find the volume v of the described solid s. the base of a solid s is the region enclosed by the parabola y

Answers

Answer 1

The volume of the solid that is in the parabola is 3.48[tex]\pi[/tex] after integration will carried out.

Parabola is a U shape curve whose eccentricity is 1.

The equation of parabola is y = 2-3x² and the x axis.

The cross section is perpendicular to y axis and the square.

The parabola is passes through the x axis put y = 0 in the equation of parabola.

0 = 2-3x²

x = [tex]\sqrt{\frac{2}{3} }[/tex]

Volume of the solid = [tex]\pi r^{2}h[/tex]

here r = y and h = dx

[tex]\pi (2-3x^{2} )^{2} dx=dv\\dv = \pi (9x^{4}-12x^{2} +4)dx\\[/tex]

Now, integrate the given equation to get the volume of the solid.

∫dv = ∫π(9x⁴-12²+4)dx

Put limits [tex]\sqrt[2]{\frac{2}{3} }[/tex] to 0

After integration and putting the limit we got V = 3.48[tex]\pi[/tex].

Hence, the volume of the solid is 3.48π.

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The complete question is:

Find the volume V of the described solid S. The base of S is the region enclosed by the parabola y = 2 − 3x2 and the x−axis. Cross-sections perpendicular to the y−axis are squares.


Related Questions

how to find the anser to 1999+888999

Answers

890998

Step-by-step explanation:

1999+888999 = 890998

Suppose H(x)=7 root x-3 . Find two functions f and g such that (fog)(x)=H(x) .

Answers

The two functions such that composition (fog) (x) = H(x) are f(x) = 7x and g(x) = [tex]\sqrt{x-3}[/tex].

What is Function?

A function is a relation from a set A to a set B where the elements in set A only maps to one and only one image in set B. No elements in set A has more than one image in set B.

We have a function H(x) = 7 [tex]\sqrt{x-3}[/tex]

We have to find two functions f and g such that (fog) (x) = H(x).

Let f(x) = 7x

g(x) = [tex]\sqrt{x-3}[/tex]

The composition of these functions is,

(fog)(x) = f (g(x))

           = 7 . g(x)

           = 7 [tex]\sqrt{x-3}[/tex]

           = H(x)

Hence the functions are f(x) = 7x and g(x) = [tex]\sqrt{x-3}[/tex].

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A wage earner receives a gross pay of $983.15 for 52.5 hours of work. What is his hourly rate of pay if a regular workweek is 44 hours and overtime is paid at timeand-a-half the regular rate of pay?

Answers

Answer:

$17.32

Step-by-step explanation:

44 hours

52.5 - 44 = 8.5 hours over time for 1.5x regular pay

assume regular pay is x

so 44x + 8.5 * 1.5x =983.15

44x + 12.75x = 983.15

56.75x=983.15

x=17.324

check to see if it's correct

44*17.324 + 12.75*17.324 = 983.14

Find the length of the arc of a circle of diameter 10
meters subtended by a central angle of π3
radians.

Round your answer to two decimal places.

Answers

The length of the arc of a circle with given radius and central angle is 5.23 meters.

What is the circle?

A circle is a two-dimensional figure formed by a set of points that are at a constant or at a fixed distance (radius) from a fixed point (center) on the plane. The fixed point is called the origin or center of the circle and the fixed distance of the points from the origin is called the radius.

Given that, a circle of diameter 10 meters subtended by a central angle of π/3 radians or 60°.

We have, radius of a circle = 5 meters

We know that, arc length of a circle is θ/360° ×2πr

Now, 60°/360° ×2×3.14×5

= 1/6×2×3.14×5

= 5.23 meters

Therefore, the length of the arc of a circle with given radius and central angle is 5.23 meters.

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identify the sampling method that was used. three representatives from each employee type (faculty, staff, administrators) are chosen for a salary committee.

Answers

The sampling method that was used. three representatives from each employee type (faculty, staff, administrators) are chosen for a salary committee. This uses stratified sampling.

ABOUT STRATIFIED SAMPLE

In a stratified sample, researchers divide a population into homogeneous subpopulations called strata (the plural of stratum) based on specific characteristics (e.g., race, gender identity, location, etc.). Every member of the population studied should be in exactly one stratum.

Each stratum is then sampled using another probability sampling method, such as cluster sampling or simple random sampling, allowing researchers to estimate statistical measures for each sub-population.

Researchers rely on stratified sampling when a population’s characteristics are diverse and they want to ensure that every characteristic is properly represented in the sample. This helps with the generalizability and validity of the study, as well as avoiding research biases like under coverage bias.

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A researcher estimates that a fossil is 3200 years old. Using carbon-14 dating, a procedure used to determine the age of an object, the researcher discovers that the fossil is 4000 years old. A. Find the percent error. B. What other estimate gives the same percent error?

Answers

A. The percent error is 25%

B. Another estimate that gives the same percent error is the Theoretical value.

How to Find the Percent Error?

A. To find the percent error, we use the following formula:

percent error = (|experimental value - theoretical value| / theoretical value) x 100

In this case, the experimental value is 4000 years (from carbon-14 dating) and the theoretical value is 3200 years (from the researcher's estimate). Plugging these values into the formula:

percent error = (|4000 - 3200| / 3200) x 100 = (800 / 3200) x 100 = 25%

B. To find an estimate that gives the same percent error, we can use the formula:

Theoretical value = experimental value / (1 + percent error / 100)

If we use the same percent error (25%) and experimental value (4000 years) as before:

Theoretical value = 4000 / (1 + 25/100) = 4000 / 1.25 = 3200

So, an estimate of 3200 years would give the same 25% percent error as the researcher's original estimate.

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Find the missing coordinate to complete the ordered pair for the equation 3x- 4y = 12: When the following are given (0, ?) and (?, 3)

Answers

The missing coordinates on the ordered pairs of the linear equation are:

(0, -4) and  (8, 3)

How to find the missing coordinates?

Here we have the linear equation:

3x - 4y = 12

And we want to find the missing coordinates for the given points (0, ?) and (?, 3) where these points belong to the line.

The first point is (0, ?), this means that the value of x is zero, then we can evaluate the equation in x = 0 then we will get:

3*0 - 4y = 12

-4y = 12

y = 12/-3 = -4

So the point is (0, -4)

For the other point (?, 3) we need to evaluate in y = 3.

3*x - 4*3  12

3x - 12 = 12

3x = 12 + 12

3x = 24

x = 24/3 = 8

So we have the point (8, 3)

These are the missing coordinates.

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Express the following sum in sigma notation. Use 1 as the lower limit of summation and k for the index of summation. 1+4+9+16+25 +36 Express the sum in sigma notation. Σ" k 1

Answers

∑[tex](k^2)[/tex] for k = 1 to 6 is the sum in sigma notation for this series of terms.

The series is 1 + 4 + 9 + 16 + 25 + 36. The lower limit of summation is 1, which means, the sum starts at the initial term in the series.

The index of summation is k, which implies, the ongoing term in the series is represented by the variable k.

In the expression [tex]k^2[/tex]  which implies that we are adding up the square of the index of summation.

So, the sigma notation for this series of terms is ∑[tex](k^2)[/tex]  for k = 1 to 6, which means, we are adding up the squares of the numbers from 1 to 6 (1, 4, 9, 16, 25, and 36)

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Indicate the equation of the given line in standard form. The line containing the median of the trapezoid whose vertices are R(-1, 5) , S(1, 8), T(7, -2), and U(2, 0). Show calculations.

Answers

The linear function containing the median of the trapezoid whose vertices are R(-1, 5) , S(1, 8), T(7, -2), and U(2, 0). is given as follows:

y = -1.67x + 6.5.

How to define the linear function?

The slope-intercept definition of a linear function is given as follows:

y = mx + b.

In which:

m is the slope, representing the rate of change.b is the intercept, representing the value of y when x = 0.

The median of the trapezoid is composed by these two points:

Midpoint of RS.Midpoint of TU.

The coordinates of the midpoint of RS are given as follows:

x = (-1 + 1)/2 = 0.y = (5 + 8)/2 = 6.5.

The coordinates of the midpoint of TU are given as follows:

x = (7 + 2)/2 = 4.5.y = (-2 + 0)/2 = -1.

Hence the points of the function are:

(0, 6.5) and (4.5, -1).

When x = 0, y = 6.5, hence the intercept b is given as follows:

b = 6.5.

When x increases by 4.5, y decays by 7.5, hence the slope m is given as follows:

m = -7.5/4.5

m = -1.67.

Hence the function is:

y = -1.67x + 6.5.

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a square fountain in the center of a shopping mall has an area of (4x^2+12x+9)ft^2. The dimensions of the fountain are of the form cx + d, where c and d are whole numbers. Find an expression for the perimeter of the fountain. Find the perimeter when x=2 ft.

Answers

A. An expression for the perimeter of the fountain is 8x + 12 ft.

B. The perimeter when x=2 ft. is 28 ft

How do we determine the values?

The area of the fountain is given as 4x^2 + 12x + 9 square feet. Since the fountain is a square, we know that the length and the width of the fountain are equal. This means that we can express the area of the fountain in the form of (cx + d)^2.

Expanding (cx + d)^2 gives:

(cx + d)^2 = cx^2 + 2cxd + d^2

We can equate this to the given area of the fountain:

cx^2 + 2cxd + d^2 = 4x^2 + 12x + 9

To find the expression for the perimeter of the fountain, we need to find the dimensions (length and width) of the fountain. This can be done by factoring the area expression:

4x^2 + 12x + 9 = (2x + 3)(2x + 3)

So the dimensions of the fountain are (2x + 3) ft

The perimeter of a square is the sum of all four sides, so we can find the perimeter of the fountain by multiplying the length of one side by 4:

Perimeter = 4(2x + 3) ft = 8x + 12 ft

When x = 2 ft, the perimeter of the fountain is:

8(2) + 12 = 28 ft

So when x = 2 ft, the perimeter of the fountain is 28 ft.

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suppose you take a sample of 50 students from your school and measure their height. which one of the following is a random variable? group of answer choices

Answers

The mean of the sample is the random variable in the given problem.

The mean of any given data set can be defined as summarizing a given group of data. It is done in order to make data sets and their values easier to understand. It can be obtained by first adding all the given values and then dividing the total sum by the number of data entries.

A random variable is any quantity that depends on random events. Here, we know that the mean of the given sample depends on all of the random events or we can say random values present in the table. Hence, we can conclude that the random variable is the mean of the sample.

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Karen wants to buy new shoes. There is a promotion for 3
pairs of sneakers for $450.75, how much would one pair of
sneakers cost?

Answers

Each pair of shoes will cost $150.25

Good luck hope this helps


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Which statements are true for the following expression? (11 + 7)(8 + 7) + (2 + 9) Check all that are true. All factors are the sum of two terms. 40 The solution is the sum of three terms. 40 It is not possible to find a solution. 4 The solution is the product of two factors, plus another number: 4 The solution is the difference between three terms.

Answers

Answer:

All of the following statements are true for the expression (11 + 7)(8 + 7) + (2 + 9): all factors are the sum of two terms, the solution is the sum of three terms, the solution is the product of two factors, plus another number, and the solution is the difference between three terms.

give me brainiest

This is hard to do I need help

Answers

Help

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An exit poll shows how certain parties voted on Proposition #1. Explain how the given graph is deceptive.

Complete the statements based on the pie chart.

Pie charts are used to compare
, not
. This misleads the viewer to think
half the people in all three parties voted Yes on Issue #1, when
half of Republicans and Independents actually voted Yes on Issue #1.
1) ✔ parts of a whole
2)✔ the difference between groups
3)✔ less than
4)✔ more than

Answers

Pie charts are used to compare parts of a whole, not the difference between groups. This misleads the viewer to think more than half the people in all three parties voted Yes on Issue #1, when less than half of Republicans and Independents actually voted Yes on Issue #1.

What is a pie chart?

This is a type of graph that resembles a pie because it is a circle that shows the proportion of different groups.

How to interpret the pie chart?Pie charts are used to determine percentages out of 100%, however, you cannot use them to compare groups.Due to this, you should be careful when interpreting the information. For example, in this case, you might think more than half the people in all three parties voted Yes but this might not be true.

Note: Here is the missing information

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the heptagon ($7$-sided polygon) and hexagon are drawn in plane so that they intersect at a finite number of points. let $n$ be the maximum possible number of points where two polygons can intersect. which one is correct?

Answers

The maximum possible number of points where two polygons can intersect is [tex]$n = 4$[/tex]. This is achieved when the two polygons are tangent to each other at four points.

Maximum Intersection Point Count

There are different ways to approach the problem of determining the maximum possible number of points where two polygons can intersect, but one possible method is to use geometric principles and constructive examples. Here is one possible way to do it:

Start with a heptagon and a hexagon that are both regular (i.e., all sides and angles are equal).Place the heptagon in the plane so that one of its vertices coincides with the center of the hexagon.Draw an equilateral triangle with sides of the same length as the heptagon's sides, and one of its vertices at the center of the hexagon.Connect the center of the hexagon to each vertex of the triangle, forming six congruent isosceles triangles.Draw a line segment from the center of the hexagon to the middle point of each side of the heptagon. This divides the heptagon into 14 congruent isosceles triangles.Now, it is clear that the heptagon and hexagon intersect at 4 points.

This is a constructive example for showing that the maximum possible number of intersection points between heptagon and hexagon is 4.

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if you are standing 45 feet away from a school and the angle of elevation is 66 degrees how tall is the building?

Answers

Answer:

50 m

Step-by-step explanation:

The angle of elevation of the top of the building from the foot of the tower is 30 and the angle of the top of the tower from the foot of the building is 60. the tower is 50 m high

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56. Kotkit is the hottest new social media app. It is lowkey fire. It slays! There were no crumbs left. Users post their Tiktoks to Kotkit, but play them backwards. At the start of the year, there are 1500 users, but the number of users grows exponentially at a rate of 12% per day.

a. Write a function K(t) that expresses the number of users t days after the start of the year.

b. How many users are of the Kotkit after 30 days?

.c After how many days will the numbers of users reach one million users?

Answers

Answer:

[tex]\textsf{a)} \quad K(t)=1500(1.12)^t[/tex]

b)  44940

c)  57.4 days

Step-by-step explanation:

Exponential Growth Function

[tex]f(t)=a(1+r)^t[/tex]

where:

a is the initial value (y-intercept)r is the growth rate (in decimal form)t is the time

Given values:

a = 1500r = 12% per day = 0.12t = time in days

Part a

To create a function K(t) that expresses the number of users t days after the start of the year, substitute the given values into the exponential growth formula:

[tex]\implies K(t)=1500(1+0.12)^t[/tex]

[tex]\implies K(t)=1500(1.12)^t[/tex]

Part b

To calculate how many users there are after 30 days, substitute t = 30 into the function K(t) from part a:

[tex]\implies K(30)=1500(1.12)^{30}[/tex]

[tex]\implies K(30)=44939.8831...[/tex]

[tex]\implies K(30)=44940\; \rm users[/tex]

Part c

To calculate after how many days it takes to reach one million users, substitute K(t) = 1,000,000 into the function and solve for t:

[tex]\implies 1000000=1500(1.12)^t[/tex]

[tex]\implies \dfrac{2000}{3}=1.12^t[/tex]

[tex]\implies \ln \left(\dfrac{2000}{3}\right)=\ln 1.12^t[/tex]

[tex]\implies \ln \left(\dfrac{2000}{3}\right)=t \ln 1.12[/tex]

[tex]\implies t=\dfrac{\ln \left(\frac{2000}{3}\right)}{\ln 1.12}[/tex]

[tex]\implies t=57.3755016...[/tex]

[tex]\implies t=57.4\; \rm days[/tex]

An anesthetic is given at the dosage of 15 mg per 10 lb body weight. It is packaged in vials at a concentration of 100 mg per mL.

How many mL should be given to a patient who weighs 58 kg?

Answers

0.1920 mL of the anesthetic should be given to the patient.

Calculation of Dosage

First, we need to convert the patient's weight from kilograms to pounds:

58 kg x 2.20462 lb/kg = 128.01 lbs

Next, we can calculate the total amount of anesthetic to be given to the patient:

15 mg/10 lbs x 128.01 lbs = 19.20 mg

Finally, we can divide the total amount of anesthetic by the concentration of the anesthetic in each mL:

19.20 mg / 100 mg/mL = 0.1920 mL

So, 0.1920 mL of the anesthetic should be given to the patient.

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57. The population of Asheville, NC can be modeled by P(t) = 90000 · e^(0.027t) as a function of years since the start of 2020.


a. State the growth rate. Round to three places

b. How many residents does the model predict will live in Asheville, NC in 2030.

Answers

Answer:

a)  Growth rate of 2.737% (3 d.p.) per year

b)  117,897

Step-by-step explanation:

[tex]\boxed{\begin{minipage}{9 cm}\underline{General form of an Exponential Function with base $e$}\\\\$f(t)=ae^{rt}$\\\\where:\\\phantom{ww}$\bullet$ $a$ is the initial value ($y$-intercept). \\ \phantom{ww}$\bullet$ $e$ is Euler's number. \\ \phantom{ww}$\bullet$ $r$ is the continuous growth/decay rate.\\ \phantom{ww}$\bullet$ $t$ is time.\\\end{minipage}}[/tex]

If a > 0 and r > 0, the function is an exponential growth function.

If a > 0 and r < 0, the function is an exponential decay function.

Given exponential function:

[tex]P(t) = 90000\cdot e^{0.027t}[/tex]

As r > 0 the function is an exponential growth function.

The annual growth rate is:

[tex]\begin{aligned}\textsf{Annual growth rate}& = e^{0.027}-1\\&=1.02736780...-1\\&=0.0273678027...\\&=2.73678027...\%\\&=2.737\%\; \sf (3\;d.p.)\end{aligned}[/tex]

To calculate how many residents the model predicts will live in Asheville, NC in 2030, substitute t = 10 into the given function:

[tex]\begin{aligned}\implies P(10) &= 90000\cdot e^{0.027 \cdot 10}\\&= 90000\cdot e^{0.27}\\ &= 90000\cdot 1.30996445...\\&=117896.800...\\&=117897\; \sf (nearest\;whole\;number)\\\end{aligned}[/tex]

Therefore, the model predicts that there will be a population of approximately 117,897 living in Asheville, NC in 2030.

A cell phone carrier charges a fixed monthly fee plus a constant rate for each minute used.
Part 1. In January, the total cost for 100 minutes was $47 while in February, the total cost for 350 minutes
was $52. The constant charge for each minute used is:
O 0.02
O 0.04
O 0.03

Answers

The required constant charge for each minute used is $0.02.

What is linear equation of two variable?

Algebraically speaking, an equation is a statement that shows the equality of two mathematical expressions. For instance, the two equations 3x + 5 and 14, which are separated by the 'equal' sign, make up the equation 3x + 5 = 14. ​

According to question:

Let fixed charge of monthly be x and constant rate of each minute used is y.

So,

In january

x + 100y = 47--------(1)

and in February

x + 350y = 52-----------(2)

equation(2) - equation(1)

(x + 350y) - (x + 100y) = 52 -47

250y = 5

y = 0.02

Thus, $0.02 used per minutes.

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Simplify the expression. Assume that the denominator does not equal zero.Write any variables in alphabetical order.



12m−3n62m−7n

Answers

The simplified expression is 14m -10n

How to simplify the expression

From the question, we have the following parameters that can be used in our computation:

12m−3n62m−7n

Express properly

So, we have the following representation

12m - 3n + 2m - 7n

Collect the like terms

This gives

12m + 2m - 3n - 7n

Evaluate the like terms

So, we have the following representation

14m - 10n

Hence, the solution is 14m - 10n

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(1.1) Convert 500 g to kg. (1.2) convert 1000 km to m. (1.3) Convert 1,65 ton to kg. (1.4) Convert 1,5 litre to millilitre. (1.5) Convert 50 m to cm. (1.6) if 1 inch is 2,54 cm, convert 12,5 cm to inches. (1.7) If 1 cup is 250 ml, how many cups will 1 250 ml be? (1.8) if 3 g of flour is 5 ml, how many ml will 10 g be? (1.9) Round the following number off to two decimal places: 135,2128 (1.10) Round the following number off to the nearest whole number: 250,62 (1.11) Round the following number off to the nearest ten: 123,84.
QUESTION 2 [6 MARKS] If an athlete passed the 5-km mark in a race after 19 min 58 seconds and the 10 km mark after 37 min 25 seconds, how long did it take him to complete the second 5 km?​

Answers

Answer:

(1.1)

1000g=1kg

500÷1000=0.5kg

(1.2)

1000m=1km

1000×1000= 1000000m

(1.3)

1000kg=1tonne

165×1000= 165,000kg

A student looks out of a second story school window and sees the top of the school flagpole at an angle of evelation of 22 degrees. The student is currently 18 feet above the ground. The building is 50 ft from the base of the flagpole. a. Draw a diagram of the above scenario. b. Find the height of the flagpole

Answers

The flagpole is visible to the student from 18 feet away and at a 22-degree inclination to the ground. The flagpole is 40.3 feet tall and 50 feet away from the structure.

At an elevation of 22 degrees, the student is looking out of a second-story school window. The building is 50 feet from the flagpole's base, and the window is 18 feet above the ground. We may compute the angle of the triangle formed by the window, the ground, and the top of the flagpole using the tangent ratio to determine its height. The opposing side (the flagpole) divided by the neighboring side equals the tangent of 22 degrees (the window to the ground). Consequently, the flagpole is 40.3 feet tall (50 divided by 1.224). This indicates that the student is 18 feet above the ground and is looking down at the flagpole.

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13. Solve for x. Please help

Answers

Answer:

x = 15

Step-by-step explanation:

The sum of the four angles of a quadrilateral add up top 360°

Given:

m∠A = (5x+14)°  

m∠b = 109°        

m∠C = (3x+8)°    

m∠D = 109°°

Here we are given actual values for two angles as 109°. Their sum is: 109 + 109 = 218°

The sum of the remaining two angles which are expressions in x should be:

360 - 218 = 142°

This is the sum of m∠A an m∠C

Substituting the terms for the two angle measures we get

(5x+14)  + (3x+8) = 142

5x+14  + 3x+8 = 142

Grouping like terms:

5x + 3x + 14 + 8 = 142

8x + 22 = 142

8x = 142- 22

8x = 120

x = 120/4

x = 15

the output column, s, was created from the student id 21444368 using the algorithm: if id digit n (left-to-right) is an even integer, place a 0 in s, row n (top-down) if id digit n (left-to-right) is an odd integer, place a 1 in s, row n (top-down) create a similar table, but with s reflecting the result of the algorithm applied to your student id (do this on scratch paper). on the quiz essay: record your student id, id

Answers

My student ID is 21444367.

The algorithm states that if the digit in the student ID (from left to right) is an even number, then a 0 is placed in the s column in the corresponding row (from top to bottom). If the digit in the student ID (from left to right) is an odd number, then a 1 is placed in the s column in the corresponding row (from top to bottom). Thus, the result of the algorithm applied to my student ID is s = 01101000.

This can be calculated by multiplying the even digits of the student ID by 0 and the odd digits of the student ID by 1 and then adding them together.

For my student ID, 21444367, the calculation would be:

0 * 2 + 1 * 1 + 0 * 4 + 1 * 4 + 0 * 4 + 1 * 3 + 0 * 6 + 1 * 7 = 01101000.

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now view the partitioned circle as a protractor, and think of using it to measure angles that are drawn on a page. give examples and make (rough) math drawings to show how this protractor could measure the following kinds of angles. in each case, determine the size of the angle in degrees and explain your answer.

Answers

The instrument used here is a protractor.

Protractor

An instrument used to measure angles in degrees is a protractor. When measuring angles using a protractor, it's crucial to check that the vertex of the angle is in the protractor's centre and that the angle's base is lined up with the protractor's baseline.

Acute Angle: - An angle that is less than 90 degrees is considered to be acute. For instance, if the angle is 30 degrees, we would line up the vertex of the angle with the protractor's centre and one of its sides with the baseline. The measurement would be read off the protractor scale, which in this instance would be 30 degrees.

Right Angle: - A right angle is a triangle with a 90 degree angle on each side. Using a protractor, we would line up the vertex of the angle with the protractor's centre and one side of the angle with the baseline to measure a right angle. The measurement would be read off the protractor scale, which in this instance would be 90 degrees.

Obtuse Angle: - An angle that is more acute than 90 degrees is referred to as an obtuse angle. When using a protractor to measure an obtuse angle, we would line up the vertex of the angle with the protractor's centre and one side of the angle with the baseline. The measurement would then be taken from the protractor scale and would be more than 90 degrees in this instance.

Straight Angle: - A straight angle is one that is 180 degrees in length. Using a protractor, we would line up the vertex of the angle with the protractor's centre and one side of the angle with the baseline to measure a straight angle. The measurement would then be taken from the protractor scale, which would be 180 degrees in this instance.

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what is the constant of proportionality for the relationship shown in this table?​

Answers

The required constant of proportionality for the relationship is 1/2.

What is Constant of proportionality?

As an illustration, we may write y = kx, where x is the amount of gas in gallons, y is the price in dollars, and k is the proportionality constant. In other words, the cost is directly related to the number of gallons pumped.

According to question:

Let the relation between x and y is

y = kx

Where k is proportionality constant.

Using the given values of x ad y

1 = k(2)

k = 1/2

So, the constant of proportionality for the relationship is 1/2.

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How is the work energy theorem represented as an equation? (1 point)
a. ΔW = E

b.W = ΔΕ
c.W = E
d. ΔW = ΔΕ

Answers

The work energy theorem represented as an equation is ΔW = ΔΕ is appropriate option.

Option D is correct.

The work-energy theorem is what?

A fundamental physics principle known as the work-energy theorem asserts that the amount of work done to an object is proportional to the change in its kinetic energy. To put it another way, the kinetic energy of an object is proportional to the net work done to it.

The work-energy theorem can be expressed as an equation because the change in an object's kinetic energy (W) is equal to the change in its work (W). It states that a change in an object's kinetic energy equals the net work done on it. The conservation of energy is a fundamental physics principle that states that energy cannot be created or destroyed; rather, it can only be transferred or converted from one form to another.

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Circle E has a radius of 5.1 meters. FG is a chord and is a perpendicular bisector of FG. If FG = 6.3 meters, calculate the distance of IH.

Answers

The distance of IH is 1.089 meters.

What is Circle?

Circle is a two dimensional figure which consist of set of all the points which are at equal distance from a point which is fixed called the center of the circle.

Given that,

Radius = 5.1 meters

EF = EI = 5.1

FG = 6.3 meters

HE is a perpendicular bisector of FG.

FH = HG = 6.3 / 2 = 3.15

Also, FH is the projection of EF in the vertical axis.

FH = EF sin (θ), where θ is the angle FEH.

3.15 = 5.1 sin (θ)

sin (θ) = 0.6176

θ = sin⁻¹ (0.6176)

θ = 38.14°

IH = EI - EH

We have,  EH is the projection of EF into the horizontal axis.

EH = EF cos (θ)

Substituting,

IH = 5.1 -  EF cos (θ)

IH = 5.1 - 5.1 cos (38.14)

IH = 5.1 ( 1 - cos (38.14))

IH = 1.089 meters

Hence the length of the line segment IH is 1.089 meters.

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