What is the equation in standard form of the line that passes through the point (6, 1) and is parallel to the line represented by 8x + 3y= 15?.

The vector C is 1.00 x + 3.00 y

Therefore, the correct answer is C) 1.00 x + 3.00 y.

In mathematics and computer science, a vector is an ordered list of numbers that can be used to represent things like position, direction, and magnitude. Vectors can be added and subtracted, and they can be multiplied by scalars (numbers).

To subtract two vectors, we need to subtract the corresponding components. So, the x-component of vector C is

(-3.00 x) - (-2.00 x) = -3.00 + 2.00

= 1.00

and the y-component of vector C is

(4.00 y) - (1.00 y) = 4.00 - 1.00

= 3.00.

Therefore, vector C = 1.00 x + 3.00 y.

--The question is incomplete, answering to the question below--

"Vector A = -2.00x + 1.00y and vector B = -3.00x + 4.00y .What is vector C =  B - A?

A) 1.00x+5.00y

B) -100x+-3.00y

C) 1.00x+3.00y

D) -100x+3.00y

E) -100x+-5.00y"

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The sound and unsound deductive reasoning is differentiated below.

Deductive reasoning is a logical approach where you go from general ideas to specific conclusions.

Given is the difference between sound and unsound deductive reasoning.

Sound deductive reasoning -

If an argument is both valid and has all true premises, we will say that the argument is sound.

Unsound deductive reasoning -

An argument is unsound if it either has a false premise, or is invalid.

Therefore, the sound and unsound deductive reasoning is differentiated above.

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The ratio of their volumes is 3: 1

If two solids are identical, their volume ratio is equal to the cube of their corresponding side ratio. (It should be noted that volume is a 3-D measurement, not a “length” measurement. When the base and height of a pyramid and a prism are the same, their volumes are always in the ratio of 1:3Volume of prism.

A triangular prism and a triangular pyramid with identical bases and heights with the volume of the prism being three times that of the pyramid. Students should use manipulatives such as water, rice, or beans to physically represent this connection.

The volume of a prism =Base Area× Height and Volume of Pyramid = 1/3 × base area × Height

Given:

Height of both pyramid and a prism is 8.2 cm.

Area of base is 22.3 cm cube.

Volume of Prism = 22.3 × 8.2

Volume of Pyramid = 1/3 × 22.3 × 8.2

Ratio of volume of prism and volume of pyramid = (22.3 × 8.2) : 1/3 × (22.3 × 8.2)

Ratio of volume of prism and volume of pyramid = 1: 1/3

Ratio of volume of prism and volume of pyramid = 3: 1

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Steps are:

Step: 1

Given,

AE ≅ EB

∠DAE ≅ ∠CBE

Step: 2

congruent angles added to congruent angles form congruent angles

∠DAB ≅ ∠CBA

Step: 3

corresponding parts of congruent Triangles are congruent

DA ≅ CB

Step 4:

Vertical angles are congruent

∠DEA ≅ ∠CEB

Step 5:

Reflexive property

AE ≅ EB

Step 6:

In a triangles, angles opposite of congruent sides are congruent

∠EAB ≅ ∠EBA

Step 7:

SAS property

ΔDAB ≅ ΔCBA

Step 8:

ASA property

ΔDEA ≅ ΔCEB

Angles which are equivalent with one another are referred to as congruent angles. As a result, these angles have the same measure. In general, not all congruent angles are supplementary angles. Angles must be additional in order to add up to 180°. Due to the fact that they have the same measure and add up to 180, only right angles and supplementary angles are congruent.

Correct order is as follows:

Step: 1

Given,

AE ≅ EB

∠DAE ≅ ∠CBE

Step: 2

congruent angles added to congruent angles form congruent angles

∠DAB ≅ ∠CBA

Step: 3

corresponding parts of congruent Triangles are congruent

DA ≅ CB

Step 4:

Vertical angles are congruent

∠DEA ≅ ∠CEB

Step 5:

Reflexive property

AE ≅ EB

Step 6:

In a triangles, angles opposite of congruent sides are congruent

∠EAB ≅ ∠EBA

Step 7:

SAS property

ΔDAB ≅ ΔCBA

Step 8:

ASA property

ΔDEA ≅ ΔCEB

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The c/a ratio is divided by the density of the material and then multiplied by the square root of two thirds. This gives the atomic radius of the magnesium atom.

