2x - 3 > -4x + 6 whats the answer to this

To find the area of the resulting surface when the curve x^(2/3) y^(2/3) = 9 is rotated about the y-axis within the interval 0 ≤ y ≤ 27, we can use the surface area formula for revolution.

The area can be computed by integrating the surface area element along the curve and then evaluating the integral over the given interval.

To calculate the surface area, we use the formula for the surface area of revolution, which states that the surface area is equal to the integral of 2πy ds, where ds represents the infinitesimal element of integral along the curve.

First, we rewrite the equation x^(2/3) y^(2/3) = 9 in terms of y to isolate y: y = (9/(x^(2/3)))^(3/2).

Next, we calculate ds using the formula for arc length: ds = √(1 + (dy/dx)^2) dx.

Taking the derivative of y with respect to x, we find dy/dx = \((-9x^(-5/3))/(2x^(-1/3)) = -9/(2x).\)

Substituting this value into the expression for ds, we have ds = √(1 + (-9/(2x))^2) dx.

Now, we can set up the integral for the surface area:

Surface Area = ∫[from x = 1 to x = 27] 2πy ds

Substituting the expressions for y and ds, the integral becomes:

Surface Area = ∫[from x = 1 to x = 27] \(2π(9/(x^(2/3)))^(3/2) √(1 + (-9/(2x))^2)\)dx.

Evaluating this integral will give us the area of the resulting surface.

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So the radius of the circle at that instant is 1.

Let's call the radius of the circle at that instant "r."

The formula for the area of a circle is A = pi * r^2 and the formula for the circumference of a circle is C = 2 * pi * r.

If the rate of increase in the area of the circle is numerically equal to twice the rate of increase in its circumference, we can set up the following equation:

2 * (2 * pi * r) = (pi * r^2)

Solving this equation for r, we find that the radius of the circle at that instant is r = 1.

So the radius of the circle at that instant is 1.

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Answer:

330 cubic inches

Step-by-step explanation:

The formula for a rectangular prism is l x w x h

so, let's input the numbers:

2 x 15 x 11

and solve:

330

So, the volume of a rectangular prism is 330 cubic inches

The least three numbers that when added together give a number multiple of 7 are:

2, 3 and 7

Prime numbers are numbers that have only two divisors, but these two divisors are always the same number and the number 1.

If we want to know a number that comes from the sum of three prime numbers and that in turn is divisible by 7, then let's identify the prime numbers from 0 to 20:

2, 3, 5, 7, 11, 13, 17, 19

Let's start with the lowest ones:

The three numbers are: 2, 3 and 7.

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Transformation doesn't depend on the shape of the figure if it has an overlap or not

The transformation \(8d\) can be applied to a figure with overlap or not with overlap.

Transformations are operations on a plane that change the position, shape, and size of geometric figures.

When a geometric figure is transformed,

its new image has the same shape as the original figure.

However,

it is in a new position and may have a different size.

Let's talk about different types of transformations.

Rotation:

It occurs when a shape is turned around a point, which is the rotation center.

Translation:

It moves the shape from one point to another on a plane.

Reflection:

It is an operation that results in the mirror image of the original shape.

Scaling:

The shape is transformed by changing the size without changing its orientation.

Transformation on \(8d\):

In the given problem, the transformation of \(8d\) can be applied to the figure with or without overlap.

This means that \(8d\) transformation doesn't depend on the shape of the figure if it has an overlap or not.

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Zone(area) = L x W = 2.5 x 2.5 = 6.25 square meters. 

Of all rectangles with an edge of 10 meters, the one that has the greatest zone(area) could be a square.

To see why, let's assume that a rectangle with a border of 10 meters has measurements of length L and width W.

At that point, we know that:

2L + 2W = 10

Rearranging this condition, we get:

L + W = 5

Presently, we need to discover the most extreme range encased by the rectangle, which is given by:

Area = L x W

Able to illuminate for one variable in terms of the other utilizing the condition L + W = 5:

L = 5 - W

Substituting this expression for L into the condition for the zone, we get:

Zone = (5 - W) x W

Extending and disentangling this expression, we get:

Area = 5W - W²

To discover the most extreme esteem of this quadratic expression, we will take its subsidiary with regard to W and set it to break even with zero:

dArea/dW = 5 - 2W =

Tackling for W, we get:

W = 2.5

Substituting this esteem back into the condition for the edge, we get:

L = 2.5

Hence, the measurements of the rectangle that has the greatest region are L = 2.5 meters and W = 2.5 meters, which implies it could be a square. The most extreme zone enclosed by the rectangle is:

Zone(area) = L x W = 2.5 x 2.5 = 6.25 square meters. 

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Answer:

The required answers:

Step-by-step explanation:

2.0.4,0.47

3.1.3,1.33

4.0.1,0.19

5.0.8,0.89

!! for 2 and 3 these values are rounded

1) 693.5/18,250 = .038 x 100% = 3.8% commission

2) ~118.5%  --- divide tip/meal then x 100%

3) ~21.33%   divide sale price/over org., then subtract by 100%

For the expression (x - 8)(x + 8), using the arithmetic operation the value for x is x = 8.

What is arithmetic operation?

A subject of mathematics known as arithmetic operations deals with the study and use of numbers in all other branches of mathematics. Basic operations including addition, subtraction, multiplication, and division are included.

The given expression is - (x - 8)(x + 8)

Use the arithmetic operation of multiplication -

(x - 8)(x + 8)

x(x + 8) - 8(x + 8)

x² + 8x - 8x -64

Now, use the arithmetic operation of addition and subtraction -

x² + 8x - 8x -64

x² - 64

Now, collect the like terms on each side -

x² = 64

x = √64

Now, solve the radical form to get the value of x -

x = √64

x = 8

Therefore, the value of x is obtained as x = 8.

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The number of combinations of 6 boys and 20 girls that can exist among 26 children born in a hospital on a given day is 230,230.

]To calculate the number of combinations, we can use the concept of binomial coefficients. The formula for calculating the number of combinations is C(n, k) = n! / (k!(n-k)!), where n is the total number of objects and k is the number of objects we want to select.

In this case, we have 26 children in total, and we want to select 6 boys and 20 girls. Plugging these values into the formula, we get C(26, 6) = 26! / (6!(26-6)!) = 230,230. Therefore, there are 230,230 different combinations of 6 boys and 20 girls that can exist among the 26 children born in the hospital on that given day.

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Patrick received a total of approximately $6,785.97 over the course of 52 weeks.

To calculate the total amount of money Patrick received over the 52 weeks, we can use the concept of a geometric sequence. The first term of the sequence is $10, and each subsequent term is 10% more than the previous term.

To find the sum of a geometric sequence, we can use the formula:

Sn = a * (r^n - 1) / (r - 1),

where Sn is the sum of the first n terms, a is the first term, r is the common ratio, and n is the number of terms.

In this case, a = $10, r = 1 + 10% = 1.1 (common ratio), and n = 52 (number of weeks).

Plugging these values into the formula, we can calculate the sum of the sequence:

S52 = 10 * (1.1^52 - 1) / (1.1 - 1)

After evaluating this expression, we find that Patrick received approximately $6,785.97 over the 52 weeks.

As a result, Patrick collected about $6,785.97 in total over the course of 52 weeks.

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Answer:

It's 20

Step-by-step explanation:

