Calculate the curved surface area of a cone of height 8cm and base radius 6cm . Leaving your answers in terms of pie.

To evaluate the given integral using Green's theorem, we need to express it in the flux form.  The result of the integral is -r/6.

Green's theorem states that for a region R bounded by a simple closed curve C, the flux of the vector field F = (P, Q) across C is equal to the double integral of the curl of F over R.

In this case, we have the vector field F = (r^2xy, 1/2y^3), where r is the position vector (x, y).

The flux form of Green's theorem is:

\(∫∫R (curl F) · dA = ∫∫R (∂Q/∂x - ∂P/∂y) dA\)

Let's calculate the curl of F:

∂Q/∂x = 0

∂P/∂y = 2rxy

So, the curl of F is given by\((∂Q/∂x - ∂P/∂y) = 0 - 2rxy = -2rxy.\)

Now, let's evaluate the integral using the flux form of Green's theorem:

∫∫R (-2rxy) dA

Since the region R is a triangle with vertices (0,0), (1,0), and (0,1), we can express it as:

\(R = {(x, y) | 0 ≤ x ≤ 1, 0 ≤ y ≤ 1 - x}\)

Now, we can rewrite the integral:

\(∫₀^(1-x) (-2rxy) dy = -2rxy²/2 ∣₀^(1-x) = -rxy² ∣₀^(1-x) = -r(x-x²)\)

Let's evaluate the inner integral first:

\(∫₀^(1-x) (-2rxy) dy = -2rxy²/2 ∣₀^(1-x) = -rxy² ∣₀^(1-x) = -r(x-x²)\)

Now, evaluate the outer integral:

\(∫₀¹ -r(x-x²) dx = -r(x²/2 - x³/3) ∣₀¹ = -r(1/2 - 1/3) = -r(3/6 - 2/6) = -r(1/6) = -r/6\)

Therefore, the result of the integral is -r/6.

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Answer:

figure is missing mate

Answer:

2.92

Step-by-step explanation:

Answer:

2.92

Step-by-step explanation:

12×.59=7.08 10-7.08=2.92

Answer:

x=1

Step-by-step explanation:

To get the vertical line you leave out the y. Since it goes up in all y's, and then you only need the 1 for the x. easy peasy once you know what it is.

Answer:

1695.6 in3 ;)

Step-by-step explanation:

Answer:

CE = 20

Step-by-step explanation:

Given a line parallel to a side of a triangle and intersecting the other 2 sides then it divides those sides proportionally, that is

\(\frac{6}{8}\) = \(\frac{15}{CE}\) ( cross- multiply )

6 CE = 120 ( divide both sides by 6 )

CE = 20

The measure of angle COA is 160 degrees. (option c)

In triangle ACO, we know that AC and CO are equal because they are radii of the same circle. Therefore, angle ACO and angle CAO must be equal.

We also know that the sum of the angles in a triangle is always 180 degrees, so we can write:

angle ACO + angle CAO + angle COA = 180 degrees

We can substitute angle ACO for angle CAO because they are equal, giving us:

2(angle ACO) + angle COA = 180 degrees

Solving for angle ACO, we get:

2(angle ACO) = 180 degrees - angle COA

angle ACO = (180 degrees - angle COA)/2

Now we can substitute this expression for angle ACO into our earlier equation for angle COA:

angle COA = angle AOC + angle ACO

angle COA = 80 degrees + [(180 degrees - angle COA)/2]

We can simplify this equation by multiplying both sides by 2:

2(angle COA) = 160 degrees + (180 degrees - angle COA)

Distributing the 2 on the left side, we get:

2angle COA = 160 degrees + 180 degrees - angle COA

Combining like terms, we get:

3angle COA = 480 degrees

Dividing both sides by 3, we get:

angle COA = 160 degrees (rounded to two decimal places)

Hence the correct option is (c).

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Answer:

Reflecting a function over any axis can be complicated if you do not know the proper way to do it, so I am going to use examples to show you.

If f(x)=x is your normal function, then flipping it across the y-axis would look like f(x)=-x.

Step-by-step explanation:

Placing a - sign before the X will make it flip across the y-axis. After the X, and it flips across the X-axis.