The atomic radius of an atom can be calculated by using the c/a ratio and the density of the material. The c/a ratio is the ratio between the lattice parameter c and lattice parameter a. The density is the amount of mass per unit volume of a substance. The formula for calculating the atomic radius of magnesium is

Atomic Radius= (c/a)√((2/3)*density)

Using the provided data for magnesium, the c/a ratio is 1.624 and the density is 1.74 g/cm^3. Plugging these values into the formula above gives an atomic radius of 1.6708 angstroms. To calculate the atomic radius, the c/a ratio of the crystal structure for magnesium is used, as well as the density of the material. The c/a ratio is divided by the density of the material and then multiplied by the square root of two thirds. This gives the atomic radius of the magnesium atom.

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As a result, the x-coordinate of the point on the curve closest to the origin is 2.

Coordinates are a pair of integers that are used to locate a point or object in a two-dimensional plane. A point's location on a 2D plane is defined by two integers called the x-coordinate and the y-coordinate. The distance of a point from the y-axis scaled with the x-axis is known as its abscissa or x coordinate. The ordinate is the distance of a point from the x-axis scaled with the y-axis. Coordinates are the abscissa and ordinate combined. To find the coordinates of a point in a coordinate system, do the inverse. Start at the point and trace a vertical line up or down to the x-axis. There you have your x-coordinate.

Here,

The x-coordinate of the point on the curve that is closest to the origin can be found by minimizing the distance between the point on the curve and the origin. The distance between two points (x1, y1) and (x2, y2) is given by the Pythagorean theorem:

d = √((x2 - x1)^2 + (y2 - y1)^2)

For the origin and a point on the curve, we have x1 = y1 = 0, so the distance between the origin and a point (x, y) on the curve is:

d = √(x^2 + y^2)

Using the equation of the curve, we have y = 2 * √(9 - x), so the distance can be expressed as:

d = √(x^2 + (2 * √(9 - x))^2)

= √(x^2 + 4(9 - x))

= √(x^2 + 36 - 4x)

To find the x-coordinate of the point that minimizes d, we can use calculus. Setting the derivative of d with respect to x equal to zero and solving for x, we obtain:

d' / dx = 2x - 4 = 0

x = 2

So the x-coordinate of the point on the curve that is closest to the origin is 2.

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S = {(t, 1, 1), (1, 0, 1), (1, 1, 3t)} is linearly independent of t.

Therefore the answer is b) S = {(t, 1, 1), (1, 0, 1), (1, 1, 3t)}.

(a) S is linearly independent for all values of t if the following equation has a non-trivial solution:

a(t, 1, 1) + b(1, t, 1) + c(1, 1, t) = (0, 0, 0).

Expanding this equation, we get:

at + b + c = 0

a + bt + c = 0

a + b + ct = 0.

Solving this system of linear equations, we find that a = b = c = 0. This implies that any linear combination of the vectors in S results in the zero vector, so S is linearly dependent for all values of t.

(b) S is linearly independent if the following equation has a non-trivial solution:

a(t, 1, 1) + b(1, 0, 1) + c(1, 1, 3t) = (0, 0, 0).

Expanding this equation, we get:

at + b + 3ct = 0

b = 0

a + c = 0.

Since a and c cannot both be zero, this system has no trivial solution, which means that S is linearly independent for all values of t.

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The area bounded by the given curve is =4.44.

There are several ways to calculate the area under the curve, but the antiderivative approach is the most widely used. Knowing the curve's equation, its bounds, and its enclosing axis will allow you to determine the area under the curve. In general, there are formulas for calculating the areas of standard shapes like squares, rectangles, quadrilaterals, polygons, and circles, but there isn't one specifically designated for calculating the area beneath curves. The integration method aids in equation solution and area determination.

The antiderivative methods are highly useful for locating the regions of irregular plane surfaces. In this lesson, we'll learn how to calculate the curve's area under the axis.

the area of the region that is bounded above by the curve f(x)=(x- 9)2 and the line g(x)=x−7.

The area enclosed by the curves is-

[tex]A=\int_a^b[{f(x)-g(x)]dx[/tex]

[tex](x-9)^2=x-7\\\\x^2-19x+88=0\\(x-8)(x-11)=0\\x=8 , x=11\\\\\int_8^{11}[(x-9)^2-(x-7)]dx\\\\=\int_8^{11}[x^2-19x+88]dx\\\\\\=[x^3/3-19x^2/2+88x]_8^{11}\\\\=4.44[/tex]

The area bounded by the given curve is =4.44.

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// Returns an array C[1..n] of the number of coins of each value, where

// the sum from 1 to n of C[i]*A[i] will equal t.

Greedy-Coins( t, A )

Define array C as an array of length n with all values zero for i = 1 to n

C[i] = t / A[i] // Note use INTEGER arithmetic here

t = C[i] mod A[i] // Note using integer modulo here to get the remainder

end fo ... ro

return C

An easy counterexample would be to use V = ( 5, 3, 1 ), and t= 9. The greedy algorithm will return values ( 1, 0, 4), but a little intuition shows that the array ( 0, 3, 0 ) will use fewer coins.

c) If we consider the array A = ( kn-1, kn-2, ..., k0), and k >0, then we can see that for any k < (n-1), there will be at most (k-1) coins of that value; if there had been sufficient \"value\" remaining to select k coins o that value, the greedy algorithm would have selected one more coin of the next coin up. Another way to look at this is that for any selection by the greedy algorithm from ki ... k0, the value MUST be less than ki+1, since ki+1 is by definition a multiple of k.

Complete question:

Let An = { a1, a2, ..., an } be a finite set of distinct cointypes (e.g., a1= 50 cents, a2= 25 cents, a3= 10 cents etc.). We assume each ai is an integer and that a1 > a2 > ... > an. Each type is available in unlimited quantity. The coin-changing problem is to make up an exact amount C using a minimum total number of coins. C is an integer > 0.

(a) Explain that if an != 1 then there exists a finite set of coin types and a C for which there is no solution to the coin-changing problem.

(b) When an = 1 a greedy solution to the problem will make a change by using the coin types in the order a1, a2, ..., an. When coin type ai is being considered, as many coins of this type as possible will be given. Write an algorithm based on this strategy.

(c) Give a counterexample to show that the algorithm in (b)doesn\'t necessarily generate solutions that use the minimum total number of coins

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The surface area of square pyramid is 207.04 square inches.

Surface area is the area of all outer facing surfaces on an object. The total surface area is calculated by adding all the areas on the surface: the areas of the base, top, and lateral surfaces (sides) of the object.

The formula to find the surface area of square pyramid is A=a²+2a√(a²/4+h²)

Here, a=8 inches and h=8 inches

Now, A= a²+2a√(a²/4+h²)

A= a²+2a√(a²/4+h²)

A= 8²+2×8√(8²/4+8²)

A= 64+16√(16+64)

A= 64+16√80

A= 64+16×8.94

A= 207.04 square inches

Therefore, the surface area of square pyramid is 207.04 square inches.

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The value of x in the given equation, 3/5x - 1/3x = 42, is x = 157.5

From the question, we are to determine the value of x in the given equation.

The given equation is

3/5x - 1/3x = 42

To determine the value of x,

First, we will eliminate the denominators.

Multiply through by 15

15 × 3/5x - 15 × 1/3x = 15 × 42

3 × 3x - 5 × x = 630

9x - 5x = 630

4x = 630

Divide both sides by 4

4x/4 = 630/4

x = 157.5

Hence, the value of x is 157.5

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The value of h for which b in the plane spanned by a1 and a2 is 11.

A vector b is in the plane spanned by two vectors a1 and a2 if it can be written as a linear combination of a1 and a2. This means that there exist scalars x and y such that:

b = xa1 + ya2

[5, 4, h] = x[1, 4, -1] + y[-6, -20, 2]

Solving for x and y, we have:

5 = x - 6y

4 = 4x - 20y

h = -x + 2y

Using the first two equations, we can solve for x and y:

x = 5 + 6y

20y + 4 = 4x = 4(5 + 6y)

20y + 4 = 20 + 24y

4y = -16

y = -16/4 = -4

Substituting this value of y back into the first equation:

x = 5 + 6y

= 5 + 6 * -4

= 5 - 24

= -19

Finally, substituting x and y into the third equation:

h = -x + 2y

= -(-19) + 2 * (-4)

= 19 - 8

= 11

So for h = 11, the vector b is in the plane spanned by a1 and a2.

--The question is incomplete, answering to the question below--

"Let a1 = [1 4 -1], a2 = [-6 -20 2], and b = [5 4 h]. For what value(s) of h is b in the plane spanned by a1 and a2?"

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One square mile contains 640 acres. 640 acres in a square mile.

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92% is the percent of decrease.

A relation is a function if it has only One y-value for each x-value.

The function [tex]M(t)=975.(0.92)^{t}[/tex]

Function represents the number of milligrams of a medication in a patients body as a function of time.

t represents the time.

0.92×100=92%

975 is the initial value and 0.92 is the percent of decrease.

Hence, 92% is the percent of decrease.

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Therefore , the solution of the given problem of ratio comes out to be

x has length of 5.2 .

The simple formula "a / b" can be used to create a pair of similar variables "a" and "b," where "b" may also be greater than zero. One ratio is created by combining two ratios. If there were only one man and three women, the ratio would be 1:1. There are 1/4 boys and 3/4 girls in the group. A separation between a or more objects, a numeral, or a piece of a component's volume are all examples of parts.

Here,

Given :

A figure of star shape

having diameter of 3.6 and length x

and other star having same shape but

having diameter 5.76 and length 8.32

Since , both the figures are same ,

Thus , there length ratio will also be same.

=> 8.32/5.76 =  x / 3.6

=> 832/576 =  10x/36

=>  832/576 * 36 /10 = x

=> x = 1.44 * 3.6 =5.2

Therefore , the solution of the given problem of ratio  comes out to be

x has length of 5.2 .

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The limit as h→0 of f(x+h) − f(x) / h is 0. the denominator of the fraction is 0, the limit is undefined.

To evaluate this limit, we need to plug in the given value for x and the function f(x). We are given that f(x) = x2 and x = 3.

Therefore, we have:

limh→0 f(3+h)−f(3) h

Since f(3) = 3^2 = 9, we can rewrite the limit as:

limh→0 f(3+h)−9

We can now plug in the value of h=0 to get the value of the limit:

limh→0 f(3+0)−9 0

Since the denominator of the fraction is 0, the limit is undefined.

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The pair of variables with an inverse relationship is y = 1/x. This relationship can be seen by graphing the two variables on a coordinate plane and observing the shape of the graph.

As x increases, y decreases and as x decreases, y increases. This is because the equation y = 1/x can be written as y = c/x, where c is a constant. Since c is a constant, as the value of x increases, the value of y decreases, and vice versa.

For example, if x = 4, then y = 1/4, or 0.25. If x increases to 8, then y decreases to 1/8, or 0.125. On the other hand, if x decreases to 2, then y increases to 1/2, or 0.5. As can be seen, as x increases, y decreases, and as x decreases, y increases, which shows the inverse relationship between the two variables.

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The value of k given sequence is =300 and the value of the term Sk=4875,

In mathematics, we may come across different types of numbers, and patterns. One of the number patterns includes sequences. The sequence is a specified collection of objects in which repetitions are allowed and order matters. Formally, a sequence is a function from natural numbers to the elements at each position. Similar to a set, it contains members, and they are called elements or terms. The number of elements is called the length of the sequence. Unlike a set, the same elements can appear multiple times at different positions in a sequence, and the order does matter.

value of k

U1 =1.3

U2= 1.4

Uk = 31.2

a = 1.3

d = 1.4 - 1.3 = 0.1

Uk = 1.3 + (k - 1)(0.1)

=> 1.3 + (k - 1)(0.1) = 31.2

=>  (k - 1)(0.1) = 29.9

=> k - 1 = 299

=> k = 300

Sk  = (300/2)(1.3 + 31.2)

= 150 * (32.5)

= 4875

F is the sum of the terms for which the term is not a multiple of 3

3rd term = 1.5

6th term = 1.8

300th term = 31.2

Total terms = 100

Sum = (100/2)(1.5 + 31.2)  =  1635

F = 4875 - 1635   = 3240

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The measure of angle B is m∠B = 71°

If ABCD is a kite, then ∠A and ∠C must be equal to each other.

