I need help on this question I have attached it on this assignment. THX

The centroid of the region in the first quadrant bounded by the curves [tex]\(y = x^9\)[/tex] and [tex]\(x = y^9\)[/tex] is [tex]\(\left(\dfrac{10}{11}, \dfrac{10}{11}\right)\)[/tex].

The centroid is given by the following formulas:

[tex]\[\bar{x} = \dfrac{\int_{a}^{b} x \cdot f(x) \, dx}{\int_{a}^{b} f(x) \, dx}\][/tex]

[tex]\[\bar{y} = \dfrac{\int_{c}^{d} y \cdot g(y) \, dy}{\int_{c}^{d} g(y) \, dy}\][/tex]

Where f(x) and g(y) are the functions that define the curves bounding the region.

Since we want to find the centroid of the region in the first quadrant, the intersection points of the two curves in the first quadrant.

The curves intersect at (1, 1).

Now, let's find the centroid of the region in the first quadrant.

First,  find the limits of integration:

1. For x:

The curve  [tex]\(y = x^9\)[/tex] is the upper curve, and it intersects the x-axis at x = 0  and the y-axis at x=1.

So, the limits of integration for x are [tex]\(0 \leq x \leq 1\)[/tex].

2. For y: The curve [tex]\(x = y^9\)[/tex] is the right curve, and it intersects the y-axis at y=0 and the x-axis at y=1.

So, the limits of integration for y are [tex]\(0 \leq y \leq 1\)[/tex].

Now,  set up the integrals:

[tex]\[\bar{x} = \frac{\int_{0}^{1} x \cdot x^9 \, dx}{\int_{0}^{1} x^9 \, dx}\][/tex]

[tex]\[\bar{y} = \dfrac{\int_{0}^{1} y \cdot y^9 \, dy}{\int_{0}^{1} y^9 \, dy}\][/tex]

1. [tex]\(\int_{0}^{1} x \cdot x^9 \, dx\):[/tex]

[tex]\[\int_{0}^{1} x \cdot x^9 \, dx = \int_{0}^{1} x^{10} \, dx[/tex]

                 [tex]= \left[\dfrac{x^{11}}{11}\right]_{0}^{1} = \dfrac{1}{11}\][/tex]

2. [tex]\(\int_{0}^{1} x^9 \, dx\):[/tex]

[tex]\[\int_{0}^{1} x^9 \, dx = \left[\dfrac{x^{10}}{10}\right]_{0}^{1}[/tex]

             [tex]= \dfrac{1}{10}\][/tex]

3.[tex]\(\int_{0}^{1} y \cdot y^9 \, dy\):[/tex]

[tex]\[\int_{0}^{1} y \cdot y^9 \, dy = \int_{0}^{1} y^{10} \,[/tex] dy

                 [tex]= \left[\dfrac{y^{11}}{11}\right]_{0}^{1} = \dfrac{1}{11}\][/tex]

4. [tex]\(\int_{0}^{1} y^9 \, dy\):[/tex]

[tex]\[\int_{0}^{1} y^9 \, dy = \left[\frac{y^{10}}{10}\right]_{0}^{1}[/tex]

            [tex]= \dfrac{1}{10}\][/tex]

Now, the centroid coordinates:

[tex]\[\bar{x} = \dfrac{\frac{1}{11}}{\dfrac{1}{10}} = \dfrac{10}{11}\][/tex]

[tex]\[\bar{y} = \dfrac{\frac{1}{11}}{\dfrac{1}{10}} = \dfrac{10}{11}\][/tex]

So, the centroid of the region is [tex]\(\left(\dfrac{10}{11}, \dfrac{10}{11}\right)\)[/tex].

