In evaluating a double integral over a region D. a sum of iterated integrals was obtained as follows: Sketch the region D and express the double integral as an iterated integral with reversed order of integration.

Slicing a solid horizontally or vertically creates a cross section that looks like the Rectangle or one of the Square of the solid.

A cross section is the intersection of a figure in three-dimensional space with a plane. It is the face you obtain by making a "slice" through a solid object. A cross section is two-dimensional. The figure (face) obtained from a cross section depends upon the orientation (angle) of the plane doing the cutting.

Slicing a solid horizontally or vertically creates a cross section that looks like the Rectangle or one of the Square of the solid.

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Answer:0.8p+1 and 1+0.8p

Step-by-step explanation:

0.5p+0.3p=0.8p

7-6=+1

0.8p+1

and

Swap both numbers

(0.5p+7)+(0.3p-6)=1+0.8p

Answer:

  499.338 feet

Step-by-step explanation:

You want to know the distance traveled by an object in 25 seconds when its velocity is described by 20+5cos(t) feet per second.

The distance an object travels is the integral of its velocity. For the given velocity and time period, the distance is ...

  \(\displaystyle d=\int_0^{25}{v(t)}\,dt=\int_0^{25}{(20+5\cos(t))}\,dt=(20t+5\sin(t))|_0^{25}\\\\d=500+5\sin(25)\approx\boxed{499.338\quad\text{feet}}\)

The distance traveled in 25 seconds is 499.33 feet.

It is required to find the distance traveled in 25 seconds.

The distance of an object can be defined as the complete path travelled by an object .Distance is a scalar quantity that refers to "how much ground an object has covered" during its motion.

Given:

We have to find the distance , we will integrate v(t) from 0 to 25 second.

Consider an object traveling at constant velocity v = k. Then, each second, it travels k feet, so after t seconds, the distance traveled is k*t.

Now, suppose its speed increases by 1 feet/sec . So, estimate for distance traveled after t seconds is

1 + 2 + 3 + 4 + ... + t = t(t+1)/2, or approximately 1/2 t^2.

According to given question we have

Given a velocity function v, the distance s is figured by taking the integral. In this case,

v = 20 + 5 cos(t)

s = 20t + 5 sin(t) from 0 to 25

= s(45)-s(0)

s(0) = 0

so, the distance is

s(25) = 20*25 + 5sin(25)

= 500 -0.661

=499.33 feet.

Therefore, the distance traveled in 25 seconds is 499.33 feet.

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The value of \(x_5\), rounded to the nearest decimal place using Newton's method of approximation is 1.466.

The correct answer is option B.

To find the value of \(x_5\)using Newton's method of approximation, we need to iterate the following formula:

\(x_(_n_+_1_) = x_n - f(x_n) / f'(x_n)\)

where f'(x) represents the derivative of the function f(x). Let's calculate the values step by step.

Given function: f(x) = \(x^3 - x^2 - 1\)

Step 1: Find the derivative of f(x)

f'(x) = \(3x^2 - 2x\)

Step 2: Initialize the starting value

\(x_0\)= 1

Step 3: Calculate \(x_1\)

\(f(x_0) = f(1) = (1^3) - (1^2) - 1 = 1 - 1 - 1 = -1\)

\(f'(x_0) = f'(1) = (3(1^2)) - (2(1)) = 3 - 2 = 1\)

\(x_1 = x_0 - f(x_0) / f'(x_0)\)

   = 1 - (-1) / 1

   = 2

Step 4: Calculate \(x_2\)

\(f(x_1) = f(2) = (2^3) - (2^2) - 1 = 8 - 4 - 1 = 3\)

\(f'(x_1) = f'(2) = (3(2^2)) - (2(2)) = 12 - 4 = 8\)

\(x_2 = x_1 - f(x_1) / f'(x_1)\)

   = 2 - 3 / 8

   = 1.625

Step 5: Repeat the process until we reach \(x_5\)

Performing the calculations for \(x_3, x_4, andx_5\), we find:

\(x_3\) ≈ 1.465

\(x_4\) ≈ 1.466

\(x_5\)≈ 1.466

After applying Newton's method of approximation to the function f(x) = \(x^3 - x^2 - 1,\)starting with,\(x_0 = 1,\) we iteratively calculated the values of \(x_1, x_2, x_3, x_4, and x_5\). The final approximation, \(x_5\), is approximately 1.466 when rounded to the nearest decimal place. This aligns with option B as the correct answer.

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Answer: g -4/a

Step-by-step explanation:

Answer:

Cans of soup = 10

Frozen dinners = 5

Step-by-step explanation:

To determine the number of cans of soup and frozen dinners Caleb purchased, set up and solve a system of equations based on the given information.

Let x be the number of cans of soup Caleb purchased.

Let y be the number of frozen dinners Caleb purchased.

Each can of soup has 200 mg of sodium and each frozen dinner has 500 mg of sodium. The total amount of sodium in the purchased cans and frozen dinners is 4500 mg. Therefore:

\(200x + 500y = 4500\)

Caleb purchased a total of 15 cans of soup and frozen dinners. Therefore:

\(x + y = 15\)

To solve the system of equations, rearrange the second equation to isolate x:

\(\begin{aligned}x + y &= 15\\x + y -y&= 15-y\\x&=15-y\end{aligned}\)

Substitute this into the first equation to eliminate the term in x, and solve for y:

\(\begin{aligned}200(15-y) + 500y &= 4500\\3000-200y + 500y &= 4500\\3000+300y &= 4500\\3000+300y-3000 &= 4500-3000\\300y&=1500\\300y \div 300&=1500 \div 300\\y&=5\end{aligned}\)

Therefore, Caleb purchased 5 frozen dinners.

Substitute the found value of y into the rearranged second equation and solve for x:

\(\begin{aligned}x&=15-y\\x&=15-5\\x&=10\end{aligned}\)

Therefore, Caleb purchased 10 cans of soup.

Answer:

Caleb purchased 10 cans of soup and 5 frozen dinners.

Step-by-step explanation:

Caleb purchased 10 cans of soup and 5 frozen dinners.

Let no. of can of soup be x and no. of frozen dinner be y.

To solve this, we can set up the following system of equations:

\(\tt x + y = 15\)......[i]

\(\tt 200x + 500y = 4500\)......[2]

Let's find the value by elimination method:

Multiplying equation one by 200.

we get,

\(\tt 200 x+ 200 y = 15*200\)

\(\tt 200x +200 y =3000\)

Subtracting equation 2 with equation 1.

\(\tt (200x+500y)-(200x +200 y) =4500-3000\)

\(\tt \tt 300y = 1500\)

\(\tt y =\dfrac{1500}{300}\)

\(\tt y = 5\)

Substitute the value of y into the first equation to find x.**

\(\tt x + 5 = 15\)

\(\tt x = 15 - 5\)

\(\tt x = 10\)

Therefore, Caleb purchased 10 cans of soup and 5 frozen dinners.

The width of the frame for the image is about 1.5 inches.

Area is the amount of space occupied by a two dimensional object or figure.

Let w represent the width of the frame, hence:

Length of image and frame = 7 + w + w = 2w + 7

Width of image and frame = 5 + w + w = 2w + 5

Area of width and frame = (2w + 7)(2w + 5)

80 = 4w² + 24w + 35

4w² + 24w - 45 = 0

w = 1.5 inches

The width of the frame for the image is about 1.5 inches.

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Step-by-step explanation:

from which text book please

Answer:

The numbers:

1, -3, 2, -9, 3, -15, 4, -21,

are not linear.

Step-by-step explanation:

If it was linear:

4, 3, 2, 1, -3, -9, -15, -21

The percentage of the students who are absent when 81 of the 1350 students are absent is 6%.

Percentage in simple words can be defined as a part per hundred.

In other words, it is the ratio which can be defined as a fraction of 100. It  is usually denoted by the symbol %.

Percentage can also be said as dimensionless number as it does not have any dimensions.

Percentage of a number can be calculated by dividing the number with the whole part and then multiplying by 100.

Total number of students in the school = 1350

Number of students absent = 81

Here we have to calculate the percentage of 81 out of 1350.

Percentage of the students who are absent = \(\frac{81}{1350}\) × 100 = 6%

Hence 6% of the students are absent that day.

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Answer:

y = x + 15

Step-by-step explanation:

If two lines are perpendicular to each other, they have opposite slopes.

The first line is y = - x - 2. Its slope is -1. A line perpendicular to this will have a slope of 1.

Plug this value (1) into your standard point-slope equation of y = mx + b.

y = 1x + b or y = x + b

To find b, we want to plug in a value that we know is on this line: in this case, it is (-5, 10). Plug in the x and y values into the x and y of the standard equation.

10 = (-5) + b

Simplify.

10 = -5 + b

Now, add 5 to both sides to isolate b.

15 = b

Plug this into your standard equation.

y = x + 15

This equation is perpendicular to your given equation (y = -x - 2) and contains point (-5, 10)

Hope this helps!

1/4π radians is approximately equal to 45 degrees.

To convert a value from radians to degrees, multiply the value by 180/π. For example, to convert π/4 radians to degrees, multiply π/4 by 180/π to get 45 degrees. This conversion is useful for converting angles between the two units of measurement.

Degrees = Radians × 180/π.

Therefore, to convert 1/4π radians to degrees, we have:

Degrees = (1/4π) × (180/π) ≈ 45°

Hence, 1/4π radians is approximately equal to 45 degrees.

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The number she'd have is:

Explanation:

First, let's see which number is in the tens place and which number is in the ones place (the units place).

In the number 548, the place value of 5 is hundreds, the place value of 4 is tens, and the place value of 8 is ones (or units).

So if Sera adds two to the units, she'll have 10. But, since we can't write the number as 5410 (that would be a totally different number), we just write 0 in the units place, and shift 1 to the tens place, which gives us :

550

That's not all, since we also add 1 to the tens:

560

$5

Step-by-step explanation:

   Note. There are no options to select.

Let the notebook cost x, then Mark spent:

   25x + 25*1.25 = 156.25

   25x + 31.25 = 156.25

   25x = 156.25 - 31.25

   25x = 125

   x= 125/25

   x= 5

Answer:

380 seconds

Step-by-step explanation:

Convert 6 minutes to seconds by multiplying 6 times 60, because there are 60 seconds per minute.
6 x 60 = 360

Now add the 20 seconds.
360 + 20 = 380

6 minutes and 20 seconds are equal to 380 seconds.

The Total length of two sides based on the information will be 7x²+2x+1

The Length of the third side will be 4 x³-10x²-7.

Total length of two sides= Side 1 + Side 2

= 8x² − 5x − 2+ 7x − x²+ 3

= 8x²-x²-5x+7x-2+3

= 7x²+2x+1

Length of the third side = Perimeter - Total length of two sides

Length of the third side=4x³ − 3x² + 2x − 6-(7x²+2x+1)

= 4x³ − 3x² + 2x − 6-7x²-2x-1

= 4 x³-10x²-7

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Answer:

A) \(6(8x)=78\)

B) \(x=1.625\)

Step-by-step explanation:

\(6(8x)=78\)

hope this helped!

brainliest please!

Answer:

a) 8 + x

b) x = 5

Step-by-step explanation:

width = 6 in

length = 8 in

a)  extend length by x inches ⇒ length = 8 + x

b)  area of a rectangle = width x length

Given enlarged rectangle area = 78:

⇒ 6(8 + x) = 78

⇒ 48 + 6x = 78

⇒ 6x = 30

⇒ x = 5

Answer:

x= 1/a-1/b

Step-by-step explanation:

use math.way

The answer to your question is 1 because:

'ax' and 'bx' have no values, they are missing numbers.

We have to cancel out one 1, and our answer is 1.

Carry on Learning!

By factoring out the GCF from each problem are ab(2a - 3b), 5a(3a - 4a³ + 2b) and 2a²c³(7a³ + ac - 3c).

What is GCF?

GCF stands for Greatest Common Factor, which is the largest number or expression that divides two or more numbers or expressions without leaving any remainder.

4) To factor it out, we divide each term by the GCF, the GCF (Greatest Common Factor) of the given terms is "ab".

2a²b ÷ ab = 2a²b/ab = 2a

-3ab² ÷ ab = -3ab²/ab = -3b

Therefore, we can write:

2a²b - 3ab² = ab(2a - 3b)

So, the factored form of the expression 2a²b - 3ab² is ab(2a - 3b).

5) To factor out the GCF (Greatest Common Factor) from the given expression:

15a² - 20a⁴ + 10ab

First, we can look for the common factors of the coefficients (15, -20, and 10), and we find that they all have a common factor of 5. So, we can factor out 5 from all three terms:

5(3a² - 4a⁴ + 2ab)

Next, we can look for the common factors of the variables (a^2 and ab), and we find that they both have a common factor of a. So, we can factor out a from all three terms:

5a(3a - 4a³ + 2b)

Therefore, the fully factored form of the given expression is 5a(3a - 4a³ + 2b)

6) To factor out the GCF (Greatest Common Factor) from the given expression, we need to find the largest possible factor that divides each term of the expression. The terms in the given expression have common factors of a and c, and the highest power of a that appears in all the terms is a², while the highest power of c that appears in all the terms is c³. So, the GCF of the given expression is 2a²c³.

We can factor it out as follows:

14a⁵c³ + 2a³c³ -6a²c⁴ = 2a²c³(7a³ + ac - 3c)

Note that we factored out a positive GCF, even though the last term is negative, because the negative sign is part of the term, not the GCF.

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Answer:

Dimensions of the box:

x =  1,26  ( the side of the square base )

h = 2,52   the heigh of the cube

Step-by-step explanation:

V(b)  = x² *h      x is the side of the square base, and h the heigh of the cube

The surface area of such cube is:

Area of the base   A(b)  = x²

Lateral area is  4*x*h

A(c) = x²  +  4*x*h

Now   x² * h  = v = 4 m³       ⇒  h = 4/x²   and

A(x)   =  x²   +  4/x

Tacking derivatives on both side of the equation:

A´(x)  =  2*x - 4/x²

A´(x) = 0       2*x  - 4/x²  =  0        ⇒   2*x³  -  4   = 0

x³  = 2

x  = 1,26 m

And  h = 4/(1,26)²        ⇒     h  =  2,52 m

How do we know the value of  x  =  1,26 is for a minimum value of A(x)

We find the second derivative of  A(x)

A´´(x)  =  2  -  (-4*2*x/x⁴)

A´´(x)  =  2  + 8/x³       is positive  A´´(x)  >  0

Then function A(x) has a minimum value at x = 1,26

Answer:

42-x = James' money now

Step-by-step explanation:

James has "42-x dollars" after purchasing a gift for his sister.

Expression for money left to James to be determine if he spend x dollars from $42.

Arithmetic is branch of math that teach how  a word statement can be transform to mathematical expression.

Here, James spend x dollars to bought his sister a gift from $42.
Now, James has only 42-x dollars left in his pocket.

Thus, James has '42-x' dollars after purchasing a gift for his sister.

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The answer is A. x y 2 4 3 6 4 9 for the given values.

What is proportional relationship ?

A proportional relationship is a type of relationship between two quantities, where the ratio of one quantity to the other remains constant. In other words, as one quantity increases or decreases, the other quantity changes in a way that maintains the same ratio between them.

For example, if we have a proportional relationship between

The table that shows a proportional relationship between x and y is A.

In a proportional relationship, the ratio of y to x remains constant. We can check this ratio for each table:

A. For x=2, y=4, so y/x=2. For x=3, y=6, so y/x=2. For x=4, y=9, so y/x=2. The ratio of y to x remains constant at 2.

B. For x=3, y=4, so y/x=4/3. For x=9, y=16, so y/x=16/9. For x=15, y=20, so y/x=4/3. The ratio of y to x is not constant.

C. For x=4, y=12, so y/x=3. For x=5, y=15, so y/x=3. For x=6, y=18, so y/x=3. The ratio of y to x remains constant at 3.

D. For x=1, y=4, so y/x=4. For x=2, y=8, so y/x=4. For x=3, y=15, so y/x=5. The ratio of y to x is not constant.

Therefore, the answer is A. x y 2 4 3 6 4 9 for the given values.

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Answer:

Step-by-step explanation:

3x + x + 60 = 180.

first, we add the x's together.

4x + 60 = 180

then we see if they all have a common multiple. in this case, they do. they are all divisible by 4, so we can use that.

x + 15 = 45

then, just subtract 15 from both sides, that way we get the variable by itself.

x = 30

also, it is a right triangle. the top angle (3x) multiplied by 3 is 90. any triangle that has a 90 degree angle is automatically a right triangle.

Step-by-step explanation:

3x+X+60=180

4x=180-60

X=120/4

X=30

SOLVED

Answer:

The result can be written as (a + 1)².

Answer:

Z= 0.75

Step-by-step explanation:

Z = (X - μ) / σ

Z = (50 - 44) / 8

The missing values in the quantitative reasoning given are : -2, 13 and 9

Given the rule :

We can deduce that :

For the left circle :

circle = -6 - (-4) = -6 + 4 = -2

For the right circle :

circle = 11 - (-2) = 11 + 2 = 13

For the left square :

square = 13 + (-4)

square = 13 -4 = 9

Therefore, the missing values are : -2, 13 and 9

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Answer:

Dollars per passenger would be $252.
The maximum revenue is $63,404.

Step-by-step explanation:

Let's define the number of passengers above 212 as x.

The revenue function is given by R(x) = (212 + x)(292 - x).

We can expand and simplify the revenue function:

\(R(x) = 212 * 292 + 212 * (-x) + x * 292 + x * (-x)\)

= \(61804 - 212x + 292x - x^2\)

= \(-x^2 + 80x + 61804\)

The revenue function is a quadratic function in the form\(R(x) = -x^2 + 80x + 61804\), representing a downward-opening parabola.

To find the x-coordinate of the vertex (which gives the number of passengers for maximum revenue), use the formula \(x = -b/2a\), where \(a = -1\) and \(b = 80\).

\(x=\frac{-80}{2*(-1)}\)

\(= \frac{80}{2}\)

\(= 40\)

Therefore, the number of passengers above 212 for maximum revenue is 40.

Substitute x = 40 into the revenue function to find the maximum revenue:

\(R(x) = -(40)^2 + 80(40) + 61804\)

\(= -1600 + 3200 + 61804\)

\(= 61804 + 1600\)

\(= 63404\)

Hence, the maximum revenue is $63,404.

To determine the fare per passenger, subtract x from the base fare of $292:

Fare per passenger = Base fare - x

\(= 292 - 40\)

\(= 252\) Dollars per passenger.