Answer:

uuhhhh  t=2/3n-2/3

Step-by-step explanation:

Answer:

Judah's hourly wage is $7/hr.

Step-by-step explanation:

x=(86+12)/14

x=98/14

x=7

To determine the mean difference in leisure time between adults with and without children, a confidence interval is calculated based on sample data.

A random sample of 40 adults with no children under the age of 18 has a mean daily leisure time of 5.55 hours and a standard deviation of 2 hours. Another random sample of 40 adults with children under the age of 18 has a mean daily leisure time of 4.26 hours and a standard deviation of 1.65 hours.

To construct a 95% confidence interval for the mean difference in leisure time between the two groups, we can use the formula:

Confidence interval = (mean difference) ± (critical value * standard error)

The critical value for a 95% confidence level is typically 1.96. The standard error is calculated as the square root of [(standard deviation 1^2 / sample size 1) + (standard deviation 2^2 / sample size 2)].

By plugging in the given values, we can calculate the confidence interval. The interpretation of the confidence interval is that we are 95% confident that the true mean difference in leisure time between adults with and without children falls within the calculated interval. If the interval includes zero, it suggests there is insufficient evidence of a significant difference in leisure hours between the two groups.

It's important to note that the question's formatting makes it difficult to discern the specific choices provided. However, the explanation above outlines the general process and interpretation of constructing a confidence interval in this context.

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1) (a) The transformations that occur from the parent function are horizontal translation of 2 units to the left and vertical translation of 4 units to the down.

(b) (-2, -4)

(c) Graph is given below.

1) Given a function,

g(x) = (x + 2)² - 4

(a) Given a parent function p(x) = x².

We can write g(x) as,

g(x) = p(x + 2) - 4

So the transformation is horizontal translation of 2 units to the left and vertical translation of 4 units to the down.

(b) Vertex formula of a parabola is,

y = a (x - h)² + k, where (h, k) is the vertex.

Comparing the given function with vertex form,

Vertex of the parabola = (-2, -4)

(c) Graph of g(x) will be a parabola with vertex at (-2, -4).

It is given below.

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Answer:

2 x 2 x 2 x 2 x 3.

Step-by-step explanation:

The number 48 expressed as a product of its prime factors is 2 x 2 x 2 x 2 x 3.

Answer:

2 x 2 x 2 x 2 x 3.

Step-by-step explanation:

^^^

Answer:

15.6

Step-by-step explanation:

Answer:

i chose two points on the line and i got 5/1 (by using the rise over run method) which is simplified to 5 so the slope is going to be m= 5

Step-by-step explanation:

Answer:

the answer is c

Step-by-step explanation:

Answer:the Circumference of the outer cycle is longer than the circumference of the inner circle.

Step-by-step explanation:

Answer:

4.24

Step-by-step explanation:

First, let's set up the equation: \(\frac{2+x^2}{2}=10\)

Next, clear the fraction by multiplying both sides by 2:\(2*(\frac{2+x^2}{2}=10)=2+x^2=20\)

Then, subtract 2 from both sides: \(x^2=18\)

Finally, take a square root of both sides and round: \(\sqrt{x^2=18} =\)(Rounded to the nearest hundredth) 4.24

We will see that the base of the triangle measures 4 units.

For a triangle of base b and height h, the area is:

A = b*h/2

In this case, we know that:

A = 10 square units.

h = b + 2

Then we can write:

10 = b*h/2

If we replace the second equation into the above one, we get:

10 = b*(b + 2)/2

Now we can solve this for b:

\(20 = b^2 + b\)

Then we need to solve the quadratic equation:

\(b^2 + b - 20 = 0\)

The solutions are given by Bhaskara's formula.

\(b = \frac{-1 \pm \sqrt{1^2 - 4*1*(-20)} }{2} \\\\b = \frac{-1 \pm 9 }{2}\)

The solution that we care for is the positive one:

b = (-1 + 9)/2 = 4

The base measures 4 units.

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Answer: 878

Step-by-step explanation:

sorry i dont know

The area of quadrilateral ABCD = 4√6314 sq cm. +  15√663 sq. cm

For this given question:

In ΔABD , using Heron's formula.

semi perimeter s = a + b + c / 2

s = 27 + 25 + 30 / 2

s = 41 cm

Now,

Area ( ΔABD ) = √s(s - a)(s - b)(s - c)

Area ( ΔABD ) = √41(41 - 27)(41 - 25)(41 - 30)

Area ( ΔABD ) = √41x14x16x11

Area ( ΔABD ) = 4√6314 sq cm.

Now,

In ΔBCD

semi perimeter s = a + b + c / 2

s = 32 + 28 + 30 / 2

s = 45cm

Area ( ΔBCD ) = √s(s - a)(s - b)(s - c)

Area ( ΔABD ) = √45(45 -32)(45 - 28)(45 - 30)

Area ( ΔABD ) = 15√663 sq. cm

Thus, the area of quadrilateral ABCD = 4√6314 sq cm. +  15√663 sq. cm

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Tank 1 initially contains brine with 10 lb of salt, while Tank 2 has pure water. Water flows into Tank 1 and then into Tank 2, both at a rate of 5 gal/min. The initial value problem for the amounts of salt in the tanks, x₁(t) and x₂(t), is solved by integrating the differential equations. The solutions are x₁(t) = ± e^(- (5/150) t + C₁) and x₂(t) = ± (50/3) e^(- (5/150) t + C₁) + C₂. The maximum amount of salt in Tank 2 depends on the initial conditions and integration constants, with the upper bound being x₂_max = (50/3) e^C₁ + C₂.

a. The initial value problem for x₁(t) and x₂(t) can be written as follows:

  dx₁/dt = (5/100)(10) - (5/150)x₁

  dx₂/dt = (5/150)x₁ - (5/50)x₂

  where dx₁/dt represents the rate of change of salt in Tank 1 with respect to time, dx₂/dt represents the rate of change of salt in Tank 2 with respect to time, and x₁(t) and x₂(t) represent the amounts of salt in Tank 1 and Tank 2, respectively, at time t.

b. To find x₁(t) and x₂(t), we solve the initial value problem using the given conditions. Let's integrate the equations with respect to time:

  ∫ dx₁/dt dt = ∫ [(5/100)(10) - (5/150)x₁] dt

  ∫ dx₂/dt dt = ∫ [(5/150)x₁ - (5/50)x₂] dt

  Integrating the first equation, we have:

  x₁(t) = 10 - (5/150)∫ x₁ dt

  Differentiating both sides of the equation, we get:

  dx₁/dt = - (5/150) x₁

  This is a separable differential equation, which can be solved by separating variables and integrating:

  ∫ dx₁/x₁ = - (5/150) ∫ dt

  ln|x₁| = - (5/150) t + C₁

  Exponentiating both sides of the equation, we have:

  |x₁| = e^(- (5/150) t + C₁)

  x₁(t) = ± e^(- (5/150) t + C₁)

  Similarly, integrating the second equation, we get:

  x₂(t) = (5/150)∫ x₁ dt + C₂

  Substituting the expression for x₁(t) into x₂(t), we have:

  x₂(t) = (5/150)∫ (± e^(- (5/150) t + C₁)) dt + C₂

  x₂(t) = ± (5/150) ∫ e^(- (5/150) t + C₁) dt + C₂

  Solving the integral and simplifying, we get:

  x₂(t) = ± (50/3) e^(- (5/150) t + C₁) + C₂

c. To find the maximum amount of salt in Tank 2, we need to determine the maximum value of x₂(t). Since x₂(t) depends on the arbitrary constant C₁, we can't find the exact maximum without additional information about C₁. However, we can find the upper bound for x₂(t) by considering the limiting case.

  As t approaches infinity, the exponential term e^(- (5/150) t + C₁) approaches zero. Therefore, the maximum value of x₂(t) occurs when the exponential term is zero, resulting in:

  x₂_max = ± (50/3) e^C₁ + C₂

  The sign of ± depends on the initial condition and the integration constant C₂. If we assume positive values, then x₂_max = (50/3) e^C₁ + C₂.

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The width of each column is 2 inches.

Width is the measurement of something from side to side.

Let x = width of each column.

If a "gutter" is one eighth as wide as each column, then the width of the gutter can be expressed as

gutter = (1/8)x

If the document is 8.5 in. wide, then the sum of the widths of the left and right margins, the 3 columns and the 2 gutters in between columns is equal to 8.5 in.

left margin + right margin + 3 columns + 2 gutters = 8.5in

1 in + 1 in + 3x + 2(1/8)x = 8.5 in

3x + 2(1/8)x = 8.5 in - 1 in - 1 in

3 1/4 x = 6.5 in

x = 2 in

width of each column = 2 inches

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The value of x is -(5 + 3√2).

Equations are mathematical statements with two algebraic expressions flanking the equals (=) sign on either side. It demonstrates the equality of the relationship between the expressions printed on the left and right sides. LHS = RHS is a common mathematical formula.

Coefficients, variables, operators, constants, terms, expressions, and the equal to sign are some of the components of an equation. The "=" sign and terms on both sides must always be present when writing an equation.

Given:

7- 3√2-x=12

Now solving

7- 3√2-x=12

Subtract 7 from both side

7- 3√2-x - 7 =12 - 7

- 3√2-x = 5

Now, add 3√2 both side

-3√2 -x + 3√2 = 5 + 3√2

-x= 5 + 3√2

x= -(5 + 3√2)

Hence, the value x is -(5 + 3√2).

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Using the table your total monthly fixed expenses is 977.43.

Rent payment $953. 20/month

Auto payment $165. 87/month

Telephone $56. 98/month

Auto insurance $714. 36/six months

Once-a-week outing $35. 00/week

= 953.20 + 165.87 + 56.98 + 714.36/6 + (35*4)

= 1435.11

= 2412.54 - 1435.11

=977.43.

An expense is something that calls for the transfer of funds, or fortune in general, from one person or organization to another as payment for a good, service, or other type of cost. Rent is a cost to a tenant. Tuition is a cost to parents or students. Purchasing anything like food, clothing, furniture, or a car is frequently referred to as a cost.

A cost that is "paid" or "remitted" usually in exchange for anything of value is referred to as an expense. "Expensive" refers to something that appears to be very expensive. "Inexpensive" refers to something that appears to be inexpensive. "Expenses of the table" include costs associated with eating, drinking, a feast, etc.

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The type directions that lie in the (110) plane are Crystal planes are equivalent planes that represent a group of crystal planes with a common set of atomic indexes.

Crystallographers use Miller indices to identify crystallographic planes. A crystal is a three-dimensional structure with a repeating pattern of atoms or ions.In a crystal, planes of atoms, ions, or molecules are stacked in a consistent, repeating pattern. Miller indices are a mathematical way of representing these crystal planes.

Miller indices are the inverses of the fractional intercepts of a crystal plane on the three axes of a Cartesian coordinate system.Let us now determine which of the type directions lie in the (110) plane.[101] is not in the (110) plane because it has an x-intercept of 1, a y-intercept of 0, and a z-intercept of 1. So, this direction does not lie in the (110) plane.[110] is in the (110) plane since it has an x-intercept of 1, a y-intercept of 1, and a z-intercept of 0.

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Answer:

the answer is number 2

Step-by-step explanation:

hope this helps u

Answer:

30.34 degree

Step-by-step explanation:

Apply sine formula

\(\frac{sin\left(A\right)}{a}=\frac{sin\left(B\right)}{b}\)

\(\frac{\sin \left(45^{\circ \:}\right)}{7}=\frac{\sin \left(b\right)}{5}\)

->simplify

\(\frac{\sin \left(b\right)}{5}=\frac{\frac{\sqrt{2}}{2}}{7}\)

you will get

\(\sin \left(b\right)=\frac{5\sqrt{2}}{14}\)

which
sin b is about 0.50507

\(sin^{-1}\left(0.50507\right)\)

->arc sine in degree mode

the answer is 30.34

Answer:

Product is rational

Step-by-step explanation:

A rational number is any integer, fraction, terminating decimal, or repeating decimal.

Answer:

the product is rational

Answer:

4,400 yards

Step-by-step explanation:

2.5 x 1,760