table.

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ud7e7urfueitsisurwo6krwowi5ai6woaowi5

Answer:

48

Step-by-step explanation:

66*2=132

180-132=48

Hope this helps!

If not, I am sorry.

The number of reflectional symmetry that an object has depends on the object itself and its shape.

If an object can be reflected across a line or plane and yet look the same, it possesses reflectional symmetry. A square, for example, has four lines of reflectional symmetry, one on each side, whereas a circle has an infinite number of lines of reflectional symmetry since it looks the same no matter where it is reflected.

The following are some popular shapes and the number of lines of reflectional symmetry they have:

4 lines of symmetry in a square

2 lines of symmetry in a rectangle

3 lines of symmetry in an equilateral triangle

1 line of symmetry in an isosceles triangle

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An equation of line having slope 1/4 and passes through the point (-4,-3) is y = 1/4x - 2

We know that the slope-point form of line is:

(y - y1) = m(x - x1)

Here, we need to find an equation of line having slope 1/4 and passes pae through the point (-4,-3)

let (x1, y1) = (-4, -3)

and m = 1/4

substitute values in above formula,

(y - (-3)) = 1/4 (x +4)

y + 3 = 1/4 (x+4)

y = 1/4x -2

which is slope-intercept form of line (y = mx + b)

Therefore, equation of line is y = 1/4x - 2

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Given:

Ratio of ounces of oil to gallons of gasoline = 9 : 11

Gallons of gasoline = 55 gallons

Let's find the ounces of oil.

To find the ounces of oil, we have the equation:

Thus, we have:

Let x represent the ounces of oil.

Cross multiply:

Therefore, there are 45 ounces of oil.

ANSWER:

45 ounces of oil

Answer:

They spent $3.75

Step-by-step explanation:

That was really simple

Answer:

$3.75

Step-by-step explanation:

my name is also Jordan BTW

Having a rectangular pasture for the animals to graze in is something a farmer wants in order to start growing cows, horses, goats, and sheep. She has decided to purchase 7500 ft of fencing. 1875 square feet is the maximum possible area that each of the four pens will enclose.

The maximum possible area of each pen is 1875 square feet. To calculate this, first calculate the total area of the large rectangle that the farmer is enclosing. To do this, multiply the total length of the fencing (7500 feet) by the width of the fence (1 foot). This gives us 7500 square feet as the area of the large rectangle.

Next, divide the area of the large rectangle by 4 to get the area of each pen. This gives us 1875 square feet as the maximum area of each pen.

Total Area of Large Rectangle = 7500 ft x 1 ft = 7500 sq ft

Area of Each Pen = 7500 sq ft / 4 = 1875 sq ft

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Kirk must earn an annual rate of return of approximately 6.07% on his investment to accumulate enough money to pay for the ring.

To calculate the annual rate of return Kirk must earn on his investment, we can use the formula for compound interest:
A = P(1 + r/n)^(nt)
where:
A = final amount (the cost of the ring, which is $13,000 in 9 years)
P = initial amount (the amount Kirk currently has, which is $4,532)
r = annual interest rate (what we need to solve for)
n = number of times interest is compounded per year (assuming it's compounded annually, n = 1)
t = number of years (9 years)

Plugging in the given values:
$13,000 = $4,532(1 + r/1)^(1*9)
Next, simplify the equation:
(1 + r)^(9) = 13000/4532
Take the ninth root of both sides:
1 + r = (13000/4532)^(1/9)
Solve for r:
r = (13000/4532)^(1/9) - 1
Now, plug the value into a calculator to find r:
r = 0.0607

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Answer:B 73

Step-by-step explanation:

The term "intercepted arc" refers to an arc that is "cut off" or "lies between" the specified angle's sides.

The measure of < LRQ is 112.5.

The term "intercepted arc" refers to an arc that is "cut off" or "lies between" the specified angle's sides.

An arc is a segment of a circle's circumference. An intercepted arc is thus one formed when one or two different chords or line segments cut across a circle and meet at a common point known as a vertex.

If an angle is inscribed in a circle, then the measure of the angle equals one half the measure of its intercepted arc.

So, \($m \angle L R Q=\frac{1}{2}(m \overparen{L N Q})$\)

The sum of the measures of the central angles of a circle with no interior points in common is 360 .

Here, 360 is divided into 8 equal arcs and each arc measures

360/ 8 = 45.

Then, m LNQ = m LM + m MN + m NO + m OP + m PQ = 5(45) = 225.

\($m \angle L R Q=\frac{1}{2}(225)=112.5$\).

Therefore, the measure of < LRQ is 112.5.

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Answer:

The answer to the question is 24

Answer:

-2x-24

Step-by-step explanation:

-5x+3x-24 = - 2x-24

Answer:

-2x-24 hope dis helped