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Answer: 6

Step-by-step explanation:

12 ÷ 6 = 2

30 ÷ 6 = 5

Answer:

92.5 cubic units

Choice A

Step-by-step explanation:

To approach this problem, separate out the composite solid figure into individual easily manageable components

At the bottom we have a rectangular prism which has a base length of 2a, a height of a and a width of c

Its volume = L X H X W = 2a·a·c= 2a²c

Plugging in values for a and c we get

Volume of rectangular prism

= 2 x (3.7)² x 2

= 54.76 cubic units

On top of this rectangular prism are two right-angled triangular prisms

The volume of a right-angled triangular prism =

Here height = b (confusing :)

base = a

width = c

So volume of each triangular prism
[tex]=\textrm{$\dfrac{1}{2} \times $ base x height x width}\\\\= \dfrac{1}{2} a \times b \times c\\\\ = \dfrac{1}{2} \times 3.7 \times 5.1 \times 2\\\\= 18.87[/tex]

Since there are 2 such prisms the volume of both

= 18.87 x 2 = 37.74 cubic units

Total volume of composite solid = 54.76 + 37.74 = 92.5 cubic units

Answer: 3/2

Step-by-step explanation:

Answer:

3/2 or 1 1/2

Step-by-step explanation:

[tex]2\frac{1}{4}/1\frac{1}{2} \\\frac{9}{4}/\frac{3}{2} \\(\frac{9}{4})(\frac{2}{3})\\\frac{18}{12} \\\frac{3}{2} or 1\frac{1}{2}[/tex]

The area between the x-axis and y = x from x = 3 to x = 6 will be 13.50 square feet.

Integration is a way of finding the total by adding or summing the components. It's a reversal of differentiation, in which we break down functions into pieces. This approach is used to calculate the total on a large scale.

The function is given below.

y = x

Integrate the function under the limit from  x = 3 to x = 6 will be given as,

[tex]\begin{aligned} I &= \int^6_3 y dx\\\\ I &= \int^6_3x dx\\\\I &= \left [\dfrac{x^2}{2} \right ]^6_3 \\\\I &= \dfrac{6^2 - 3^2}{2} \end{aligned}[/tex]

Simplify the equation further, then we have

I = (36 - 9) / 2

I = 27 / 2

I = 13.50 square units

The area between the x-axis and y = x from x = 3 to x = 6 will be 13.50 square feet.

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The 427 is in the sets of the whole number, real number, rational number, natural number, and integers.

What is set?

A set is a collection of clearly - defined +ique items. The term "well-defined" applies to a property that makes it simple to establish whether an entity actually belongs to a set. The term 'unique' denotes that all the objects in a set must be different.

As we know, a number is a mathematical entity that can be used to count, measure, or name things. For example, 1, 2, 56, etc. are the numbers.

It is given that:

The number is 427

The number 427 is in the set of whole numbers

The number 427 is in the set of real numbers

The number 427 is in the set of rational numbers because it can be written as in the form of p/q.

The number 427 is in the set of natural numbers

The number 427 is in the set of integer numbers

Hence, the 427 is in the sets of the whole number, real number, rational number, natural number, and integers.

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Answer:

180.4 is 140.9% of 128.

Step-by-step explanation:

180.4 is what percent of 128 Rounded to the nearest tenth?

Answer:

Step-by-step explanation:

I think doubles facts are when you use a different equation to get the same sum, right?

In that case here are some doubles.

1+4=5

2+3=5

3+2=5

4+1=5

5+0=5

=========================================================

Explanation:

Part A

x = number of years after 1983

Example: x = 2 is the year 1985 since 1985-1983 = 2.

The number of people who drink this beverage declines by 6.5% each year. The multiplier is 1+r = 1+(-0.065) = 0.935

Meaning that if 6.5% of the people leave, then 93.5% remain. The two percentages add to 100%.

This value 0.935 is the base of the exponent portion. We have 0.935^x as the exponent portion.

Out front is the value 5480 which is the starting amount of people.

This leads to the exponential equation y = 5480*0.935^x

It is of the form y = ab^x

a = 5480 = starting population

b = 0.935 = decay factor

---------------------------------------

Part B

The timespan from 1983 to 2023 is 40 years (because 2023-1983 = 40).

Which means we plug x = 40 into the equation we found in part A.

y = 5480*0.935^x

y = 5480*0.935^40

y = 5480*0.06799303620922

y = 372.601838426526

y = 373

Be sure to round to the nearest whole number.

We expect or predict there will be approximately 373 people who remain loyalists to this root beer as of September 2023.

Answer:

Part (a)

[tex]y=5480(0.935)^x[/tex]

where:

Part (b)

373

Step-by-step explanation:

[tex]\boxed{\begin{minipage}{9 cm}\underline{General form of an Exponential Function}\\\\$y=ab^x$\\\\where:\\\phantom{ww}$\bullet$ $a$ is the initial value ($y$-intercept). \\ \phantom{ww}$\bullet$ $b$ is the base (growth/decay factor) in decimal form.\\\end{minipage}}[/tex]

The initial number of people who drink Root Beer (in September 1983):

If the number of people that drink Root Beer instead of Coca-Cola has been declining at the rate of 6.5% per year, then:

Therefore, an exponential equation that represents the number of Root Beer loyalists in Outback for any year is:

[tex]y=5480(0.935)^x[/tex]

where:

The number of years between September 1983 and September 2023 is:

To calculate how many Root Beer loyalists should there be as of September 2023, substitute x = 40 into the equation found in part (a):

[tex]\implies y=5480(0.935)^{40}[/tex]

[tex]\implies y=5480(0.0679930362...)[/tex]

[tex]\implies y=372.601838...[/tex]

[tex]\implies y=373[/tex]

Therefore, there should be approximately 373 Root Beer loyalists as of September 2023.

Answer:

[tex]8x-10[/tex]

Step-by-step explanation:

[tex]5x+3(x-4)+2[/tex]

Distribute:

[tex]=5x+(3)(x)+(3)(-4)+2\\=5x+3x+-12+2[/tex]

Combine Like Terms:

[tex]=5x+3x+-12+2\\=(5x+3x)+(-12+2)\\=8x+-10\\= 8x - 10[/tex]

Since the graph of an exponential function passes through (minus 10, minus 1), (2, 8) also intercepts the x-axis at minus 2 units and y-axis at 2 units, a statement which correctly compares the two functions include the following: A. They have the same x-intercept and the same end behavior as x approaches ∞.

In Mathematics, the y-intercept of any graph such as an exponential function, generally occur at the point where the value of "x" is equal to zero (x = 0).

In Mathematics, the x-intercept can be defined as the point at which the graph of an exponential function crosses the x-coordinate and the value of "y" is equal to zero (0).

Based on the information provided about the graph of function f, the x-intercept and y-intercept include the following:

x-intercept = (-2, 0).

y-intercept = (0, 2).

Furthermore, the x-intercept and y-intercept of function g include the following:

x-intercept = (-2, 0).

y-intercept = (0, 8).

Therefore, we can logically conclude that both functions have the same x-intercept of -2.

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The number of minutes to read is 6.25 pages and taking the test will be 5 minutes and 0.50 minutes, respectively.

The rate is the ratio of the amount of something to the unit. For example - If the speed of the car is 20 km/h it means the car travels 20 km in one hour.

It takes you 0.8 of a minute to read each page of your health book. It takes you 5.5 minutes to take the test at the end.

The number of minutes to read 6.25 pages will be given as,

⇒ 6.25 x 0.8

⇒ 5 minutes

The number of minutes to take the test will be given as,

⇒ 5.5 - 5

⇒ 0.50 minute

⇒ 0.50 x 60

⇒ 30 seconds

The number of minutes to read is 6.25 pages and taking the test will be 5 minutes and 0.50 minutes, respectively.

