Evaluate the following integral in cylindrical coordinates.∫3−3∫√9−x20∫2011+x2+y2dzdydx

a) Measurement of arcCD is 40°

b) Measurement of arcVW is 134°

The Circle identities refer to a set of fundamental identities in trigonometry that relate the six trigonometric functions of an angle in a right-angled triangle.

a) Given that, ∠CED=∠AEC =50°  arcAB=140° we have to find out arcCD

We know the formula for external angle as per given diagram,

∠AEC = [tex]\frac{1}{2} (arcAB-arcCD)[/tex]

50° = [tex]\frac{1}{2} *(140-arcCD)[/tex]

Simplify, arcCD = 140° - 100° = 40°

Therefore, measurement of arcCD is 40°

b) Given that, ∠VYW =36°  arcVX=62° we have to find out arcVW

We know the formula for external angle as per given diagram,

∠VYW = [tex]\frac{1}{2} (arcVW-arcVX)[/tex]

36° = [tex]\frac{1}{2} *(arcVW-62)[/tex]

Simplify, arcVW = 72° + 62° = 134°

Therefore, measurement of arcVW is 134°

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According to the question the a) Measurement of arcCD is 40° and b) Measurement of arcVW is 134°

The Circle identities refer to a set of fundamental identities in trigonometry that relate the six trigonometric functions of an angle in a right-angled triangle.

a) Given that, ∠CED=∠AEC =50°  arcAB=140° we have to find out arcCD
We know the formula for external angle as per given diagram,
∠AEC = 1/2 (arcAB - arcCD)
50° = 1/2*(140 - arccd)
Simplify, arcCD = 140° - 100° = 40°
Therefore, measurement of arcCD is 40°

b) Given that, ∠VYW =36°  arcVX=62° we have to find out arcVW
We know the formula for external angle as per given diagram,
∠VYW = 1/2(arcVW - arcVX)
36° = 1/2*(arcVW - 62)
Simplify, arcVW = 72° + 62° = 134°
Therefore, measurement of arcVW is 134°

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Answer:

A (-439)

Step-by-step explanation:

To find the value of (s•t)(-7), we need to first evaluate s(t(-7)) which means we substitute -7 for x in the function t, and then substitute the resulting value in the function s.

So, we have:

t(-7) = 3(-7) = -21

s(-21) = 2 - (-21)^2 = 2 - 441 = -439

Therefore, the value of (s•t)(-7) is -439, which corresponds to option A.

So, the correct answer is A(-439).

Answer:

A

Step-by-step explanation:

I believe you mean

(s ￮ t)(- 7)

to evaluate, first evaluate t(- 7) then substitute the value obtained into s(x)

t(- 7) = 3(- 7) = - 21 , then

s(- 21) = 2 - (- 21)² = 2 - 441 = - 439

Step-by-step explanation:

the law of sine is

a/sin(A) = b/sin(B) = c/sin(C)

a, b, c are the sides. A, B, C are the corresponding opposing angles.

you fill in what you know and then solve for what you don't know. these are just regular equations. you multiply or divide or add or subtract the same things on both sides and try to get the missing side isolated on one side of an equation.

Answer:

1/5 and 25

5 and -1

Step-by-step explanation:

There are infinitely many pairs of rational numbers that have a product of -5. However, two possible pairs are:

1/5 and 25

5 and -1

In general, the product of two rational numbers can be negative if one of them is positive and the other is negative.

Answer: b

Step-by-step explanation: just took it on edge.

the equivalent closed form for the original rate function is

.[tex]S π/t 4tan (t) dt  = -4 ln |cos (t)| + C.[/tex]

a. [tex]S π / π /4 5t+4 / t² + 1 dt[/tex]We can write this rate function as a sum of two functions by expanding the denominator:

[tex]S π / π /4 5t+4 / (t² + 1) dt  = S π / π /4 5t+4 / (t² + 1) (t+1/t - 1/t) dt  = S π / π /4 5t+4 (t+1 - 1/t²) dt  = S π / π /4 5t+4 (t+1) dt - S π / π /4 5t+4 (1/t²) dt[/tex]

Now, integrating the two functions gives us the closed form:

[tex]S π / π /4 5t+4 (t+1) dt = 5/2 (t² + 2t + 2) + CS π / π /4 5t+4 (1/t²) dt = -5/2 (t + 1/t) + C[/tex]

