What is 129,543 rounded to the nearest ten thousand

All of the given expressions for v are various stages in the process of "simplifying" the product of length, width, and height. Each and every one of them represents the volume of the box.

A double integral of Sin(x^2 + y^2) over a region between two circles with radii 2 and 5 is transformed into polar coordinates for simplification. The limits of the polar coordinates correspond to this region, and the integral becomes ∫ ∫ rSin(r^2) dr dθ, with r ranging from 2 to 5, and θ from 0 to π/2.

The student asked about the calculation of a double integral over a region between two circles, presented in polar coordinates, where the function is Sin(x^2 + y^2). For simplification, we can change to polar coordinates. In polar coordinates, x = rcosθ and y = rsinθ. Thus, x^2 + y^2 becomes r^2, and the function becomes Sin(r^2).

For a region between two circles of radii 2 and 5 in the first quadrant, we can describe the limits of the polar coordinates. r will range from 2 to 5, and θ from 0 to π/2. Thus, the integral will be ∫(from 0 to π/2) ∫(from 2 to 5) rSin(r^2) dr dθ. Evaluation of the integral will require techniques of polar integration.

It's important to note that this is a theoretical discussion and the actual integration may have complex results depending on the function to integrate.

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We need solve the given integral, convert coordinates to polar form and integrate step by step. First we will solve the inner integral from 2 to 5 and then the outer integral from 0 to π/2

We need to evaluate the double integral of Sin(x² + y²) over the region between the circles with radii 2 and 5.

In polar coordinates, where x = r cos(θ) and y = r sin(θ), this integral becomes:

∫(from 0 to π/2) ∫(from 2 to 5) sin(r²) r dr dθ

Let's solve the inner integral first, with respect to r:

Firstly, set up the integral: ∫(from 2 to 5) sin(r²) r dr.

Then Use the substitution u = r², then du = 2r dr.

Now Rewriting the integral: (1/2) ∫(from 4 to 25) sin(u) du = (1/2) [-cos(u)] (from 4 to 25).

and evaluating this: (1/2) [-cos(25) + cos(4)].

Next, integrate the result with respect to θ:

Set up the outer integral: (1/2) ∫(from 0 to π/2) [-cos(25) + cos(4)] dθ.

Now since [-cos(25) + cos(4)] is constant, the integral is straightforward: (1/2) [-cos(25) + cos(4)] * (π/2).

Hence the final answer: (π/4) [-cos(25) + cos(4)].

Therefore, the integral evaluates to (π/4) [-cos(25) + cos(4)].

EDITED QUESTION

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Find the double integral  Sin(x² + y²) over the region between the circles with radii 2 and 5.

Answer:

c

Step-by-step explanation:

Answer:

The sum is fraction therefore rational

Step-by-step explanation:

Given two numbers

[tex]-2\frac{3}{4}\text{ and }\frac{5}{9}[/tex]

we have to tell that how their sum is rational.

we add the above two number

[tex]-2\frac{3}{4}+\frac{5}{9}[/tex]

[tex]\frac{-11}{4}+\frac{5}{9}[/tex]

[tex]\frac{-99+20}{36}=\frac{-79}{36}=-2.194444...[/tex]

Hence, the sum is we can say fraction or non-terminating but repeating which is the definition of a rational number.

∴ from the given options answer C is correct.

The sum is fraction therefore rational.

The required measure of the length of the given line is 8.6 units.

Distance is defined as the object traveling at a particular speed in time, from one point to another.

here,
Locate the end point of line in the graph,
end point of the line from the graph is given as (0, 8) and (7, 3)

Applying the distance formula,
D = √[[x₂ - x₁]² + [y₂ - y₁]²]

Substitute the point in the above equation,

D = √[[7]² + [3 - 8]²]
D = √49 + 25
D = √74
D = 8.6

Thus, the required measure of the length of the given line is 8.6 units.

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The 15/26 fraction of the students is hearing​ impaired if in an American Sign Language​ (A.S.L) class of 26 ​students, 15 are hearing impaired.

Fraction number consists of two parts, one is the top of the fraction number which is called the numerator and the second is the bottom of the fraction number which is called the denominator.