Adding and Subtracting

~~~~~~~~~~~~~~~~~~~~~~~~~

GL :)

The solution to the equation 8^x/2=2^3/8×4^3/4 is x = 15/14

To simplify an expression: to remove brackets, unnecessary terms and numbers

\(8^{x/2} = 2^{3/8} * 4^{3/4}\)

\(2^{3x/2} = 2^{3/8} * 2^{2 (3/4)}\)

using law of Indices

\(2^{3x/2} = 2^{3/8 + 6/4}\)

\(\frac{3x}{2} = \frac{3}{8} + \frac{3}{2}\)

\(\frac{3x}{2} = \frac{3+12}{8}\)

\(\frac{3x}{2} = \frac{15}{8}\)

cross multiply

24x =30

Divide both sides by 24

\(\frac{24x}{24} = \frac{30}{28}\)

x = 15/14

Therefore, the solution to the equation is x = 15/14

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The average velocity of the first half-second. Calculate the change in displacement and divide it by the change in time to obtain .

By integrating the supplied velocity function throughout the range [0, 0.5], the displacement can be calculated. Now let's figure out the displacement:

∫(6400t^2 - 6505t + 2686) dt

When we combine each term independently, we obtain:

\((6400/3)t3 - (6505/2)t2 + 2686t = (6400t2) dt - (6505t) dt + (2686t)\)

The displacement function will now be assessed at t = 0.5 and t = 0:

Moving at time\(t = 0.5: (6400/3)(0.5)^3 - (6505/2)(0.5)^2 + 2686(0.5)\)

Displacement at time zero: (6505/2)(0) + 2686(0) - (6400/3)(0)

We only need to determine the displacement at t = 0.5 because the displacement at t = 0 is 0 (assuming the bullet is launched from the origin):

Moving at time \(t = 0.5: (6400/3)(0.5)^3 - (6505/2)(0.5)^2 + 2686(0.5)\)

Streamlining .

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To find the total differential of the function w = e^y * cos(x) * z^2, we can take the partial derivatives with respect to each variable (x, y, and z) and multiply them by the corresponding differentials (dx, dy, and dz).

The total differential can be expressed as:

dw = (∂w/∂x) dx + (∂w/∂y) dy + (∂w/∂z) dz

Let's calculate the partial derivatives:

∂w/∂x =   \(-e^{y} * sin(x) * z^{2}\)

∂w/∂y =  \(e^{y} * cos(x) * z^{2}\)

∂w/∂z =  \(2e^{y} *cos (x)* z\)

Now, let's substitute these partial derivatives into the total differential expression:

\(dw = (-e^{y} * sin(x) * z^{2} ) dx + (e^{y}* cos(x) * z^{2} ) dy + 2e^{y} *cos (x)*z) dz\)

Therefore, the total differential of the function w = e^y * cos(x) * z^2 is given by:

\(dw = (-e^{y} * sin(x) * z^{2} ) dx + (e^{y} * cos(x) * z^{2} ) dy + ( 2e^{y} * cos(x) * z) dz\)

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We need to calculate the 8% of $45

The total charge will be

ANSWER

The total charge is $48.60

Answer:

THe y intercept  is 30 and it represents the registration fee

Step-by-step explanation:

Answer: t ≈ 2,403,603

Step-by-step explanation:

z = the z-score associated with the desired level of confidence (for a 5% precision, z = 1.96)

σ = the standard deviation of the background count rate (which is equal to the square root of the background count rate)

E = the desired level of precision (in this case, 5% or 0.05)

Substituting the given values, we get:

σ = sqrt(600) = 24.49

t = (1.96 * 24.49 / 0.05)^2

Step-by-step explanation:

Answer:

C=(4,6)

HAVE A BEAUTIFUL DAY

Answer:

The answer is 1/12.

Step-by-step explanation:

Think about it this way, 1/3÷8= 1/24.

Double that is 1/12.

Answer:

x = 7

Step-by-step explanation:

Step 1: Subtract 5x from both sides.

7x − 4 − 5x = 5x + 10 − 5x

2x − 4 = 10

Step 2: Add 4 to both sides.

2x − 4 + 4 = 10 + 4

2x = 14

Step 3: Divide both sides by 2.

2x / 2 = 14 / 2

x = 7

Hope this helps! :)

The given paragraph states that a stationery shop has been running for 10 years near campus in Jakarta.

Students like the asker often visit this store to purchase stationery, markers, rulers, and photocopiers.

The word "been" is a past participle of the verb "be." It is used to show the completion of an action in the past.

In this case, it implies that the stationery shop has been operating for the past 10 years near the campus.

The sentence can be rewritten as follows to make use of the word "been":

"The stationery shop has been providing stationery, markers, rulers, and photocopiers to students near the campus for 10 years."

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Answer:

19 inches and 60 inches

Step-by-step explanation:

The rate of change of the area of the square when the side length is 8 inches and the side length is increasing at a rate of 14 inches per minute is 224 square inches per minute.

To find the rate of change of the area of the square, we need to use the formula for the area of a square:

A = s^2

where A is the area of the square and s is the length of the side of the square.

To find the rate of change of the area, we need to take the derivative of this formula with respect to time:

dA/dt = 2s(ds/dt)

where dA/dt is the rate of change of the area, ds/dt is the rate of change of the side length, and s is the side length of the square.

Since the side length is increasing at a rate of 14 inches per minute, we can substitute ds/dt = 14 into the above equation, and we are given that the side length is 8 inches, so we can substitute s = 8.

dA/dt = 2s(ds/dt)

dA/dt = 2(8)(14)

dA/dt = 224

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Answer:

Step-by-step explanation:

I will be using the equation \(y=mx+b\) for this explanation.

Graph 1:

- The equation for the positive slope is \(y=x-1\). The positive slope (m) has a slope of positive 1 (x), and intersects the y-axis at -1, creating the equation \(y=x-1\).

- The equation for the negative slope is \(y=-3x+3\). If you look, the first point is at (0,-3) with the next point being (1,0), which shows that the slope has a negative slope (m) of 3. The negative slope intersects at (0,3), giving us the b variable in the equation. Putting these values into the equation, we get \(y=-3x+3\).

Graph 2:

- The steeper of the two functions will have the equation \(y=2x-4\). The function has a positive slope (m) of \(\frac{2}{1}\), or simply 2, and intersects the y-axis (b) at (0,-4). Put these variables into the equation \(y=mx+b\), and you get \(y=2x-4\).

- The lower function will have the equation \(y=\frac{1}{2} x+2\). For every 1 square, the line moves up, it takes 2 squares to the right to get to the next point, which gives us the variable m of \(\frac{1}{2}\). This function intersects the y-axis at (0,2), which gives the variable b of +2.

The point of intersection of the two lines is (x, y) = (- 45 / 37, - 250 / 37).

Vectorially speaking, a line is represented by the following parametric expression:

(x, y) = (a, b) + t · (c - a, d - b)        (1)

Where:

Two points intercept each other when they share the same point (x, y). Then,

(- 2, 5) + t₁ · (1, - 15) = (5, 15) + t₂ · (- 2, - 7)

t₁ · (1, - 15) - t₂ · (- 2, - 7) = (7, 10)

t₁ · (1, - 15) + t₂ · (2, 7) = (7, 10)

Which is equivalent to the following system of linear equations:

t₁ + 2 · t₂ = 7

- 15 · t₁ + 7 · t₂ = 10

Then, the solution of the system is (t₁, t₂) = (29 / 37, 115 / 37) and the point of intersection is:

(x, y) = (- 2, 5) + (29 / 37) · (1, - 15)

(x, y) = (- 45 / 37, - 250 / 37)

The point of intersection of the two lines is (x, y) = (- 45 / 37, - 250 / 37).

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To prove that the maximum number of vertices at level k of a binary tree is 2^k, we can use mathematical induction.

Base Case (k = 0):

At level 0, there is only one vertex (the root). Therefore, the maximum number of vertices at level 0 is 2^0 = 1.

Inductive Hypothesis:

Assume that the maximum number of vertices at level k of a binary tree is 2^k.

Inductive Step:

We need to show that the maximum number of vertices at level k+1 is 2^(k+1).

At level k+1, each vertex at level k can have two children, resulting in a maximum of 2^k vertices at level k+1. Therefore, the maximum number of vertices at level k+1 is 2 * 2^k = 2^(k+1).

By mathematical induction, we have proven that the maximum number of vertices at level k of a binary tree is 2^k.

Now, let's prove that a tree with 2^k vertices at level k must have 2^(k+1) - 1 vertices.

Base Case (k = 0):

At level 0, there is one vertex (the root), which satisfies the condition 2^(0+1) - 1 = 1 - 1 = 0 vertices.

Inductive Hypothesis:

Assume that a tree with 2^k vertices at level k has 2^(k+1) - 1 vertices.

Inductive Step:

Consider a tree with 2^k vertices at level k. At level k+1, each vertex at level k can have two children, resulting in a maximum of 2^(k+1) vertices. Therefore, the total number of vertices in the tree is 2^k + 2^(k+1) = 2^k + 2 * 2^k = 2^k + 2^k+1 = 2^k(1 + 2) = 3 * 2^k.

By the inductive hypothesis, we know that a tree with 2^k vertices at level k has 2^(k+1) - 1 vertices. Therefore, a tree with 2^k vertices at level k+1 will have 3 * 2^k - 1 vertices.

Hence, we have proven that a tree with 2^k vertices at level k must have 2^(k+1) - 1 vertices.

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