Therefore, the equivalent closed form for the original rate function isS π / π /4 5t+4 / t² + 1 dt  = 5/2 (t² + 2t + 2) - 5/2 (t + 1/t) + C.

b. S π/t 4tan (t) dt
We can use a trig identity to change the form of this rate function:

S π/t 4tan (t) dt  = S π/t 4 (sin (t) / cos (t)) dt  = 4/cos (t) S π/t sin (t) dt

Integrating the rate function gives us the closed form:

S π/t 4tan (t) dt  = 4/cos (t) S π/t sin (t) dt = -4 ln |cos (t)| + C.

Therefore, the equivalent closed form for the original rate function is:

S π/t 4tan (t) dt  = -4 ln |cos (t)| + C.

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The car will never have a value of £0 because the formula for depreciation approaches but never reaches zero.

Percent is a way of expressing a number as a fraction of 100. The word "percent" comes from the Latin per centum, which means "per hundred". Percentages are often used to represent rates, ratios, or proportions of a quantity. For example, if a student scores 90 out of 100 on a test, their score can be expressed as 90%, or 0.9 as a decimal. Similarly, if a store offers a discount of 20% on a product, it means that the customer can purchase the product for 80% of its original price, or 0.8 as a decimal. Percentages are commonly used in finance, science, and everyday life to represent various types of information, such as interest rates, probabilities, taxes, and discounts.

Here,

1. Amount after 1 year:

The amount after 1 year can be calculated using the formula for compound interest:

A = P(1 + r/n)ⁿˣ

Where A is the amount, P is the principal amount, r is the annual interest rate, n is the number of times the interest is compounded per year, and t is the time in years.

Substituting the given values, we get:

A = 1000(1 + 0.05/1)¹*¹= £1050

Therefore, the total amount in the bank account after 1 year is £1050.

2. Amount after 2 years:

Using the same formula, we get:

A = 1000(1 + 0.05/1)¹*² = £1102.50

Therefore, the total amount in the bank account after 2 years is £1102.50.

3. Amount after 3 years:

Using the same formula, we get:

A = 1000(1 + 0.05/1)¹*³ = £1157.63

Therefore, the total amount in the bank account after 3 years is £1157.63.

4. Amount after 6 years:

Using the same formula, we get:

A = 1000(1 + 0.05/1)¹*⁶ = £1345.99

Therefore, the total amount in the bank account after 6 years is £1345.99.

5. The amount of interest earned after 6 years is not equal to double the amount of interest earned after 3 years because the interest earned in each year is added to the principal amount, so the interest earned in subsequent years is based on a larger principal amount. This leads to exponential growth in the amount of interest earned over time.

6. The value of the car after n years can be calculated using the formula:

V = P(1 - r/100)ⁿ

where V is the value of the car after n years, P is the initial value of the car, r is the rate of depreciation per year, and n is the number of years.

Using this formula, we can calculate the value of the car after:

1 year: V = 1000(1 - 0.05)¹ = £950

2 years: V = 1000(1 - 0.05)² = £902.50

3 years: V = 1000(1 - 0.05)³ = £857.38

6 years: V = 1000(1 - 0.05)⁶ = £735.03

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Answer:

Since the lines are parallel, we know that alternate interior angles are congruent. Therefore, angles 1 and 5 are congruent, as they are alternate interior angles. So any angle that is congruent to angle 5 is also congruent to angle 1.

Looking at the answer choices, we see that angle 2 is adjacent to angle 5 and therefore also congruent to angles 1 and 5. So the correct answer is:

Therefore, the answer is "2".

The score that could not be your exam score is 70.The correct option is (a).To calculate the standard deviation of a set of data, you take the square root of the average of the squared differences of the values from the mean.

The question is asking which of the given scores could not be your exam score if your exam score is 2.12 standard deviations below the mean. The mean score on the exam is 82, so the score that is 2.12 standard deviations below the mean is: 82 - (2.12 x standard deviation) = 82 - (2.12 x 10) = 70.Therefore, the score that could not be your exam score is 70.

To explain further, standard deviation is a measure of how spread out the numbers in a set of data .The other options (85, 80, and 90) are not correct because they are not 2.12 standard deviations below the mean. To summarize, the score that is 2.12 standard deviations below the mean score of 82 is 70.

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The wave is polarized parallel to the y-axis, and the magnetic field lines are parallel to the x-axis. Here option D is the correct answer.

The oscillating electric dipole along the z-axis creates an electromagnetic wave with electric and magnetic fields perpendicular to each other and to the direction of wave propagation. At a position on the y-axis far from the origin, the electric field will be parallel to the y-axis.

The polarization of the wave refers to the orientation of the electric field vector. Since the electric field is parallel to the y-axis, the wave is polarized parallel to the y-axis.

According to the right-hand rule, the direction of the magnetic field lines will be perpendicular to both the electric field and the direction of wave propagation, which is along the z-axis. Therefore, the magnetic field lines will be parallel to the x-axis.

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Answer:

The cost per apple is $1.45

Step-by-step explanation:

I will help with the solution, as I do not know the standard for the picture/estimate.

$37.70 / 26 is simply the cost per apple.

The cost per apple is $1.45

Hope this helps!

Combining these, we have[tex]$6 \times 6 = \boxed{36}$[/tex] different arrangements of the numbers [tex]${}1,$ ${}2,$ ${}3,$ ${}4,$ ${}5,$ $6$[/tex] in a row where the sum of any adjacent numbers is even.

Products intended for exporting after processing into goods or processed products are referred to as "basic products," as are goods planned for export after processing. Samples 1 - 3 Samples 2 - 3.

We may start by noting that at minimum one of the neighboring numbers must be even for the sum of both numbers to be even. This means that a even numbers (2, 4, 6) as well as the odd numbers (1, 3, 5) should be arranged in the appropriate positions.

Let's start by thinking about the even positions. The second, fourth, and sixth places are the only even positions. We can choose any variant of the 3 even numbers to occupy these spots, giving us[tex]$3! = 6$[/tex] ways.

Let's now think about the unusual positions. The first, third, and fifth positions are the only ones that are odd. We have an additional [tex]$3! = 6$[/tex]ways to fill these spots by using any combination of the 3 odd numbers.

Consider the odd locations now. The first, third, and fifth places are the three odd positions. We have an additional[tex]$3! = 6$[/tex]ways by using any permutation of the three odd numbers to fill these positions.

Together, this give us [tex]$6 \times 6[/tex] = [tex]\boxed{36}$[/tex] different ways to arrange the numbers [tex]${}1,$ ${}2,$ ${}3,$ ${}4,$ ${}5,$ $6$[/tex]in a row so that the sum of any two adjacent numbers is even.

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Answer:

Violet and blue light have the shortest wavelengths and red light has the longest. Therefore, blue light is scattered more than red light and the sky appears blue during the day. When the Sun is low in the sky during sunrise and sunset, the light has to travel further through the Earth's atmosphere.

Answer:

32π cm³/sec

Step-by-step explanation:

List given information

[tex]\displaystyle V=\frac{4}{3}\pi r^3\\\\r=4\\\\\frac{dr}{dt}=\frac{2}{r}\\ \\\frac{dV}{dt}=\,\,?[/tex]

Solve for dV/dt

[tex]\displaystyle V=\frac{4}{3}\pi r^3\\\\\frac{dV}{dt}=4\pi r^2\biggr(\frac{dr}{dt}\biggr)\\\\\frac{dV}{dt}=4\pi r^2\biggr(\frac{2}{r} \biggr)\\\\\frac{dV}{dt}=4\pi (4)^2\biggr(\frac{2}{4} \biggr)\\\\\frac{dV}{dt}=4\pi(16)\biggr(\frac{1}{2} \biggr)\\\\\frac{dV}{dt}=4\pi(8)\\\\\frac{dV}{dt}=32\pi[/tex]

Hence, the volume of the balloon is increasing at a rate of 32π cm³/sec when the radius is 4 cm.

To place two bench press machines in a small area, you will need a space of approximately 10 feet by 10 feet. Let's discuss it in detail below. Here are the dimensions of the bench press machine, which can help determine the amount of space required to fit two bench press machines in a small area:

The length of the bench press machine is between 48 inches and 54 inches.

The width of the bench press machine is between 28 inches and 32 inches.

The height of the bench press machine is between 48 inches and 56 inches.

