A 15N birthday cake remains sitting on a table with two collapsed legs after someone fell into it.
The accident has left the table inclined above the horizontal 23°. Find the X and Y components
of the cake's weight.

The value of the integral can be calculated by using the simple rules of definite integral and double integral.

The first integral is a bit tricky, as the limits of integration are not in the standard order (with respect to x and y). However, we can change the order of integration by switching the limits of integration, so that we can use Fubini's theorem.

The double integral can be solved by converting the rectangular region R into polar coordinates.

The double integral is ∫∫R 5xsin(x+y)dA, R=[0,pi/3]×[0,pi/6]. This can be further solved as

= ∫(0,pi/3) ∫(0,pi/6) 5rrsin(rcos(θ)+rsin(θ))dθ dr

= ∫(0,pi/3) ∫(0,pi/6) 5r^2sin(r(cos(θ)+sin(θ)))dθ dr

= ∫(0,pi/3) 5r^2(-cos(r*(cos(θ)+sin(θ))) | (0,pi/6))dr

= ∫(0,pi/3) 5r^2(-cos(r*(√(2)/2)))dr

= -5/2∫(0,pi/3) r^2cos(r*(√(2)/2))dr

The integral above is not in a closed form but can be evaluated using numerical integration techniques.

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Complete Question:

Calculate the iterated integral. integral_0^3 integral_0^1 5xy Square root x^2 + y^2 dy dx = Calculate the double integral. double integral R 5x sin (x + y) dA, R = [0, pi/3] times [0, pi/6] The value of integral is

Answer:

7 students.

Step-by-step explanation:

A trick for this is to find 10% of the students in the Environmental Club and then divide by 2.

10% of 140 is simple; just remove the 0 and you got 14.

Next, divide 14/2 to get 5%

14/2 = 7

7 students are apart of the Environmental Club

The area of trapezoid is 16 m².

Given in the figure,

Height of trapezoid = 4 m

Length of 1st parallel base = 2 m

Length of 2nd parallel base = 6 m

We know that,

Area of trapezoid = 1/2 * sum of bases * height

∴

Area of trapezoid = 1/2 * (2+6) * 4

                             = 8 * 2 = 16 m²

Therefore, the area of trapezoid is 16 m².

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Answer: 4/7

Step-by-step explanation:

pretty simple, 1/7 and 3/7 both has a denominator of "7", so the seven stays the same. (While writing this I made a chart to see where I put everything)

Write:

 1/7 = (denominator 7)

+ 3/7 = (denominator 7)

Now we start doing the math, what goes into 7? 7x1 so 1 x 3 = 3

know we go up to the numerator, 7x1=7, so 1 x 1 = 1

add 3 + 1 and that adds up to 4

so your answer is 4/7, hope it helps

Answer:

x=8

Step-by-step explanation:

Answer:

3x+y+4-(y + 6) = 14 + x

x=8              

a. Yes, it is possible for a line (y = mx + b) that passes through the origin (0, 0) to pass through no other rational points. An example of such a line is y = sqrt(2)x. This line passes through the origin (0,0), but the y-coordinate will only be a rational number if the x-coordinate is also a rational number and a perfect square.

b. Yes, it is possible for a line to pass through no rational points. An example of such a line is y = sqrt(2)x + sqrt(3). This line will never pass through any rational points because the y-coordinate will only be a rational number if both x and b are rational numbers and perfect squares, which is not possible in this case.

Answer:

  B, C

Step-by-step explanation:

You want to graph the inequalities y≤1/4x+3 and y≥-x+2 and identify points that are solutions to the system.

The graph is attached. It matches selection B of the graphs you are shown. The points that lie in the solution area are B(2, 1) and C(3, 3).

The correct graph of the solution to the compound inequality as given in the task content is;

As evident from the task content, it follows that the correct graph of the solution to the compound inequality is to be determined.

Since the given compound inequality is; -13 > -5x + 2 > -28.

To solve the inequality, subtract 2 from all sections of the compound inequality;

-15 > -5x > -30

Divide through the inequality by -5 while flipping the inequality signs so that we have;

3 < x < 6

Therefore, the correct graph for the compound inequality in discuss is as represented in the attached image.

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Answer:

the answer is 54 to the question 5 17 18 -2 23

The new point that will be formed when the point (-4,5) is rotated 270 degrees counterclockwise is; (5, 4)

There are different types of transformations namely dilation, rotation, reflection e.t.c

Now, when we rotate a point 270 degrees counterclockwise about the origin our point A(x,y) becomes A'(y,-x). This means that we switch x and y and make x negative.

Now, we are told that the point (-4,5) is rotated 270 degrees counterclockwise. Thus, following the transformation rule as described above gives us;

(-4,5) → (5, 4)

Thus, we conclude that the new coordinate we will obtain in this process is (5, 4)

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The given series is convergent and the sum(S) is 5.555.

Consider 10 - 8 + 6.4 - 5.12 + ...

A geometric progression will converge if the common ratio of the series is between -1 and 1.

Here is the common ratio,

r = -8/10

⇒ r = -0.8

Which is -1 < -0.8 < 1.

Hence, the given series is convergent.

Sum of series = S = a/(1 - r)

Here, first term(a) = 10,

common ratio(r) = -0.8,

S = a/(1 - r)

⇒ S = 10/(1 - (-0.8))

⇒ S = 10/(1 + 0.8)

⇒ S = 10/1.8

⇒ S = 5.555

Therefore, the given series is convergent and the sum( S)is 5.555.

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The equation of the line in slope intercept form is y = 1 / 2 x - 3 / 2.

The equation of a line can be represented in slope intercept form as follows:

y = mx + b

where

Let's find the slope of the line using the coordinates.

Therefore, using (-1, -2) and (-5, -4)

Hence, the slope of a line is the change in the dependent variable with respect to the change in the independent variable.

Therefore,

m = -4 + 2 / -5 + 1

m = - 2 / -4

m = 1 / 2

Therefore, let's find the y-intercept using (-1, -2)

y = 1 / 2 x + b

-2 = 1 / 2 (-1) + b

-2 + 1 / 2 = b

- 3 / 2 = b

Therefore, the equation of the line is y = 1 / 2 x - 3 / 2.

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If Loretta accidentally recorded a deposit of $47.88 as a debit in her register, her check register will differ from the bank statement by $0.

A deposit amount is debited to the check register as an asset, increasing the amount the account holder has in the bank.

It is the bank's responsibility to credit the deposit since it is a liability to them, not an asset.

Under accounting principles, assets are debited while liabilities are credited.  Loretta's debit entry in her register does not constitute an accounting error under the generally-accepted accounting principles.

Thus, Loretta has not committed an accounting error by recording a deposit of $47.88 as a debit in her register, and her register will not differ from the bank statement for this reason.

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Answer:

y = 5/6x - 1/12

Step-by-step explanation:

The slope-intercept form is y = mx + b

10x - 12y = 1

We subtracted 10x from both sides

-12y = -10x + 1

Divided by -12 both sides

y = -10/-12x - 1/12

To simplify we can get

y = 5/6x - 1/12

It is a scale factor of 2.

You could see that the JKL triangle has only 4 grids on one side and J'K'L' has 8. So 8/4=2, so, therefore, it is a scale factor of 2. Please correct me if I am wrong.

Answer:

18 sattelites

Step-by-step explanation:

Let's make an equation

n is number of sattelites on Saturn

n-2 is number of sattelites on Jupiter

n-16 is number of sattelites on Mars

Equation would be like:

n+(n-2)+(n-16)=36

3n-18=36

3n=54

n=18

Answer:

Welcome to Gboard clipboard, any text that you copy will be saved here.Touch and hold a clip to pin it. Unpinned clips will be deleted after 1 hour.Tap on a clip to paste it in the text box.

Numbers divisible by 2 and 5:

Check:

[tex]10\div2=5\\10\div5=2[/tex]  

[tex]20\div2=10\\20\div5=4[/tex]

[tex]30\div2=15\\30\div5=6[/tex]

Radius, diameter, center, and circumference--all are parts of a circle .Every point in the plane that is a certain distance away from a certain point forms a circle (center).

Every point in the plane that is a certain distance away from a certain point forms a circle (center). It is, thus, a curve formed by points moving in the plane at a fixed distance from a point. A circle is a closed two-dimensional object where every pair of points in the plane are equally spaced out from the "center." A line that goes through the circle creates a specular symmetry line. At every angle, it is also rotationally symmetric about the center.

Area of circle =  

[tex]\pi r^2\\r = 10\\A = 3.14 X 10 X 10\\A = 314 unit sq\\[/tex]

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On solving the provided question, we can say that area of circle = [tex]\pi r^2 =[/tex] 3.14*.3.4*3.4 = 1.28112 cm sq.

Every point in the plane that is a certain distance away from a certain point forms a circle (center). It is, thus, a curve formed by points moving in the plane at a fixed distance from a point. At every angle, it is also rotationally symmetric about the center. A circle is a closed two-dimensional object where every pair of points in the plane are equally spaced out from the "center." A line that goes through the circle creates a specular symmetry line. At every angle, it is also rotationally symmetric about the center.

here,

in the circle

the given radius is as = 3.4

area of circle = [tex]\pi r^2 =[/tex] 3.14*.3.4*3.4 = 1.28112 cm sq.

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The answer is 2¾. You can also buy calculators that do this for you automatically.

Answer:

Step-by-step explanation:

2 3/4

The quotient of the division is x^3 - 3x^2 - 10x + 64

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

quotient of (x^4-6x^3-19x^2+24x) divided by (x+3)

Using the long division method of quotient, we have

x + 3 | x^4 -6x^3 -19x^2 +24x

The division steps are as follows

            x^3 - 3x^2 - 10x + 64

x + 3 | x^4 -6x^3 -19x^2 +24x

         x^4 + 3x^3

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

              -3x^3  -19x^2 +24x

              -3x^3 - 9x^2

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

                          -10x^2 + 24x

                          -10x^2 - 30x

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

                                           64x

                                           64x + 192

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

                                            -192

Hence, the quotient is x^3 - 3x^2 - 10x + 64

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The statement that complete the proof that quadrilateral EFGH is a square is; A) Line EF, FG, GH, and EH are congruent

The four sides of a square are always congruent to each other which means that they are equal to each other.

Now, we see that;

EF = 3√2

GH = 3√2

FH =3√2

EH = 3√2

Thus, all four sides are equal.

We also see that the slopes that form 90 degrees with each other are perpendicular and as such that is also a requirement for the quadrilateral to be a square.

Thus, we can conclude that all four sides are congruent to each other from the evidence above.

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Answer:

Statement 4 of the proof should be:

segment EH is parallel to segment FG

Step-by-step explanation:

They have the same slope which is -1.

Answer:

f(8) = 51

Step-by-step explanation:

f(x) = 6x + 3

Let x = 8

f(8) = 6(8) + 3

     = 48+3

     = 51

Answer:

51

Step-by-step explanation:

f ( x ) = 6x + 3

To find the value of f ( 8 ), replace x with 8.

f ( 8 ) = 6 × 8 + 3

f ( 8 ) = 48 + 3

f ( 8 ) = 51

The formula for the area of a trapezoid is (a+b)*h/2, where a and b are the lengths of the bases and h is the height.

To estimate the total area between the curve and the x-axis using trapezoids, we can divide the region between the curve and the x-axis into a number of trapezoids, and calculate the area of each trapezoid. The sum of the areas of all the trapezoids will estimate the total area.

For example, consider the curve y = x^2 and the x-axis between x = 1 and x = 2. We can divide this region into 3 trapezoids with bases at x = 1, x = 1.5, x = 2, and heights of 0.25, 0.5625, and 1 respectively.

The area of the first trapezoid is (1 + 1.5) * 0.25 / 2 = 0.1875

The area of the second trapezoid is (1.5 + 2) * 0.5625 / 2 = 0.40625

The area of the third trapezoid is (2 + 2) * 1 / 2 = 1

The sum of the areas of all the trapezoids is 0.1875 + 0.40625 + 1 = 1.60625. This estimates the total area between the curve y = x^2 and the x-axis between x = 1 and x = 2.

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Answer:

for perimeter add 8 17 15 together that probably not helpful lol

The answer is : [tex]X= (A^{-1} C -B^{-1})D[/tex]

According to the question,

AX [tex](D^{-1} + X^{-1} B^{-1} )[/tex] =C

⇒X[tex](D^{-1} + X^{-1} B^{-1} )[/tex]= [tex]A^{-1} C[/tex]

⇒[tex]XD^{-1} + XX^{-1} B^{-1}[/tex] = [tex]A^{-1} C[/tex]

⇒ [tex]XD^{-1} +B^{-1}[/tex] = [tex]A^{-1} C[/tex]

⇒ [tex]XD^{-1} = A^{-1} C -B^{-1}[/tex]

⇒  [tex]X= (A^{-1} C -B^{-1})D[/tex]

So, the answer is : [tex]X= (A^{-1} C -B^{-1})D[/tex]

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The value of a is 3√3/2 and value of b is 3/2. The solution has obtained using the trigonometry formulas.

What is trigonometry?

The study of the right-angle triangle's sides, angles, and connection is the main focus of the field of mathematics known as "trigonometry." Therefore, it helps to find the unknown or missing angles or sides of a right triangle using the trigonometric formulas, functions, or trigonometric identities. The angles in trigonometry can either be expressed in degrees or radians. The most used trigonometric angles for computations include 0, 30, 45, 60, and 90 degrees.

In the figure, we are given that one angle measures 30° and the other measures 90° and the hypotenuse is 3.

So, using trigonometry, we know that

Cos theta = adjacent side/hypotenuse

And, Cos 30° is √3/2

So,

⇒√3/2 = a/3

⇒a= 3√3/2

Sin theta = opposite side/hypotenuse

And, Sin 30° is 1/2

So,

⇒1/2 = b/3

⇒b= 3/2

Hence, the value of a is 3√3/2 and value of b is 3/2.

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The angle B in triangle ABC is 60° i.e. C.

What is a triangle?

In Geometry, triangles are the type of polygons, which have three sides and three vertices. This is a two-dimensional figure with three straight sides. A triangle is considered a 3-sided polygon. The sum of all the three angles of a triangle is equal to 180°. The triangle is contained in a single plane. Based on its sides and angle measurement, the triangle has six types.

Based on the sides of a triangle, a triangle is classified into 3 types, namely:

Scalene Triangle – All the sides are of different measures.

Isosceles Triangle – Two sides of a triangle are of the same measure and the remaining side has a different measure.

Equilateral Triangle – All the 3 sides of a triangle are of the same measure.

Based on the angles of a triangle, a triangle is classified into 3 types, namely:

Acute Angle Triangle – All the angles of a triangle is less than 90°.

Obtuse Angle Triangle – One of the angles of a triangle is greater than 90°.

Right Angle Triangle – One of the angles of a triangle is equal to 90°.

Now

∠NAB+∠CAB=180°  (Supplementary angles)

∠CAB=180-∠NAB

=180-100

∠CAB=80°

As

∠A+∠B+∠C=180° (sum of all angles of a triangle =180°)

∠B=180-80-40

∠B=60°

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