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Answer:

y = -2x

Step-by-step explanation:

The equation is y = mx +b

m = the slope

b = y-intercept

The slope = rise/run

Let's pick 2 points (0,0) (2,-4); we see the y decrease by 4 and the x increase by 2, so our slope is

m = -4/2 = -2

Y-intercept is when x = 0, y-intercept is located at (0,0)

So our equation is

y = -2x

At 0 seconds and 12 seconds, the electric vehicle is not moving.

The most crucial scientific notion is measurement.

Base or physical fundamental units are used to quantify a wide range of quantifiable quantities.

One such measurable metric is speed, which calculates the ratio between the distance an object travels and the time needed to cover that distance.

The distance traveled in relation to the time it took to travel that distance is how speed is defined.

Since speed simply has a direction and no magnitude, it is a scalar quantity.

When an object travels the same distance in the same amount of time, it is said to be moving at a uniform speed.

Average speed is the constant speed determined by the ratio of the total distance traveled by an object to the total amount of time it took to travel that distance.

According to our question-

At the start of the test, x: represents the time in seconds.

Y: stands for the speed, expressed in miles per hour.

Then, we have this:

x = 0 —-> y = 0

x = 12 —-> y = 0

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Answer:

9,000

Step-by-step explanation:

5(3)=15

3000(3)=9000

The division equation that could be used to find the amount of jellybeans, b, in ounces, that were in the original bag that Rowan bought is given as follows:

6 = b/9.

The division equation is obtained applying the proportions in the context of this problem.

The number of ounces per bean is given by the division of the total amount of jellybeans and the number of bags.

The parameters for this problem are given as follows:

Hence the division equation is given as follows:

6 = b/9.

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The conditional, "If you work 20 hours a week, then you would make $125.00" would be false if this holds true:

c. You work 20 hours a week, and you make $175.00

To arrive at the wrong conclusion, we need to look out for the statement that directly violates the hypothesis that working 20 hours a week will yield $125.

The answer that is in direct conflict with this statement is option C. Here, instead of making $125, the person makes $175 and this is way above the conclusion reached in the original sentence. So, the wrong conditional is C.

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Answer:3 cm to 15 km

Step-by-step explanation:

The ratio of green to yellow marbles is 3/2.

What is ratio?

A ratio in mathematics demonstrates how many times one number is present in another. For instance, if a bowl of fruit contains eight oranges and six lemons, the ratio of oranges to lemons is eight to six. The ratio of oranges to the total amount of fruit is 8:14, and the ratio of lemons to oranges is 6:8.

Given:

For every 3 green marbles James has, he has 2 yellow marbles.

We have to find the ratio of green to yellow marbles.

As for every 3 green marbles James has, he has 2 yellow marbles.

So, the the ratio of green to yellow marbles is 3/2.

Hence, the ratio of green to yellow marbles is 3/2.

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In the given word problem amount does Teresa spends is $16.50.

A math word problem is a question that is written as one or more sentences and asks students to use their mathematical understanding to solve an issue from "real world." In order  to understand the word problem, they must be familiar with the terminology that goes along with the mathematical symbols that they are used to.

Here,

The amount does Jayson Spends = $3.75

According to the question,

Myra spends 3times as much as Jayson . then

Amount does Myra spends = 3× 3.75 = $11.25.

Now Teresa spends $5.25 more than Myra then,

Amount does Teresa spends = 11.25+5.25 = $ 16.50.

Hence In the given word problem amount does Teresa spends is $16.50.

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Therefore , the solution of the given problem of expression comes out to be sixty-seven billion five hundred eighty million.

Each variable must be replaced with a number and arithmetic operations must be performed to check an algebraic equation. Given that 6 + 6 equals 12, the answer variable in the aforementioned case is comparable to 6. We can substitute the variables values with those we know in order to evaluate the expression.

Here,

6.758 1010 in scientific notation

The scientific notation is = 6.758e10.

Engineering notation: 67.58 109 billion; prefix: giga- (G)

6.758 x 1010 standard form

10 Order of Magnitude for scientific notation and conventional forms

=>67580000000  (real number) 

=>67,580,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000  

sixty-seven billion five hundred eighty million

word form.

Therefore , the solution of the given problem of expression comes out to be sixty-seven billion five hundred eighty million.

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Answer:

Should be Ones: 1, Tenths: 2, Hundredths: 5

Step-by-step explanation:

The set W1 could be a basis for R3 if it spans R3 and is linearly independent, but without the specific elements of W1, it's not possible to determine if it meets those criteria.

The specific elements that make up the set W1. However, I can tell you that to be a basis for R3, a set of vectors must meet two criteria:

So, depending on the specific elements of W1, it could be either A, B, or C.

If the set W1 doesn't span R3, it would be A.

If the set W1 is linearly dependent, it would be C.

If both conditions are met the set is a basis, so the answer would be B.

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Answer:

2000 dollar and 6% impound will be your answer

Step-by-step explanation:

Answer:

  a) 144°

  b) 90°

Step-by-step explanation:

You want the measures of the 2nd largest, and the smallest, of the angles in a hexagon whose ratios are 5:5:6:7:8:9.

The interior angles of a hexagon will have a sum of ...

  180°×(n -2) = 180°×(6 -2) = 720°

The sum of the numbers in the given ratio is ...

  5+5+6+7+8+9 = 40

This tells us that multiplying the ratio values by 720/40 = 18 will give the angle values:

  90:90:108:126:144:162

The second largest angle is 144°.

The smallest angle, 90°, is the one that is repeated.

Answer:

Rick read for 1 hour.

Step-by-step explanation:

Tina read 3 hours, Larry read twice as long that is 6 hours, Rita read one third of Larry's so 6 times one-third is 2 hours, half that for Rick's hours and you get 1 hour

Considering the graph of the curve shown if f(x) = 0 then the value of x is

The x-intercepts of the function's graph, or the zero of a function, is the location on a graph where the function's graph crosses the x-axis.

This is the solution of the graph. it also called the x intercept or the zero

Examining the graph, the points are in exact spot in both the negative and positive part of the x axis

This spot is between 1 and 2 and not up to half way while moving from 1 to 2.

The point can be estimated to be 1.4 hence the values are

(-1.4 0), (1.4, 0)

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The cost for one pound of birdseed should be $0.67. The solution has been obtained using the unitary method.

What is a unitary method?

In the unitary method, the value of a single unit is first calculated, and only then is the value of the necessary number of units calculated. The unitary technique, to put it simply, is used to calculate the value of a single unit from a given multiple.

We know that cost per pound = Total pounds/cost

So, for Mariela

15 pounds = $10.00      

1 pound = $0.67  

For Mark,

12 pounds = $8.00  

1 pound = $0.67

For Daryl,

18 pounds = $12.00    

1 pound = $0.67

Hence, the cost for one pound of birdseed should be $0.67.

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Since, the question is incomplete, the complete question has been attached below

The number of mandarins in the bag is 3 * 33 + 3 = 102 mandarins.

This is a Diophantine equation problem, which is a type of mathematical problem that looks for integers that satisfy a given equation.

We know that the number of mandarins in the bag is equal to 4n + 3, 5m + 2 and 6p + 3 and 7q + 3 for some integers n, m, p and q.

We also know that the number of mandarins in the bag is equal to 3r, where r is an integer.

From the information provided, we can set up the following equation:

4n + 3 = 5m + 2 = 6p + 3 = 7q + 3 = 3r

Now we can use the information that when he finally put them into 3 piles and he didn't have any left over, meaning that the number of mandarins in the bag is divisible by 3, we can see that the remaining number in each case is 3.

Thus the number of mandarins in the bag is 3 * (some integer) + 3.

We can then use the information that the number of mandarins in the bag was less than 100, meaning the possible value of r is less than 34.

Testing values of r starting from 1, we can see that r = 33 satisfies the equation and the number of mandarins in the bag is 3 * 33 + 3 = 102 mandarins

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