Based on the above dimensions of the bench press machine, two machines can be placed in a small area of 10 feet by 10 feet. However, for safe use, the following guidelines should be followed:

There should be at least 6 feet of distance between the two bench press machines. There should be at least 3 feet of clearance in the front of the bench press machine to allow for safe movement during exercises. There should be at least 2 feet of clearance behind the bench press machine to allow for a safe exit in case of an emergency.

Thus, to place two bench press machines in a small area, you will need a space of approximately 10 feet by 10 feet.

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We have triangle ABC, the length of side AB is 16 inches and the length of side BC is 24 inches, the possible length of the side AC is less than 40 inches

To find the possible length of side AC, we need to use the triangle inequality theorem, which states that the sum of any two sides of a triangle must be greater than the third side, that is, a + b > c, b + c > a, c + a > b.

Now, for the given triangle ABC:

a = AB = 16 inches

b = BC = 24 inches

c = AC

We know that a + b > c (using the triangle inequality theorem)

16 + 24 > cc < 40

Therefore, By using the triangle inequality theorem, the possible length of the side AC is less than 40 inches.

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Answer:

D

Step-by-step explanation:

The square root of 50 is approximately equal to 7.07

-7.1111… can be rounded to -7.11

23/3 is equal to approximately 7.67

-7 1/5 is equal to -7.2

Answer: 118

Step-by-step explanation: 38 is the highest value, which is the fifth number in the pattern, and we need to find out what the 15th number is. We simply need to add (8x10) to 38.

Answer: 118

Step-by-step explanation:

you just keep going up at the rate of 8

Answer:

Proofs attached to answer

Step-by-step explanation:

Proofs attached to answer

a) If the number 646 from the ordered list changes to 639, c) the median stays the same.

b) a) If the number 646 from the ordered list changes to 639, a) the mean decreases by 1.

The median is the middle value in an ordered list (descending or ascending).

The mean refers to the average value.

The mean or average is computed as the quotient of the division of the total data value by the total number of items in the data set.

The ordered numbers of trading cards owned by 7 middle-school students = 360, 373, 402, 499, 548, 644, 646

The total value (sum) = 3,472

The number of cards = 7

The median = 499

The mean = 496 (3,472/7)

If the number 646 changes too 639:

The total value (sum) = 3,465

The median = 499

The mean = 495 (3,465/7)

Difference in mean = 1 (496 - 495)

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Equivalent fractions are defined as fractions that are equal to the same value, regardless of their numerators and denominators.

Equivalent fractions can be defined as fractions that may have different numerators and denominators but represent the same value. For example, 9/12 and 6/8 are equivalent fractions because both simplify to 3/4. 1/2, 2/4, 3/6 and 4/8 are equivalent fractions. Let's see how their values ​​are equal. We will represent each of these fractions with a shaded circle.

It can be seen that, seen as a whole, the hatched parts in all the figures represent the same parts.

Equivalent fractions can be written by multiplying or dividing the numerator and denominator by the same number. This is why these fractions reduce to the same number when they are simplified.

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Using equations we know that 45 pounds are included in the $1.40 worth of groceries and 55 pounds worth of groceries are being purchased for 40 cents.

An equation is a mathematical statement that contains the symbol "equal to" between two expressions with identical values.

As in 3x + 5 = 15, for example.

There are many different types of equations, including linear, quadratic, cubic, and others.

So, we have:

x + y = 100                        .........A

40 × x + 140 y = 85 × 100

40 x + 140 y = 8500         ........B

Solving (A) and (B) as follows:

(40 x + 140 y) - 40 × ( x + y ) = 8500 - 40 × 100

(40 x - 40 x) + (140 y - 40 y) = 8500 - 4000

0 + 100 y = 4500

y = 4500/100

Hence, the price per unit of grocery is $1.40 = y = 45 pounds.

Now, put the value of y in equation (A) as follows:

x + y = 100

x = 100 - y

x = 100 - 45

x = 55 pounds

The number of groceries at the 40-cent price is x = 55 pounds.

Therefore, using equations we know that 45 pounds are included in the $1.40 worth of groceries and 55 pounds worth of groceries are being purchased for 40 cents.

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Correct question:
A grocer has two kinds of candies, one selling for 40 cents a pound and the other for $1.40 per pound. How many pounds of each kind must he use to make 100 pounds worth 85 cents a pound?

The cost of covering the wall with wall paper is 495.

the lengthe of the wall = 11 feet

the width of the wall = 15 feet

so, the area of the wall

A = the length of the wall x the width of the wall

A = 11 x15

A = 165 square foot

then, the total cost is

= 165 x 3

= 495

So, the cost of covering the wall with wall paper is 495.

The surface of a shape's area is measured. You must multiply the length and breadth of a rectangle or square in order to determine its area. A has an area of x time y.

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W in terms of t can be represented as W = 7.5t + 10.

When a baby weighs 10 pounds at birth and 40 pounds four years later, we must apply the linear equation to represent W in terms of t.

y = mx + b,

where

m indictaes the slope of the line while

b is the y-intercept.

The formula to find the slope of a line is as follows:

Slope (m) = (y2 - y1) over (x2 - x1)

Given that a baby weighs 10 pounds at birth, and four years later, the child's weight is 40 pounds, we can determine the slope of the line as:

Slope (m) = (40 - 10) over (4 - 0) = 30 / 4 = 7.5

Thus, the linear equation relating childhood weight W (in pounds) to age t (in years) is:

W = 7.5t + 10

Therefore, we can express W in terms of t as W = 7.5t + 10.

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The procedure of surveying 33 people to determine which statistics courses they have taken does not result in a binomial distribution because it does not meet the condition of having only two possible outcomes for each trial.

The outcome of each trial is not a success or failure, but rather a specific course that the individual has taken. Binomial distribution requires a fixed number of independent trials with only two possible outcomes (success or failure) for each trial.

It does not satisfy the four conditions required for a binomial distribution as follows:

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Match the following with the given options:

1. An angle whose vertex is the center of the polygon and whose sides contain consecutive vertices of the polygon - Central angle of a regular polygon2. The common center of its inscribed and circumscribed circles - Center of a regular polygon3. The distance from the center of the polygon to a vertex - Radius of a regular polygon4. The perpendicular distance from the center of the polygon to a side - Apothem of a regular polygonA polygon is a two-dimensional object that has three or more straight sides and angles. A regular polygon is a polygon with equal sides and equal angles.

A regular polygon is a shape that has all its sides the same length and all of its angles the same degree. Below are the matched answers for the given options.1. An angle whose vertex is the center of the polygon and whose sides contain consecutive vertices of the polygon - Central angle of a regular polygonThe central angle of a regular polygon is defined as the angle whose vertex is the center of the polygon and whose sides contain consecutive vertices of the polygon.

The angle measures (360 / n) degrees, where n is the number of sides of the polygon.2. The common center of its inscribed and circumscribed circles - Center of a regular polygonThe center of a regular polygon is the point at which its axes of symmetry intersect. The center is also the common center of the circumscribed and inscribed circles.3. The distance from the center of the polygon to a vertex - Radius of a regular polygonThe radius of a regular polygon is defined as the distance from the center of the polygon to any vertex. It is also the distance from the center of the polygon to the midpoint of a side

.4. The perpendicular distance from the center of the polygon to a side - Apothem of a regular polygonThe apothem of a regular polygon is defined as the perpendicular distance from the center of the polygon to a side. It is also the radius of the inscribed circle.

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Answer:

D

Step-by-step explanation:

Pythag theorem for right triangles

c^2 = a ^2 + b^2

25 ^2 = 7^2 + ?^2

25^2 - 7^2 = ?^2

?^2 = 576

? = 24  units

Answer: 1260

Step-by-step explanation:

To solve for simple interest, we can use the formula:

I = P * r * t

where:

I = interest

P = principal amount

r = interest rate

t = time (in years)

In this case:

P = 2400

r = 10.5% = 0.105 (note that we convert the percentage to a decimal)

t = 5

Substituting these values into the formula, we get:

I = 2400 * 0.105 * 5

I = 1260

Therefore, the simple interest on a principal amount of 2400 at 10.5% for 5 years is 1260.

Answer: 0.96

Step-by-step explanation:

To round 0.956 to one decimal place, we need to look at the second decimal place (the hundredths place), which is 5. Since 5 is greater than or equal to 5, we need to round up the first decimal place (the tenths place), which is 9. Therefore, the rounded number to one decimal place is:

0.956 rounded to one decimal place = 0.96

Answer:

three times

Step-by-step explanation: