Solve the differential equation by variation of parameters.
y'' + y = sin2 x

Santiago can make 7 dumplings

To find out how many dumplings Santiago can make, we need to divide the total amount of dough (5 11/16 cups) by the amount of dough used per dumpling (13/16 cups).

To do this, we can first convert the fractions to have a common denominator. In this case, the denominator of 13/16 is 16, so we can convert 5 11/16 to have a denominator of 16 as well:

5 11/16 = (5 * 16) + 11/16 = 80 + 11/16

Now we can divide:

(80 + 11/16) ÷ (13/16) = (80 + 11) ÷ 13 = 91 ÷ 13

So Santiago can make 91/13 dumplings. This can be simplified further to 7 dumplings. So Santiago can make 7 dumplings with 5 11/16 cups of dough.

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The term "line of symmetry" refers to the fictitious axis or line that you fold a figure along to create its symmetrical halves.

A definition of symmetry states that whether one form is moved, rotated, or flipped, it looks precisely like the other shape. Just fold the paper, draw one-half of the heart at the fold, then cut it out to discover that the second half precisely matches the first half when you are instructed to cut out a "heart" from a sheet of paper. The heart-shaped carving is an illustration of symmetry.

Symmetry is defined in mathematics as "a mirror image." Symmetry is the property of an image that remains unchanged after a form has been rotated or flipped. There are patterns in it. In daily life, you may have heard the word "symmetrical" frequently. One half of a thing is the mirror image of the other half, which is a balanced and proportionate likeness. Asymmetrical refers to a form that is not symmetrical. In nature, architecture, and the arts, symmetrical things are all around us.

The term "line of symmetry" refers to the fictitious axis or line that you fold a figure along to create its symmetrical halves. In essence, it splits one thing into two mirror images. The symmetry line may run vertically, horizontally, or diagonally. There might be one or many symmetry lines.

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Answer:

1. Choose Your Shape: Start with a shape that you want to create a line of symmetry for. It could be a simple shape like a square, rectangle, or triangle.

2. Draw the Shape: Draw the shape neatly on a piece of paper using a pencil.

3. Identify the Line of Symmetry: Decide where you want to place the line of symmetry. This line should divide the shape into two equal halves.

4. Draw the Line of Symmetry: Draw a straight line through the center of the shape, from one side to the other. Use a ruler to ensure the line is straight and passes through the center.

5. Create the Mirror Image: To create the mirror image on the other side of the line, imagine that the line is a mirror. Reflect each point on one side of the line to the other side while maintaining the same distance from the line. You can also use a ruler or straightedge to guide you as you draw.

6. Check for Symmetry: Carefully examine both sides of the line to make sure they are mirror images of each other. The distances and angles should match.

7. Finalize the Drawing: Once you're satisfied with the symmetry, trace over your pencil lines with a pen or darken them to make your drawing more prominent.

8. Erase Construction Lines: Gently erase any construction lines or guidelines you drew in the earlier steps.

Right angled triangle is formed by the points (3, 2), (-2, -3) and (2,3).

Let the given points be,

A = (3, 2), B = (-2, -3) and C = (2, 3)

The formula for the distance between two points:

The length of the line segment bridging two points on a plane is known as the distance between the points.

The formula to find the distance between the two points is usually given by [tex]D = $$\sqrt{\left(X_2-X_1\right)^2+\left(Y_2-Y_1\right)^2}$$[/tex].

Therefore,

A = [tex](x_{1} , y_{1} )[/tex] = (3, 2), B = [tex](x_{2} , y_{2} )[/tex] = (-2, -3)

[tex]& \mathrm{AB}=\sqrt{(3+2)^2+(2+3)^2}=\sqrt{50}=5 \sqrt{2}[/tex]  units

B = [tex](x_{1} , y_{1} )[/tex] = (-2, -3), C = [tex](x_{2} , y_{2} )[/tex] = (2, 3)

[tex]& \mathrm{BC}=\sqrt{(-2-2)^2+(-3-3)^2}=\sqrt{52}=2 \sqrt{13}[/tex]  units

A = [tex](x_{1} , y_{1} )[/tex] = (3, 2), C = [tex](x_{2} , y_{2} )[/tex] = (2, 3)

[tex]& \mathrm{AC}=\sqrt{(3-2)^2+(2-3)^2}=\sqrt{2}[/tex]  units

By using the Pythagorean theorem:

According to Pythagoras's Theorem in a right-angled triangle, the square of the hypotenuse side is equal to the sum of the squares of the other two sides.

Now, we can see that,

[tex]& (2 \sqrt{13})^2=(5 \sqrt{2})^2+(\sqrt{2})^2 \\[/tex]

[tex]& \mathrm{BC}^2=\mathrm{AB}^2+\mathrm{AC}^2[/tex]

Therefore, the given triangle is a right angled triangle.

Therefore, option(A) s correct.

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What type of triangle do the points (3, 2), (-2, -3) and (2,3) form a triangle? If so, name the type.

A. right triangle

B. equilateral triangle

C. isosceles triangle

D. none of these

The simplest form   [tex]\frac{2\sqrt{3} }{\sqrt{6} }[/tex] is [tex]\sqrt{2}[/tex]

Step-by-step solution:

[tex]=\frac{2\sqrt{3} }{\sqrt{6} }[/tex]

[tex]=\frac{2\sqrt{3} }{\sqrt{2*3} }[/tex]              (write factors of [tex]\sqrt{6}[/tex] i.e. [tex]\sqrt{2*3}[/tex])

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

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

[tex]=\frac{2\ }{\sqrt{2}\ } * \frac{\sqrt{2} }{\sqrt{2} }[/tex]        (Rationalize it by [tex]\sqrt{2}[/tex])

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

[tex]=\sqrt{2}[/tex]

Therefore, the correct solution to this question is [tex]\sqrt{2}[/tex]

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The expression that correctly shows the amount remaining in the piggy bank will be; 22d + 7n + 15q - (8d + 3n) = $4.85

Expression in maths is defined as the collection of numbers variables and functions by using signs like addition, subtraction, multiplication, and division.

We are given that piggy bank contains 22 dimes, 7 nickels and 15 quarters. This morning you removed 8 dimes and 3 nickels.

LEt consider

→ dimes = d

→ nickels = n

→ quarters = q

Now the expression will be;

22 dimes + 7 nickels + 15 quarters - 8 dimes - 3 nickels

22d + 7n + 15q - 8d - 3n = $4.85

22d + 7n + 15q - (8d + 3n) = $4.85

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There are 13 pounds of peanuts present in the mixture.

An equation is a mathematical statement with an 'equal to' symbol between two expressions that have equal values.

An equation is a mathematical statement that is made up of two expressions connected by an equal sign.

For example, 3x – 5 = 16 is an equation. Solving this equation, we get the value of the variable x as x = 7. There are different types of equations like linear, quadratic, cubic, etc.

Let's consider Almonds be a and Peanuts be p.

from given conditions,

a + p = 20

and 5.95 a + 2.95 p = 4(20)

5.95 a + 2.95 p = 80

take, a = 20 - p

5.95 (20 - p) + 2.95 p = 80

119 - 5.95 p + 2.95 p =80

119 - 3 p = 80

3p = 39

p = 39/3

p = 13

Therefore, there are 13 pounds of peanuts present in the mixture.

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Step-by-step explanation:

one side : 2x - 1

so, 5 sides (the perimeter is the sum of all sides) :

5 × (2x - 1) = 10x - 5

On solving the provided question, we can say that - by the help of the unitary method 150* 3 = $450

The unit technique is an approach to problem-solving that involves first determining the value of a single unit, then multiplying that value to determine the required value. The unit method, to put it simply, is used to extract a single unit value from a supplied multiple. For instance, 40 pens would cost 400 rupees, or the price of one pen. The process for doing this may be standardized. a single country. anything that has an identity element. (mathematics, algebra) (Linear algebra, mathematical analysis, mathematics of matrices or operators) Its adjoint and reciprocal are equivalent.

so, we have

There were  = 150 tickets sold to the play

Student tickets cost $3 per ticket

so, total will be = 150* 3 = $450

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Answer: hi

11,28 pound / usd

Step-by-step explanation:

The amount of money should you deposit now to have $10,000 5 years from now is $7407.

Theoretically, continuously compounded interest means that interest is continuously earned on an account balance as well as reinvested into the balance to increase future interest earnings.

Given that If an investment company pays 6% compounded continuously and $10,000 for 5 years.

The amount of money invested will be calculated by the formula below,

[tex]P = P_o(e)^{rt}\\10000 = P_o ( e)^{0.06\times5}\\[/tex]

P₀ = 10000 / 1.35

P₀ = 7407

The amount of money invested would be 7407.

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Parallel lines are those lines that lie in the same plane and never intersect each other. They are equidistant from each other at every point and have the same slope.

Two lines are stated to be parallel when they do not meet at any point in a plane. This means that lines which do not have a common intersection point and never cross paths with each other are parallel to each other. The symbol used for representing parallel lines is ‘||’.

Two parallel lines are represented as:

AB║CD

That is line AB is parallel to CD.

The perpendicular length between the two parallel lines is always constant.

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Answer:

see explanation

Step-by-step explanation:

A

∠ UVX and ∠ WXV are alternate angles and are congruent , then

∠ UVX = ∠ WXV = 15°

∠ WVU = ∠ WVX + ∠ UVX = 24° + 15° = 39°

B

opposite sides of a parallelogram are congruent , then

UV = XW = 36

C

consecutive angles are supplementary , sum to 180° , then

∠ XUV + ∠ WVU = 180° , so

∠ XUV + 39° = 180° ( subtract 39° from both sides )

∠ XUV = 141°

D

diagonals bisect each other , so

YW = UY = 10

Answer:

37,349

Step-by-step explanation:

month 1

27870 x .05 = 1394

27870 + 1394 = 29264

month 2

29264 x .05 = 1463

29264 + 1463 = 30727

month 3

30727 × .05 = 1536

30727 + 1536 = 32263

month 4

32263 x .05 = 1613

32263 + 1613 = 33876

month 5

33876 x .05 = 1694

33876 + 1694 = 35570

month 6

35570 x .05 = 1779

35570 + 1779 = 37349

Answer:

35,570

Step-by-step explanation:

solution 1 - Multiply by 5%, 6 times. Easter to calculate without a calculator, long process.

1. 27870*1.05= 29,263.5

2. 29263.5*1.05=30726.675

3.repeat

4.repeat

5.repeat

6.repeat

if it's hard for you to multiply by 1.05, you can always divide by 20 or divide by 10 then by 2 (like the below)

1. 27870÷10= 2,787

2. 2787÷2= 1393.5

3. 27870+1393.5 = 29263.5

solution 2 -Fast but probably needs a calculator

1. 27870*1.05^(5)= 35570

1.05 = monthly increase

power of 5 = ^(5) = 6 months - 1 = 5

The Graph solution to this inequality on the number line is lies between -4 > 8.4 and their numbers are -3 -2.5 -2 -1.5 -1 -0.5 0 0.5 1 1.5 2 2.5 3.

Draw a circle around the number to indicate an inequality, such as x>3, on a number line (e.g., 3). In case the sign also states equal to, complete the circle (or ). If the sign doesn't include equal to (> or), leave the circle empty.

When plotting an inequality, use the,, >, or sign as a = sign. If the inequality is either or, graph the equation as a dotted line. If the inequality is either or, graph the equation as a solid line.

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Hence, The equation of the line is y=5x/3-3

The slope-intercept form of a line is represented by y=mx+c where m=slope and c is the y-intercept of the line

Given here: The line 3x+5y=15 , Rearranging in the slope intercept form we get y=-3x/5+3 and thus slope of the line that is perpendicular to this line must be equal to 5/3 and it passes through (3,2) then we get the equation of the line as y=5x/3+c and putting (3,2) in the equation we get the value of c as c=-3

∴ The equation of the line is y=5x/3-3

Hence, The equation of the line is y=5x/3-3

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No, a triangle with side length 4 units, 8 units , and 12 units does not exist.

As given in the question,

Let us consider the triangle be ABC,

Side length of the triangle are given as follow:

AB = 4units

BC = 8units

CA = 12units

Triangle inequality for the given triangle ABC is given by:

AB + BC > CA

AB + CA > BC

CA + BC > AB

To check whether the given side length forms a triangle apply triangle inequality we get,

AB + BC

= ( 4 + 8 )units

= 12 units

= CA

Here triangle fails.

Therefore, the given side length does not forms a triangle.

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The answer would be −6q−11

Answer:

-6q-11

Step-by-step explanation:

1) Jada does not have 90% of the total possible points before the final test.

2) If Jada gets at least 92 out of 100 on the final test, she will not get an A in the class.

From the following table of Jada’s results before the final test in the class the total number of points possible:

150 + 100 + 100 + 100 = 450

And Jada’s total points before the final test:

141 + 87 + 81 + 91 = 400

To check whether Jada have 90% of the total possible points before the final test, we find the percentgae of  Jada’s total points.

(400/450) × 100 = 88.89%

This means, Jada does not have 90% of the total possible points before the final test.

After final test, the total number of points possible:  450 + 100 = 550

And if she gets at least 92 out of 100 on the final test, her total points would be,

400 + 92 = 492    

And the percentgae of  Jada’s total points would be,

(492/550) × 100 = 89.45%

Given that Jada needs to have at least 90% of the total number of points possible.

so, she will notl get an A in the class.

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The equation of the line perpendicular to the line 5x-4y=10 and passing through the point (5,12) is y = 4x/5 + 8.

In mathematics, a line's slope, also known as its gradient, is a numerical representation of the line's steepness and direction.

To find the slope;

m =  (y₂- y₁) / (x₂ - x₁)

Given:

The line 5x-4y=10.

Simplifying,

y = (-5/4)x + 5/2

Comparing with the slope-intercept form,

y = mx + b,

where m is the slope and b is y-intercept.

The slope is = -5/4

The slope of the perpendicular line,

= negative reciprocal of the slope of the line where the line is perpendicular.

= 4/5

So, the line:

If a line passes through one point (x₁ ,y₁) and have slope m,

then the equation of line is

y - y₁ = m (x - x₁)

y - 12 = (4/5)(x-5)

y = 4x/5 + 8

Therefore, the equation of the line is y = 4x/5 + 8

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After H hours of coaching, let E indicate her profits (in dollars). She receives $20 for every hour she tutors. This indicates that her total earnings in H hours would be  E = 20H.

After H hours of coaching, let E indicate her profits (in dollars). She receives $20 for every hour she tutors. This indicates that her total earnings in H hours would be

E = 20H.

We would enter H = 17

into the formula to get Mai's pay after 17 hours of tutoring.

E = 20 × 17 E = $340 is the result.

The complete question is:

Mai tutors history. For each hour that she tutors, she earns 20 dollars. Let E be her earnings (in dollars) after tutoring for H hours. Write an equation relating E to H . Then use this equation to find Mai's earnings after tutoring for 17 hours.

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Answer:

Step-by-step explanation:

Here is how to solve the given problem above.

Given that the calculator costs $32 and has a tax of 6%, what we are going to do is to find how much is 6% of 32. So 32 times 0.06 is 1.92. So, we add this amount to 32 dollars, and the total price would be 33.92 dollars. Hope this answer helps.

Answer:

33.92

Step-by-step explanation:

32 times 6 divided by 100 gives you 1.92, the sales tax,

add it to 32 and then you get 33.92

Therefore ,the result is. It means that there exist 17 units between the two points supplied as the answer to the given distance problem.

An object's travels are quantified by distance. Simply explained, distance, or t, is the amount of space an object covers within a specific period of time. Displacement is still the quickest route a moving object can travel. We frequently take into account the concepts of range and displacement.

Here,

6 and -3 are given (2, -2)

Points (a, b) and (c, d) are now separated by

d= √(c-a)² + ( d- b) ²

 d= √(-3+2)² + (2-6)² as a result.