∠A = ∠C, so ∠C = 87°.

ABCD is a quadrilateral, so all of its interior angles must add up to 360°. We know 3 of the 4 angles, so we'll add them up and subtract the answer from 360.

∠A + ∠C + ∠D ⇒ 87 + 87 + 115 = 289

360 - 289 = 71

m∠B = 71°

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The terms minimum and infimum are both related to the concept of lower bounds in mathematics. A minimum is the smallest value in a set of numbers, whereas an infimum is the greatest lower bound of a set.

A minimum is a value that is less than or equal to all other values in the set, while an infimum is a value that is less than or equal to all other values in the set, but not necessarily the smallest value.

For example, if we consider the set {2, 4, 6}, the minimum is 2 and the infimum is also 2. However, if we consider the set {2, 4, 6, 8}, the minimum is 2 and the infimum is 4. In the latter set, 4 is the greatest lower bound, meaning that all other values in the set are greater than or equal to 4.

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The value of the variable x for the function f(x) = x² + 4x for which

f(f(x) ) = f(x) is equal to x = -1 or x = -3.

The function f(x) = x² + 4x

Substitute the value in the required function we get,

Right hand side

= f ( f(x))

= f ( x² + 4x )

= ( x² + 4x )² + 4 ( x² + 4x )

= x⁴ + 8x³ + 16x² + 4x² + 16x

= x⁴ + 8x³ + 20x² + 16x

Left hand side

f(x)

= x² + 4x

Equate left hand side is equal to right hand side we get,

x⁴ + 8x³ + 20x² + 16x = x² + 4x

⇒x⁴ + 4x³ + 4x³ + 16x² + 4x² + 16x =  x² + 4x

⇒x² ( x² +4x ) + 4x ( x² + 4x )+ 4 ( x² + 4x ) = x² + 4x

⇒( x² + 4x ) ( x² + 4x + 4 ) = x² + 4x

⇒ x² + 4x + 4 = 1

⇒ ( x + 2 )²  - 1² =0

⇒ ( x + 2 -1 ) ( x+ 2 + 1) = 0

⇒ ( x+ 1 ) ( x+ 3 ) = 0

⇒ x = -1  or x = -3

Therefore, the value of x = -1 or x = -3 for the condition f(f(x)) = f(x).

The above question is incomplete , the complete question is:

Let function f(x) = x² + 4x for what value of x is f(f(x)) = f(x).

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The elevation represents a distance from the sea level greater than 5 feet, because the original description specifies a distance greater than 5 feet below sea level.

Physical quantities like mass and electric charge are examples of scalar quantities because they only have magnitudes. In contrast, a vector quantity is a physical quantity like force or weight that has both magnitudes and directions.

The elevation is the height or distance above sea level and is expressed as a distance.

Given that it contains both magnitude (distance) and direction, elevation in the previous description is a vector (above sea level).

Distance is a scalar quantity with only one magnitude that describes the area travelled by a moving object.

A height of less than 5 feet denotes a location that is less than 5 feet above sea level, which is equivalent to a location that is more than 5 feet below sea level.

Greater than 5 feet below sea level = less than -5 feet above sea level, therefore;

A distance from (below) sea level of more than 5 feet is represented by an elevation of less than -5 feet.

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To find the width of Wyoming, we need to find the area of the state and divide by the width.

Area = population density x total population

Area = 2.16 x 564,000 people

Area = 1,222,624 square kilometers

Width = Area / Length

We don't have the length, so we'll have to rearrange the formula to solve for it:

Width = Area / Length

Length = Area / Width

Length = 1,222,624 square kilometers / Width

We'll solve for width:

Width = 1,222,624 square kilometers / Length

Since we don't know the length, we cannot solve for width.

After matching each set of values of a function to the pair of points that satisfy the function, we get

A function from a set X to a set Y assigns to each element of X exactly one element of Y.

Given the set of data

(4,3) and (6.7) rate of change = 2, and initial value = -5

k= 7-3/6-4 = 2, y=2x-5

(2,10) and (5, 19) rate of change=3, and initial value = 4

k= 19-10/5-2 = 9/3 = 3, y=3x+4

(2,5) and (5.2)→ rate of change = -1, and initial value = 7.

k= 2-5/5-2 =  -3/3 = -1, y= -x+7

(2.4) and (4,3) →→ rate of change = -0.5, and initial value =5

k= 3-4/4-2 = -1/2 =-0.5, y=-0.5x+5

A function has two sets of values: the set of input values and the set of output values. The set of input values makes up the function's domain. The set of output values makes up the function's range.

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Drag the tiles to the correct boxes to complete the pairs. Match each set of values of a function to the pair of points that satisfy the function. rate of change = -1, and initial value = 7 rate of change = 2, and initial value = -5 rate of change = -0.5, and initial value = 5 rate of change = 3, and initial value = 4 (4, 3) and (6, 7) arrowRight (2, 10) and (5, 19) arrowRight (2, 5) and (5, 2) arrowRight (2, 4) and (4, 3) arrowRight

Trade in the Vedic Age led to: A,  the rise of kingdoms because of the importance of controlling land and long-distance travel routes

The Vedic Age was a period between 1500 BC and 600 BC. This period was characterized by the next major civilization that occurred in ancient India following the decline of the Indus Valley Civilization by the year 1400 BC. The Vedas were very composed in this age.

Thus, we can say that in this vedic age;

- Indian civilization saw an unprecedented increase.

- Kingdoms were formed that gained riches and prominence.

These kingdoms mostly formed because increased trade in the area gave rise to the need to be controlled and profited from.

In conclusion, option A is correct.

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Answer:

Trade in the Vedic Age led to: A,  the rise of kingdoms because of the importance of controlling land and long-distance travel routes

Step-by-step explanation:

just did the quiz lol

Step-by-step explanation:

3/4*7.5

5.625

7.5-5.625

1.875

of blue pints

We can prove this using the product rule. Let y(x) = y1(x) y2(x). Then:

y'(x) = y1'(x) y2(x) + y1(x) y2'(x)

y''(x) = y1''(x) y2(x) + 2y1'(x) y2'(x) + y1(x) y2''(x)

Substituting into the equation yields:

y'' p(x)y' q(x)y = [y1''(x) y2(x) + 2y1'(x) y2'(x) + y1(x) y2''(x)] p(x) [y1'(x) y2(x) + y1(x) y2'(x)] q(x) [y1(x) y2(x)]

= [y1''(x) p(x)y1'(x) + 2y1'(x) p(x)y2'(x) + y1(x) y2''(x) p(x)] q(x) [y1(x) y2(x)]

= [r1(x) + r2(x)] q(x) [y1(x) y2(x)]

= r1(x)r2(x) q(x) [y1(x) y2(x)]

Since this is equal to y″ p(x)y′ q(x)y, it follows that y(x) = y1(x) y2(x) is a solution of y″ p(x)y′ q(x)y = r1(x) r2(x). We can prove this using the product rule. Let y(x) = y1(x) y2(x). Then:

y'(x) = y1'(x) y2(x) + y1(x) y2'(x)

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The value of c for the given function at x = 0 to be continuous is c = 8/15.

The following three requirements must all be met for a function to be regarded as continuous at a point:

In other words, a function is continuous at a place if you can draw it without moving your hand and the function's graph doesn't have any gaps or leaps at that location. Calculus' central idea of continuity is crucial for defining derivatives and integrals.

According to the question

Given function =  f(x)= 12x−4sin(3x)/5x3

We require f(0) = c, where c is the value given to the function at x = 0, in order to make the function continuous at that point. We may assess the limit of f(x) as x gets closer to zero to determine c.

The limit of f(x) as x approaches 0 may be determined using L'Hopital's rule as follows:

lim x→0 f(x) = lim x→0 (12x - 4 * sin(3x)) / (5x^3)

= lim x→0 (12 - 4 * 3 * cos(3x)) / (15x^2)

= 8 / 15.

So, c = 8 / 15. Therefore, the function f(x) = (12x - 4 * sin(3x)) / (5x^3), x ≠ 0 and c, x = 0 is continuous at x = 0 with c = 8 / 15.

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