It is given that:

In an American Sign Language​ (A.S.L) class of 26 ​students, 15 are hearing impaired.

The fraction:

= 15/26

We can convert the above value in the percentage as follows:

The best method for obtaining this answer is to divide 15 by 26 to obtain the number 0.5769, multiply that number by 100 to obtain the number 57.69; and then round it to the closest full number if necessary.

15/26 in percentage will be 57.69

Thus, the 15/26 fraction of the students is hearing​ impaired if in an American Sign Language​ (A.S.L) class of 26 ​students, 15 are hearing impaired.

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Answer:

Its -0.2 Because time cannot be a negative value.

Step-by-step explanation:

The correct value would be the 2.7 sec. one.

An algebraic equation with the second degree of the variable is called an Quadratic equation.

Here, Indicated when h(t) = 0, we are to find for the time where the football has reached a certain height.

⇒ - 16t² + 40t + 7 = 0

Then, the values of t would be -0.2 and 2.7.

Since,  we are to look for the time, it is impossible for us to have an answer that has a negative value.

So based from our answer, the solution that we will eliminate is the -0.2 one. Since its value is negative.

Thus, the correct value would be the 2.7 sec. one.

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Answer:

D. Width = x and Length = 3x

Step-by-step explanation:

We are given that,

The length of Box 1 is 3 times the width of Box 1.    ..................(1)

Let the width of Box 1 = x

So, from (1), we have,

Length of Box 1 = 3 × Width of Box 1

i.e. Length of Box 1 = 3x

Thus, the dimensions of Box 1 are : Width = x and Length = 3x

Hence, option D is correct.

In this exercise we have to identify which of the alternatives best represents the equation, like this:

Letter D

So we have that it is the area of ​​a box, where we have:

So is the same as:

[tex]L= 3W\\W=X\\L=3X[/tex]

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[tex]\frac{1}{132}[/tex] part of the golf course is in the trees.

To find out what part of the golf course is in the trees, we need to add the fractions of the golf course that are in the fairways and the greens, and then subtract that sum from 1 (which represents the whole golf course).

First, we add the fractions of the golf course that are in the fairways and greens:

To add these fractions, we must first find a common denominator. The denominators are 12 and 11, so the common denominator is 12 x 11 = 132.

Convert each fraction to have this common denominator:

Now, add these converted fractions together:

[tex]\frac{121}{132}[/tex] + [tex]\frac{12}{132}[/tex] = [tex]\frac{133}{132}[/tex]

Since the sum [tex]\frac{133}{132}[/tex] is greater than 1, we convert it to a whole number plus a fraction. [tex]\frac{133}{132}[/tex] = 1 + [tex]\frac{1}{132}[/tex].

Now, to find the part of the golf course in the trees, subtract this sum from the whole golf course:

1 - 1 + [tex]\frac{1}{132}[/tex] = [tex]\frac{1}{132}[/tex]

So, [tex]\frac{1}{132}[/tex] of the golf course is in the trees.

Complete question:

About [tex]\frac{11}{12}[/tex] of a golf course is in the fairways, [tex]\frac{1}{11}[/tex] in the greens, and the rest in the trees. What part of the golf course is in the trees?

The length of the original square is 9 inches

A square is defined as a polygon that has four sides and is a closed, two-dimensional (2D) object. A square has equal and parallel sides on all four sides.

Area of square  =  x * x

where x is the side of the square

According to the question,

The area of the new square is 121 square inches.

Let the side of the original square is = x  inches

Then the side of the new  square is =  x + 2 inches

Area of the new square = ( x + 2 )²

                                   121    =  ( x + 2 )²

                                      11   = x + 2

                                        x  = 9 inches

Therefore, The length of the original square is 9 inches.

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The actual cash value of Sam's furniture loss is $600.

To calculate the actual cash value of Sam's furniture loss, we first determine the amount of depreciation applied to the original purchase price. Since the furniture was 50 percent depreciated, we calculate this amount to be 50% of $1200, which is $600. This means the depreciated value of the furniture is $1200 - $600 = $600. However, because the replacement cost of new, similar furniture is now $1800, this does not affect the actual cash value of the lost furniture, which remains at the depreciated value of $600. So the actual cash value of Sam's loss is $600.