Consider the initial value problem
y′′+4y=−, y(0)=y0, y′(0)=y′0.y′′+4y=e−t, y(0)=y0, y′(0)=y0′.
Suppose we know that y()→0y(t)→0 as →[infinity]t→[infinity]. Determine the solution and the initial conditions.

We solved using elimination method, For the given set of equations, no solution exists.

To create an equation in one variable using the elimination approach, you can either add or subtract the equations. To eliminate a variable, add the equations when the coefficients of one variable are in opposition, and subtract the equations when the coefficients of one variable are in equality.

Given,

two equations as

60x-42y=0                                                          ........... (1)

-100x + 70y=0                                                     ............(2)

Now, multiplying the equation (1) by 10 and (2) with 6

we get the equation as

⇒ (60x-42y=0) × 10

⇒ 600x - 420y = 0                                         ............(3)

⇒ (-100x + 70y=0 ) × 6

⇒ -600x + 420 = 0

Solving equation 2 and 3 simultaneously

⇒ 600x - 420y = 0

⇒ -600x + 420 = 0

⇒ x = y = 0

∴ No Solution exists for this problem

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The inequality d > 3 has infinitely many solutions because 4 and any number to the right of 3 on the number line can be substituted for d to make this inequality true.

In Mathematics, an equation or an inequality is said to have an infinitely many solutions when the left hand side and right hand side of the equation or inequality are the same and equal.

This ultimately implies that, an equation or an inequality would have infinitely many solutions when both sides of the equal sign are the same, and both the slope and y-intercept for the two lines are the same.

The given inequality d > 3 simply means that the variable d is greater than three (3). Therefore, d represents the set of all possible real numbers that are greater than 3 and from the right of 4 on the number line for d > 3 because it has infinitely many solutions.

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Complete Question:

Use the drop-down menus to complete the statement about the inequality d > 3.

The inequality d > 3 has _____ solutions because ______ can be substituted for d to make this inequality true.

Options: for the first one 0 1 2 8 9 Infinitely many

For the second one: No numbers only 1 number 4 and any number to the right of 3 on the number line

Answer:

AB = 9.68, BC = 7.04

Step-by-step explanation:

AC/DC = 6.71/6.1 = 1.1    This is the proportionality factor

6.4(1.1) = BC = 7.04

8.8(1.1) = AB = 9.68

Clare's account balance is $40

Clare has $150 in her bank account

She withdraws $110 from this money to purchase a bike

The amount of money left in her account after purchasing the bike can be calculated as follows

150-110

= 40

Hence Clare has $40 in her account after purchasing the bike

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Answer:

it’s A

Step-by-step explanation:

I graphed it out

Equality is a fundamental component of a just and equitable society. It encompasses legal, social, and economic aspects, all of which are essential to ensure that all citizens are treated fairly and have access to the same rights and opportunities.

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Answer 50 for the bottom and 48 for the sides

Discriminant of the eqaution √2x²-5x+√2 is 17

The discriminant of a polynomial in mathematics is a number that relies on the coefficients and allows inference of some root features without computing them. It is basically a polynomial function of the original polynomial's coefficients.

To calculate the Discriminant of a quadratic equation which   is generally expressed as

ax² + bx + c = 0

The quadratic equation's discriminant, indicated by the letter D, is defined as

D = b² - 4ac

So D= 5*5 -4 * √ 2 *√ 2

=> 25 -4 *2

=> 25-8

=> 17

so discriminant of the eqaution √2x²-5x+√2 is 17

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Complete question :

For √2x²-5x+√2=0 find the value of discriminant​

Answer:

200/3

Step-by-step explanation:

4+5=9

5\9*120=200/3

=

Answer:

The volume of a balloon is directly proportional to the cube of its radius, so we can use the formula:

V1/V2 = (R1/R2)^3

Where V1 is the initial volume, V2 is the final volume, R1 is the initial radius, and R2 is the final radius. We know that when the radius is 4 inches, the volume is 192 cubic inches, so we can use this information to find the final volume when the radius is 3 inches.

V1 = 192 cubic inches

R1 = 4 inches

R2 = 3 inches

V1/V2 = (R1/R2)^3

V2 = V1 / (R1/R2)^3

V2 = 192 / (4/3)^3 = 192/ (4/27) = 192 * 27/4 = 192 * 6.75 = 1296 cubic inches

So, 1296 cubic inches of gas must be released to reduce the radius down to 3 inches.

The missing first term of the expression that, when fully simplified, would be a binomial with a degree of 4 include the following:

A. 0

C. 9x^2y

E. 4xy^3

In Mathematics, a polynomial function simply refers to a type of mathematical expression which comprises intermediates (variables), constants, and whole number exponents with different numerical value, that are typically combined by using mathematical operations.

In Mathematics, the canonical form for a polynomial in one variable (x) is given by this mathematical expression:

[tex]a_n x^n + a_{n-1} x^{n-1} +a_1 x^1 +a_0=0[/tex]

Since the degree of a polynomial function is the sum of exponents in each of its term, the required answer options must have exponents that are equal to those of the given polynomial function and these include the following:

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Answer: A C E

Step-by-step explanation:

The amount that they will have saved after 2 weeks is $1,737.

Tom, you can refer to a quantity or number of something using the word "amount." It is typically used to refer to an amount of money, like when people discuss their income, but it can also be used to describe a quantity of something, such as the volume of water in a tank or the time required to complete a task.

We must divide the difference between Ezra and Haley's initial deposits by the difference between their weekly installments to figure out how many weeks it will take them to save the same amount of money. In this instance, their initial deposits differed by $804 ($862 - $58), while their weekly installments differed by $402 ($71 - $473). We can calculate that it will take them two weeks to save the same amount of money by dividing $804 by $402.

After two weeks, they will have $1,737 in savings. Haley will have $1,737 ($862 + $71 + $71 + $703) and Ezra will have $1,737 ($58 + $473 + $473 + $733) in their accounts after two weeks.

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Answer:

Step-by-step explanation:

-2x-3=-7

+3 +3
-2x=-4

/-2 /-2

x=2

Y=5(2)-9

Y=10-9

Y=1

Answer:

Step-by-step explanation:

y = 5x - 9 (eq'n 1)

-2x - 3 = -7 (eq'n 2)

Solve for x in (eq'n 2)

-2x -3 = -7 (add 3 to both side of the eq'n)

(-2x - 3) + 3 = -7 + 3

-2x = -4 (divide both side by -2)

x = 2

Therefore the value of y is:

From  (eq'n 1), Substitute the value of x

y = 5x - 9

y = 5(2) - 9

y = 1

Answer:

A

Step-by-step explanation:

Your answer was correct.

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

Distribute:

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

[tex]6x-12=6x+12[/tex]

Subtract 6x from both sides:

[tex]6x-12-6x=6x+12-6x[/tex]

[tex]-12=12[/tex]

Add 12 to both sides:

[tex]-12+12=12+12[/tex]

[tex]0=24[/tex] (false)

[tex]\fbox{No solution}[/tex]

Answer:

False Expresion, Wrong , Error

Step-by-step explanation:

if solving for x

3 (2x - 4) = 3 (2x + 4) insert the 3 into the parenthesis [remember to imput for each element])

6x - 12 = 6x +12 False expression

if we decide to go further we would get

0x = 24

The exponent 3 is called the power or index. It is the number that indicates how many times the base number (in this case 3) is multiplied by itself.

To determine this

For example, 3³ means 3 multiplied by itself 3 times, or 3 x 3 x 3 = 27. So 3 is the base number and 3 is the exponent or power.

In mathematical notation, the exponent is written as a small number or variable above and to the right of the base number, with a caret symbol (^) separating them. For example, 3³ is written as 3³, and x² is written as x².

Additionally, in mathematics, exponents are also used to represent the number of times a number is multiplied by itself, the exponent number represents how many times the number is being multiplied.

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The end behavior of the graphs of polynomial functions is determined by the highest degree of the polynomial.

For example, a polynomial with degree n will eventually approach infinity as x increases or decreases without bound. This can be expressed mathematically as:

f(x) = axn -> lim x->∞ f(x) = ∞

and

f(x) = axn -> lim x->-∞ f(x) = ∞

where a is a constant.

For a polynomial of degree n, the graph will have n-1 turning points. As the degree increases, the graph approaches a smooth curve. Additionally, the graph will have either one up-turn or one down-turn depending on the sign of the leading coefficient. If the leading coefficient is positive, the graph will have an up-turn; if the leading coefficient is negative, the graph will have a down-turn.

For example, the end behavior of the graphs of the polynomial f(x) = 2x3 + 2x2 - 2x - 1 has degree 3, so it will have 2 turning points and will have an up-turn as the leading coefficient is positive.

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2 exponent is also known as the "square" of a number. When a number is raised to the power of 2, it means that the number is multiplied by itself.

For example, 2^2 means 2 multiplied by 2, which is equal to 4. The term "square" is used because the result of raising a number to the power of 2 is the same as finding the area of a square with that number as the length of each side.

This notation is widely used in mathematics, particularly in algebra and geometry. When we see a number with exponent 2, we can understand it as the number is multiplied by itself, which is the square of the number.

The term "square" is widely used in mathematics, particularly in algebra and geometry. Understanding this concept is important for solving mathematical problems, especially in algebra and geometry.

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So on solving provided question we can say that given coordinates are

(−6,4) and (−1,−8)so equation is x - y +10 = 0

A coordinate system in geometry is a method that employs one or more integers or coordinates to identify the precise placement of points or other geometrical objects on a manifold, such as Euclidean space. Pairs of integers called coordinates are used to locate a point or object on a two-dimensional plane. The position of a point on a 2D plane is described by two integers known as the x and y coordinates. a group of numbers that represent precise positions. Usually, there are two numbers in the figure. The front-to-back distance is represented by the first number, while the top-to-bottom distance is represented by the second number. like in (12.5), when there are 12 units below and 5 above.

given coordinates are

(−6,4) and (−1,−8)

so equation is

y-y1 = m(x-x1)

y-4 = x +6

x - y +10 = 0

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Answer: y=−2.8x + 11.4

To graph the inequality 2y - 4x < 8, we can start by isolating the y variable on one side of the inequality. To do this, we add 4x to both sides:

An explanation graph is what?

A graph is a representation of the relationship between two variables that are normally measured along one of a pair of axes at right angles.

2y - 4x < 8

2y < 4x + 8

Next, we divide both sides by 2 to get y by itself:

y < 2x + 4

To graph this inequality, we can start by plotting the y-intercept, which is the point where x = 0. In this case, y = 2(0) + 4 = 4, so the y-intercept is (0, 4). Next, we can find the slope of the line, which is -2.

To graph the inequality -4y > -x + 12, we can start by isolating the y variable on one side of the inequality. To do this, we add x to both sides:

-4y > 12 - x

Next, we divide both sides by -4 to get y by itself:

y < -3 + (1/4)x

To graph this inequality, we can start by plotting the y-intercept, which is the point where x = 0. In this case, y = -3 + (1/4)(0) = -3, so the y-intercept is (0, -3). Next, we can find the slope of the line, which is (1/4).

The equation | x + 3 |= y represent a vertical line with x = -3

The equation |2x – 6| + 2 = y represent a V shape with the vertex at (-3,2)

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Step-by-step explanation:

f(x) = 2x² - 7x - 7

f(6) = 2(6)² - 7(6) - 7

f(6) = 72 - 42 - 7

f(6) = 23

value of p = 7 and value of q = 10.

The word consecutive implies an unbroken sequence that means terms approaches forward by following a specific order. Within a consecutive sequence the gap between each term is the same.

given, 4, p, q, 13 are consecutive terms, find the value of P and Q.

As the above four are consecutive number so starting from the 4 we write the list in an unbroken sequence.

At first difference between highest and lowest number = 13- 4 = 9

now this difference is divided by the number of gaps between the sequence, we find there are 3 gaps between four numbers.

order of sequence = 9/ 3 = 3

now the next number after 4 will be 4+3 = 7

in the next, 7+3 =10

finally, we get 10+3 =13

so, the consecutive numbers are 4, 7, 10, 13.

As a result, p = 7 and q = 10

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The minimum speed object must have at the top of the loop is 3.8m/s.

Friction is the force that resists the motion of an object, it works in the opposite direction of applied force. Centripetal force is the force applied to the center of the body moving in a circular motion, whereas gravitational force is the pull of gravity on a body i.e., it attracts a body toward the ground.

Diameter of loop= 3m

thus radius = 1.5m

Centripetal force =< gravitational attraction the object has.

Centripetal force ,F=mv^2/r ----1

where  M= mass v= velocity and r= radius

gravitational force is F=ma -----2

let 1=2

mv^2/r=ma

m is common so can be canceled out

a=v^2/r

for v= 9.8m/s^2

a= 9.8^2/1.5

a=3.834057903

Therefore, the minimum speed object must have at the top of the loop is 3.834m/s.

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The percentage and the z-scores for specific heights of the given normal distributions are as detailed below.

The first step is to draw the Normal curve with 8 regions, and then we now label the 7 vertical dividing lines with the mean plus/minus one/two/three standard deviations:

By adding the percentage values in the areas indicated in the question, we will arrive at;

The percentage of Ixxians that are;

i) Over 30 inches tall = 100% - (2.35% + 0.15%) = 97.5%

ii) Over 45 inches tall =  13.5% + 2.35% + 0.15% = 16%

iii) Under 50 inches tall = 100% - (2.35% + 0.15%) = 97.5%

iv) under 40 inches tall = 34% + 13.5% + 2.35% + 0.15% =  50%

v) between 35 and 55 inches tall = 34% + 34% +  13.5% + 2.35% = 83.85%

vi) between 25 and 35 inches tall = 13.5% + 2.35% 15.85%

The z-score is defined as the number of standard deviations above the mean corresponding to the given value. Thus;

i. For a height of 32 inches, the z-score is;

z = [32-40]/5

z = -1.6

ii. For a height of 47 inches, the z-score is;

z = [47 - 40]/5

z = 1.4

iii. For a height of 51 inches, the z-score is;

z = [51 - 40]/5

z = 2.2

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Complete question is;

The hieghts of the people if the plant Ixx are normally distributed with a mean of 40 inches and a standard deviation of 5 inches. [ they are vertically diverse people.]

a) What percentage of Ixxians are

i over 30 inches tall?

ii over 45 inches tall?

iii under 50 inches tall?

iv under 40 inches tall?

v between 35 and 55 inches tall?

vi between 25 and 35 inches tall?

b) What is the z-score for an Ixxian of height?

i. 32 inches?

ii. 47 inches

iii. 51 inches

Answer: D

Step-by-step explanation:

The amount needs to be saved 8 times, and the phrase "at least" means the value can be greater than or equal to. So, the answer's the 4th option.

Because it has a variable and that variable is raised to a certain power, the expression 3x2+2x is a polynomial.

A polynomial is a mathematical formula that involves only the operations addition, subtraction, multiplication, and powers of positive integers of the variables and is composed of coefficients and indeterminates.

A polynomial term, a series term, or an expression's multiplicative factor is known as a coefficient in mathematics. In addition to being any statement, it is frequently a number. If the coefficients are variables in and of themselves, they may also be known as parameters.

The fact that the above phrase 3x2+2x contains a variable makes it a polynomial. The power of that variable is likewise increased. The mathematical expression that results becomes a polynomial.

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When the object's acceleration reaches 6.67 m/s2, the force is 20 N.

The mass of an object determines the acceleration it experiences.

The force is 6 N if the object's acceleration increases to 3 m/s2.

Reason:

The parameters listed are;

The occupying force the object's acceleration.

The acceleration produced by a force, F, of 18 N is equal to 6 m/s2.

Newton's Second Law of Motion states that;

F = M × A

Where;

m = The object's mass

In light of the parameters, F = 18 N and a = 6 m/s2, we may determine the mass of the

the following is the provided object;

Weight = F/A

Therefore, the force acting when the acceleration is an is;

20 = 3 kg, where a = a = 6.67 m/s2.

When the object's acceleration reaches 6.67 m/s2, the force is 20 N.

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An ordered pair is a set of two values, (x,y), where x and y are the coordinates. In an ordered pair, the first element is typically referred to as the x-coordinate, or the "first component" and it represents the horizontal position of the point on a coordinate plane. The second element is typically referred to as the y-coordinate, or the "second component" and it represents the vertical position of the point on a coordinate plane.

So, to find the first and second element of a pair, you can refer to the first element as the x-coordinate or the first component and the second element as the y-coordinate or the second component.

For example, in the ordered pair (4,3), the first element is 4, which represents the x-coordinate, and the second element is 3, which represents the y-coordinate.

Answer:

31p+13

Step-by-step explanation:

After expanding: 21p+28+10p-15

After simplifying: 31p+13