=>d = √ 1 + 16 = √17

The distance between the two places is therefore 17 units.

the result is. It follows there are 17 units between the two points supplied as the answer to the given distance problem.

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The Sides of triangle when only the angles of triangles are given can be found by using the Law Of Sines .

What is Law Of Sines ?

The Law Of Sines states that  the ratio of sides of a triangle and their respective Sine angles are equivalent to each other. The other names by which the law of sines is known  are Sine Law, Sine Rule and Sine Formula.

The Sine Law  is used to find unknown side of an oblique triangle. The oblique triangle is defined as a triangle that is not a right triangle.

Let a , b and c be the sides of a triangle ABC , and A , B and C be the angles .

So , by Sine Law : [tex]\frac{a}{SinA}=\frac{b}{SinB}=\frac{c}{SinC}[/tex] ;

Therefore , The Law Of Sines help in finding the sides of triangle that has only angles .

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The Light cream with 19.2% content will have 15.36g of milk.

A percentage is a number or ratio that can be expressed as a fraction of 100. If we have to calculate the percent of a number, divide the number by the whole and multiply by 100. Hence, the percentage means, a part per hundred. The word percent means per 100. It is represented by the symbol “%”

Given here Light cream as 19.2% of 80g

∴ 0.192×80=15.36g

Hence, The Light cream with 19.2% content will have 15.36g of milk.

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The solution of the system of equations y =0 x=4

To solve the system of equations, we must set the two equations equal to each other and solve for x.

y = -2x + 8

y = x - 4

We start by subtracting the second equation from the first equation.

-2x + 8 = (x - 4)

We then add 4 to both sides of the equation.

-2x + 12 = x

We then subtract 12 from both sides of the equation.

-3x = -12

Finally, we divide both sides of the equation by -3.

x = 4

Now that we have solved for x, we can substitute 6 for x in either equation and solve for y.

y = -2(4) + 8

y = -8 + 8

y = 0

Therefore, the solution of the system of equations is (4, 0).

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What is the solution of the system of equations  y= -2x + 8 and y = x - 4?

Answer:

[tex]108\pi[/tex] or approx. [tex]339.3 m^{2}[/tex]

Step-by-step explanation:

The question asks us to find the total surface area of the given hemisphere. The question gave us the formula for total surface area of a sphere, [tex]SA_{tot} =4\pi r^2[/tex]. But we need it for a hemisphere, so multiply the equation by [tex]\frac{1}{2}[/tex].

[tex]SA} = (\frac{1}{2}) 4\pi r^2[/tex] => [tex]SA} =2\pi r^{2}[/tex]

We also need the area of the base, which is circle. [tex]A_{circle}=\pi r^{2}[/tex].

Now add these equations together to get our equation.

[tex]SA_{tot} =2\pi r^2 +\pi r^{2}[/tex] => [tex]SA_{tot} =3\pi r^2[/tex]

Now we have the proper equation for total surface area of a hemisphere, [tex]SA_{tot} =3\pi r^{2}[/tex]. Plug in the value of [tex]r[/tex] which is given in the problem, [tex]r=6m[/tex].

=> [tex]SA_{tot} =3\pi (6)^{2}[/tex] => [tex]SA_{tot} =3\pi (36)[/tex] => [tex]SA_{tot} =108\pi m^{2}[/tex] or approx. [tex]339.3 m^{2}[/tex]

Answer:

The answer is A

Step-by-step explanation:

When looking at this image, look at A, notice how it says y and the equal to symbol is facing it? then notice at the end of answer a is -4, look at the graph and the line intercepts -4, remeber, the end number, whether positive or negative will always be the on the y axis

Answer:

No solution

Step-by-step explanation:

-(y² - 2) = y²-5-2y²

= y^2 - 5 - 2y^2 = - (y^2 - 2)

= -y^2 - 5 =  - (y^2 - 2)

= −(y^2 − 2)

= -y^2 - 5 = -y^2 + 2

-5 = 2

We know that -5 is not equal to 2

So, there is no solution

Answer:
2

Step-by-step explanation: