What are the roots of x^3 −2=2x^2 −x?

The area of the region enclosed by the inner loop of the curve is 4π/3.

The term area is defined as the total space taken up by a flat (2-D) surface or shape of an object.

Here we have Given the following values,

r = 4 + 8 sin (θ)

Now, we have to substitute the value of r = 0, then we get

⇒ 0 = 4 + 8 sin (θ)

⇒ 8 sin (θ) = -4

⇒ sin θ = -1/2

⇒ θ = -π/6

Therefore, the limit lies in the interval -π/6 to + π/6

Now, the value of Area of polar region is calculated as,

=> A = ∫

Now, by Substituting the values

A=∫π/6−π/6 (4 + 8 sin (θ)) dθ

When we simplify this one then we get the value as,

=> A = 8 [θ + 1/6 sin6θ]

Apply the limit value, then we get

=> A = 8[(π/6 + 0) - (0 + 0)]

=> A = 4π/3

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The stone face is approximately 57.8512 feet in height.

Height is a mathematical term that refers to the vertical distance between an object's top and base.

Sometimes, it has the designation "altitude."

The measurement of an item along the y-axis in coordinate geometry is referred to as height in geometry.

So, let h be the stone's face's height.

One sight is 750 feet away from the mountain's base, and there is a 33° elevation difference between it and the bottom of the face.

The distance between the mountain's base and the base of the stone face

= 750 * tan33°

= 750 * 0.64940759319

= 487.055694898

A different location, which is 36° in elevation and 750 feet from the mountain's base, can be seen from the summit of the face.

The separation between the mountain's base and the top of the stone face = (h + 487.055694898) ft

Now, using trigonometry:

h + 487.055694898/750 = tan36°

h + 487.055694898 = 0.726542525 * 750

h = 544.906896004 - 487.055694898 = 57.8512011059 = 57.8512

Therefore, the stone face is approximately 57.8512 feet in height.

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Correct question:
To measure a stone face carved on the side of a​ mountain, two sightings 750 feet from the base of the mountain are taken. if the angle of elevation to the bottom of the face is 33° and the angle of elevation to the top is 3636°​, what is the height of the stone​ face?

We check the validity that i² is equal to -1

The first thing we will do is define numerical sets and complex numbers.

Numerical sets are groupings of numerical values that have a particularity in common, they can be integers, decimals, fractions, among others.

Among the numerical sets there is one that we call complex numbers, which include values that are not real, such as "i" a letter that denotes that it is an imaginary number.

The definition of a letter value that identifies a type of complex number is the "i" which is the result of the square root of -1, then we have:

√(-1) = i

√(-1) x √(-1) = i²

[√(-1)]² = i²

(-1) = i²

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Answer:

sqrt{9(x-4)} - 4

3sqrt{x-4} - 4

Step-by-step explanation:

the third option

Answer: C

Step-by-step explanation:

Two congruent figures are similar can be proved by using theorem of similarity given by : SSS, SAS, ASA, AA, and RHS.

Congruent figures are also representing similar figure can be proved in the following ways:

Therefore, two congruent figures are similar proved by theorem of similarity given by : SSS, SAS, ASA, AA, and RHS.

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The value of [tex]-4^{-2}[/tex] without Exponent is  [tex]\frac{1}{16}[/tex]

The exponent of a number indicates how many times a number has been multiplied by itself. For instance, 3^4 indicates that we have multiplied 3 four times. Its full form is 3×3×3×3. Exponent is another name for a number's power. A whole number, fraction, negative number, or decimal are all acceptable.

How many times we must multiply the reciprocal of the base is indicated by a negative exponent. For instance, if a^-n is provided, it can be stretched to 1/a^n. It implies that we must multiply 1/a 'n' times, which is the reciprocal of a. When writing exponentiated fractions, negative exponents are employed.

Given;

(-4)⁻² , That implies we have to multiply reciprocal of -4 "2" times .

⇒[tex]\frac{1}{-4}[/tex]×[tex]\frac{1}{-4}[/tex]=[tex]\frac{1}{16}[/tex]

The value of [tex]-4^{-2}[/tex] without Exponent is  [tex]\frac{1}{16}[/tex]

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As per the concept of ANOVA, the larger the differences among the sample means, the larger the numerator of the F-ratio will be True.

Here we have given that if it is true whether the larger the differences among the sample means the larger the numerator of the F-ratio will be.

In order to find that, we must know the definition of F - ratio.

The term f - ratio is defined as the ratio of the between group variance to the within group variance.

While we consider the given situation, here for both repeated-measures design and independent-measures design then the F-ratio compares the actual mean differences between treatments with the amount of difference that would be expected if there were no treatment effect.

Based on these theory we have identified that the statement is true.

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Answer:

x can be any number, which we need to find out in an equation

Answer:

The answer is 6k⁷ - 10k⁴ + 10k³

Step-by-step explanation:

-2k³ (-3k⁴ + 5k - 5)

6k⁷ - 10k⁴ + 10k³

Thus, The answer is 6k⁷ - 10k⁴ + 10k³

If there is a y-intercept, we can find it by plugging a zero for x and evaluating the function. If this produces an undefined value, then there is no y-intercept. To find the x-intercept, set y to zero and solve for x.

Now, According to the question:

Logarithmic functions will always have an x-intercept, but they may not have a y-intercept. Let's look at a simple example:

                        y = [tex]log_1_0x[/tex]

A y-intercept would be located at the y value we get by plugging in a zero for x. The problem is that the function does not have zero as a part of its domain. It is not defined there, so there is no y-intercept. The x-intercept is the x value that causes y to be zero. For a basic logarithmic function like this, that is always x equals 1.

                            0 = [tex]log_1_0x[/tex]

                            [tex]10^0[/tex] = x

                            1 = x

Now we can shift, stretch, and reflect this model to change these results, but the basic idea is still the same. For example, let's consider this model:

                          y = [tex]log_1_0[/tex] (x + 100) + 2

As always, we look for a y-intercept by plugging in a zero for x. In this case, we do get an answer. This is because of the 100 that is added to the argument of the logarithm.

                          y = [tex]log_1_0[/tex] (0 + 100) + 2

                          y = 2 + 2 = 4

As always, to find the x-intercept, we set y to zero and solve for x

                              y = [tex]log_1_0[/tex] (x + 100) + 2

                             -2 =  [tex]log_1_0[/tex] (x + 100)

                             [tex]10^-^2[/tex]  = x + 100             [By taking antilog on both sides ]

                             0.01 = x + 100

                               x = -99.99

So, no matter what the logarithmic function is, we can find the intercepts in this way. If there is a y-intercept, we can find it by plugging a zero for x and evaluating the function. If this produces an undefined value, then there is no y-intercept. To find the x-intercept, set y to zero and solve for x.

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The x-intercept and coordinate of the vertex of the given parabola will be x = 1,7 and (4,-9) respectively.

A pair of numbers that employ the horizontal and vertical distinctions from the two reference axes to represent a point's placement on a coordinate plane. typically expressed by the x-value and y-value pairs (x,y).

As per the given parabola,

y = x² - 8x + 7

At x-intercept, y = 0

x² - 8x + 7 = 0

x² - 7x - x + 7 = 0

x(x - 7) - (x - 7) = 0

(x - 1)(x - 7) = 0

x = 1,7

For the vertex, the slope will be zero,

y' = 2x - 8 + 0 = 0

2x = 8

x = 4

Thus, y = 4² - 8 x 4 + 7

y = -9

Thus, the coordinate of the vertex is (4,-9)

Hence "The given parabola's x-intercept and vertex coordinates are x = 1,7 and (4,-9), respectively.".

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Answer:

Area of the figure =[tex]100.26[/tex]

Step-by-step explanation:

Firstly we need to find the area of the rectangle

[tex]Area \\ of \\rectangle= lb[/tex]

[tex]12X6\\= 72[/tex]

[tex]Area\\of \\the \\semicircles= \frac{\pi }{2} Xr^{2}[/tex][tex]X2[/tex]

= [tex]\frac{3.14}{2} X(3)^{2} X2[/tex]

=[tex]28.26[/tex]

Area of the figure = Area of rectangle + Area of the 2 semi circles

Area of the figure = [tex]72+28.26[/tex]

[tex]100.26[/tex]

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The measure of the altitude of the triangle shown in the figure given below is  15 inches .

The Altitude of the triangle is defined as the perpendicular distance from the top vertex of the triangle to the base of the triangle.

Also , the altitude of a right triangle is same as height of triangle.

If in the right triangle , the length of altitude is "a units" ,

the length of base is "b units " , and the length of hypotnuse is "c units" .

So , the altitude can be calculated using the formula : a = √(c² - b²) .

from the figure given below , we can see that , c = 25  and b = 20

we get , a = √(25² - 20²)

a = √(625 - 400)

a = √225 = 15 inches .

Therefore , measure of the altitude in the figure is 15 inches .

The given question is incomplete , the complete question is

How do you find the altitude of the triangle shown in the figure given below ?

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Answer:

(y2 - y1) / (x2 - x1)

Step-by-step explanation:

The equation that teacher taught to find the slope is

( y2 - y1) / (x2 - x1)

The mean of number of students who read fictional books is 4.32.

In statistics, the mean refers to the average of a set of values. The mean can be computed in a number of ways, including the simple arithmetic mean (add up the numbers and divide the total by the number of observations).

Given that, the summary of fictional books read by 37 students.

Total number of students =37

Sum =4(2)+10(3)+13(4)+10(7)

= 8+30+52+70

= 160

Now, mean =160/37

= 4.32

Therefore, the mean of number of books read by students is 4.32.

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The mean of the data 2, 3, 4, 5,0, 1, 3, 3, 4, 3 is 2.8.

Mean is the average of the given numbers and is calculated by dividing the sum of given numbers by the total number of numbers.

The basic formula to calculate the mean is calculated based on the given data set. Each term in the data set is considered while evaluating the mean. The general formula for mean is given by the ratio of the sum of all the terms and the total number of terms. Hence, we can say;

Mean = Sum of the Given Data/Total number of Data

Mean= 2 +3 +4 +5 +0 +1 +3 +3 +4 +3 / 7 = 28/10 = 2.8

Hence, The mean of the data 2, 3, 4, 5,0, 1, 3, 3, 4, 3 is 2.8.

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The equation of the circle in standard form from the given graph is

x² + y² + 2x + 2y - 45 = 0

A circle is a two-dimensional figure with a radius and circumference of 2πr

The standard equation of a circle is (x - h)² + (y - k)² = r²

Where (h, k) is the center of the circle

We have,

The standard equation of a circle is (x - h)² + (y - k)² = r²

The coordinates of the center of the circle from the figure.

= (-1, -2)

This means,

(-1, -2) = (h, k)

The radius of the circle is 5√2.

The distance between (-1, -2) and (-6, 3).

= √(-6 + 1)² + (3 + 2)²

= √(25 + 25)

= √50

= 5√2

Now,

The standard equation of a circle is (x - h)² + (y - k)² = r²

(x + 1)² + (y  + 2)² = 50

x² + 2x + 1 + y² + 2y + 4 = 50

x² + y² + 2x + 2y - 45 = 0

Thus,

The equation of the circle is x² + y² + 2x + 2y - 45 = 0

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The nature of the roots of the quadratic equation 4[tex]x^{2}[/tex] - 8x + 9 =0 are imaginary.

given equation:

4[tex]x^{2}[/tex] - 8x + 9 =0

now we need to find the nature of the quadratic equation

nature of roots :

Case I: [tex]b^{2}[/tex] – 4ac > 0

When a, b, and c are real numbers, a ≠ 0 and the discriminant is positive, then the roots α and β of the quadratic equation ax2 +bx+ c = 0 are real and unequal.

Case II: [tex]b^{2}[/tex]– 4ac = 0

When a, b, and c are real numbers, a ≠ 0 and the discriminant is zero, then the roots α and β of the quadratic equation ax2+ bx + c = 0 are real and equal.

Case III: [tex]b^{2}[/tex]– 4ac < 0

When a, b, and c are real numbers, a ≠ 0 and the discriminant is negative, then the roots α and β of the quadratic equation ax2 + bx + c = 0 are unequal and not real. In this case, we say that the roots are imaginary.

Case IV: [tex]b^{2}[/tex] – 4ac > 0 and perfect square

When a, b, and c are real numbers, a ≠ 0 and the discriminant is positive and perfect square, then the roots α and β of the quadratic equation ax2 + bx + c = 0 are real, rational and unequal.

for the above given equation:

a = 4

b = -8

c = 9

=[tex]b^{2}[/tex] - 4ac

= [tex](-8)^{2}[/tex] - 4(4)(9)

= (56) -144

= -88< 0

the roots are imaginary

The nature of the roots of the quadratic equation 4[tex]x^{2}[/tex] - 8x + 9 =0 are imaginary

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The first three consecutive numbers starting from the origin "0" are:

1, 2 and 3

Consecutive numbers are those numerical values that are found just after a specific number or value, for example consecutive numbers from 5 will be 6 onwards.

As the consecutive numbers are followed by addition operations, if we start from the origin zero, then the first three consecutive numbers will be:

1,2 and 3 are the first three consecutive terms.

Another way to know the consecutive number is with successive additions

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Answer:

1/2

Step-by-step explanation:

(Solving cos first)

= cos15 cos 45

= (√6 + √2)/4 * (√2) / 2

= (1 + √3) / 4

(solving sin)

= sin15 sin45

=  (√6 - √2)/4 * (√2) / 2

= (-1 + √3) / 4

(Subtracting both)

= (1 + √3) / 4 -  (-1 + √3) / 4

= 1/2

I hope my answer helps you.

Answer:

(solving sin)

= sin15 sin45

=  (√6 - √2)/4 * (√2) / 2

= (-1 + √3) / 4

(Subtracting both)

= (1 + √3) / 4 -  (-1 + √3) / 4

= 1/2

Step-by-step explanation:

Answer:

56 teddy bears

Step-by-step explanation:

If each teddy bear weighs 1/4 pounds, then the total weight of teddy bears that can be put on the display is 1/4 pounds * X teddy bears, where X is the number of teddy bears.

The maximum weight the display can hold is 14 pounds, so we need to find the value of X that satisfies the equation: 1/4 pounds * X teddy bears = 14 pounds.

Dividing both sides of the equation by 1/4 pounds, we get: X teddy bears = 14 pounds / 1/4 pounds = 56 teddy bears.

Therefore, the employee can put 56 teddy bears on the display.

Answer:  56 teddy bears on the display.

Step-by-step explanation: We can find the maximum number of teddy bears that can be put on the display by dividing the maximum weight of the display by the weight of each teddy bear. Since each teddy bear weighs 1/4 pounds and the display can hold 14 pounds, we can put a maximum of 14 / (1/4) = <<14/(1/4)=56>>56 teddy bears on display.

The fraction 3/4 is equivalent to 0.75, or 75%. This means that 3 out of every 4 parts is equal to 75%.

Fraction is a numerical expression that represents a part of a whole. It is represented by a numerator (top number) and a denominator (bottom number). The numerator shows how many parts of the whole are being considered, and the denominator represents the total number of parts that make up the whole. Fractions are used in everyday life, from dividing food and measuring distances to calculating discounts and percentages.

This fraction can also be expressed as a decimal, a percent, or as a mixed number.For example, 3/4 can be written as 0.75, 75%, or 3 1/4.
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The equation of the line passing through the points with coordinates (-3,-4) and (-2,0) in slope intercept form is y = 4x + 8  .

The Equation of  Line in Slope intercept form is written as " y = mx + c " , where m is the slope of line and c is the y intercept .

the required line is passing through the points (-3,-4) and (-2,0) ,

So , the slope(m) = (0+4)/(-2+3) = 4/1 = 4 ;

0 = 4(-2) + c ;

On simplifying further ,

we get ;

c = 8 .

putting the values of m and c ,

we get ;

y = 4x + 8 .

Therefore , the equation of line in slope intercept form is y = 4x + 8 .

The given question is incomplete , the complete question is

How do you find the equation in slope intercept form of the line passing through the points with the given coordinates (-3,-4) and (-2,0) ?

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The formula finds the difference between the lowest and highest value, which aids in locating the set's center.

The range of values between the highest and lowest values for a certain data collection is known as the statistical range. It is also possible to show the range by comparing the highest and lowest observational values. The sample interval is found by subtracting the highest value from the lowest. For continuously varying variables, the sample range is a key measure of variability.

here ,

Assign each number a value within the data collection, starting with the lowest and working your way up.

Take the highest value chosen from the data set and divide it by the lowest value using the range formula.

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By using the formula for the distance between two points we will see that the distance between the two points is √80 is 8.9

The length of the line connecting two places represents the distance between them. Subtracting the different coordinates will reveal the distance if the two points are on the same horizontal or vertical line.

Learn how to apply the Pythagorean theorem to find the distance between two points using the distance formula. The Pythagorean theorem can be rewritten as d=(((x 2-x 1)2+(y 2-y 1)2) to calculate the separation between any two locations.

The general formula for the distance between two points (a, b) and (c, d) is:

Distance = √[(a-d)²+(b - c)²]

In this case, we have the points (-4,1) and (4,5), replacing that in the above formula we get:

Distance = √[(-4-4)²+(1-5)²]

= √80

=8.9

Therefore the distance between the two points (-4,1) and (4,5) is 8.9

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Option d is Correct. The other ratios of right triangle's area is 1/4 of the square's size in terms of area.

Two right triangles are similar, as demonstrated in mathematics. It follows that the triangles' side ratios are equal. The triangle's height with area m is 2m in the figure because A = 1/2bh = h/2. The base of the other triangle is x, therefore 2m/1 = 1/x. Please see the file that is provided for the figure, which is X = 1/ 2m.

Area of triangle = 1/2 * base * height

The area of that triangle, which is determined by the relationship between its area and the area of the square, is

= 1/2 × 1 × 1/2m = 1/4m

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Correct Question:

Through a point on the hypotenuse of a right triangle, lines are drawn parallel to the legs of the triangle so that the triangle is divided into a square and two smaller right triangles. The area of one of the two small right triangles is m times the area of the square. The ratio of the area of the other small right triangle to the area of the square is:___________.

(A) 1/(2m + 1)

(B) m

(C) 1 - m

(D) 1/(4m)

(E) 1/(8m^2)

The error in the statement will be When reporting correlation, one does not report units because correlation has no units that is option D is correct.

The correct statement would be "The correlation between shoe size and height is 0.87." The correlation coefficient is a measure of the strength and direction of a linear relationship between two variables. It ranges from -1 to 1, with -1 indicating a strong negative relationship, 0 indicating no relationship, and 1 indicating a strong positive relationship. The correlation coefficient does not have units because it is a standardized measure of the relationship between the variables. If there is a unit given in any correlation statement then it means that the statement is a wrong statement or it has an error.

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SAS is a similarity postulate through which we can find if a given two triangles are similar or not

SAS postulate:( side angle side)

It states that if the two sides and one angle of two triangles are equal then the two triangles are said to be similar.

Let the angles ∠ABC, ∠BCA, and AB of triangle ΔABC is equal to angles∠ XYZ and ∠YZX and XY of triangle ΔXYZ then can say that triangle ABC is similar to triangle XYZ, and their remaining sides and angles will be also equal.

SAS is a similar theorem to prove that two triangles are equal.

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In total, Menaha traveled 97km 1000m (97.1km).

Distance is a numerical measurement of how far apart two objects, points, or places are in space. Distance can be measured in linear units such as meters, kilometers, feet, miles, etc. It can also be measured in angular units such as degrees or radians.

Distance can also refer to the space between two points in time, such as the time between two events. Distance can be used to measure physical distance, time, or even emotional distance.
To calculate this, the two distances must be added together.
The train distance is =86km 520m (86.52km)

and the car distance is =11km 480m (11.48km).
When added together, =86km 520m+11km 480m = 97.52km.
However, since the distances are measured in km and m,
it is necessary to convert the measurements into a single unit of measurement.
To do this, the measurements must be converted into metres.
The train distance is 86,520 metres

And the car distance is 11,480 metres.
When added together,

the total distance is 97,000 metres (97km).

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The mass and center of mass of the lamina that occupies the region D and has the given density function p is 57/14 and (14/27, 7/18) respectively.

The center of mass (x―,y―) of a lamina with density function ρ(x,y) is given by

x = M(y)/m, y = M(x)/m

Where, m=∫∫[tex]_{D}[/tex]ρ(x,y)dA

Mx=∫∫[tex]_{D}[/tex] yρ(x,y)dA

My=∫∫[tex]_{D}[/tex] xρ(x,y)dA

Given that, D is bounded by y=x^2 and x=y^2

And ρ(x,y)=19√x

Now, for the point of intersection of y=x^2,x=y^2

we have,

x = (x^2)^2

x = x^4

Subtract x^4 on both side

x - x^4 = 0

x(x^3−1) = 0

x = 0, 1

Now, x=0⇒y=0 and x=1⇒y=1

The points of intersection are (0,0),(1,1)

So, the region D can be written as

D={(x,y): 0≤x≤1, x^2≤y≤x}

So,

m = [tex]\int_{0}^{1}\int_{x^2}^{\sqrt x}19 \sqrt xdydx[/tex]

m = [tex]19\int_{0}^{1}\sqrt{x}[y]^{x^2}_{x}dx[/tex]

m = [tex]19\int_{0}^{1} \sqrt x(\sqrt{x}-x^2)dx[/tex]

m = [tex]19\int^{1}_{0}(x-x^{5/2})dx[/tex]

m = [tex]19[\frac{x^2}{2}-\frac{x^{7/2}}{7/2}]^1_{0}[/tex]

m = [tex]19[\frac{1}{2}(1^2-0)-\frac{2}{7}(1^{7/2}-0)][/tex]

m = 19(1/2−2/7)

m = 57/14

m = 5714

Now,

Mx = [tex]\int_{0}^{1}\int_{x^2}^{\sqrt x}(19xy)dydx[/tex]

Mx = 19[tex]\int^{1}_{0}x[\frac{y^2}{2}]_{x^2}^{\sqrt x}dx[/tex]

Mx = [tex]\frac{19}{2}\int^{1}_{0}x[(\sqrt{x})^2-(x^2)^2}dx[/tex]

Mx = [tex]\frac{19}{2}\int^{1}_{0}(x^2-x^5)dx[/tex]

Mx = [tex]\frac{19}{2}[\frac{x^3}{3}-\frac{x^6}{6}]_{0}^{1}[/tex]

Mx = [tex]\frac{19}{2}[\frac{1}{3}(1^3-0)-\frac{1}{6}(1^6-0)][/tex]

Mx = 19/2 (1/3−1/6)

Mx = 19/12

And

My = [tex]\int^{1}_{0}\int_{x^2}^{\sqrt x}x(19\sqrt{x})dydx[/tex]

My = [tex]19\int_{0}^{1}x^{3/2}[y]^{\sqrt{x}}_{x^2}dx[/tex]

My = [tex]19\int_{0}^{1}x^{3/2}(\sqrt{x}−x^2)dx[/tex]

My = [tex]19\int_{0}^{1}(x^2-x^{7/2})dx[/tex]

My = [tex]19[\frac{x^3}{3}-\frac{x^{9/2}}{9/2}]_{0}^{1}[/tex]

My = 19[1/3(1^3−0)−2/9(1^{9/2}−0)]

My = 19(1/3−2/9)

My = 19/9

So, x = My/m

x = (19/9)/(57/14)

x = (19/9)×(14/57)

x = 14/27

y = Mx/m

y = (19/12)/(57/14)

y = (19/12)×(14/57)

y = 7/18

Therefore, the solutions are (14/27, 7/18).

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