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For a particle having a position of function e^-(t - 3)², the velocity at 2.9s is obtained as 0.198008 m/s.

What is velocity?

The pace at which an object's position changes in relation to a frame of reference and time is what is meant by velocity. Although it may appear sophisticated, velocity is just the act of moving quickly in one direction. Since it is a vector quantity, the definition of velocity requires both magnitude (speed) and direction.

The position of a particle is denoted by a function x(t) = e^-(t - 3)², where x is the distance and t is the time.

Differentiate the function -

v(x) = d/dt(x) = d/dt[e^-(t - 3)²]

v(x) = e^-(t - 3)²[-2(t - 3)]

Now, substitute the value of t = 2.9 in the equation -

v(2.9) = e^-(2.9 - 3)²[-2(2.9 - 3)]

v(2.9) = e^-(-0.1)²[-2(-0.1)]

Use the exponent formula a^-b = 1/a^b -

v(2.9) = 1/e^(-0.1)²[0.2]

Square the digit (0.1) -

v(2.9) = 1/e^(0.01)[0.2]

Substitute the value ofe^0.01 = 1.01005 -

v(2.9) = (1/1.01005)[0.2]

Use the arithmetic operation of division -

v(2.9) = (0.99004)[0.2]

v(2.9) = 0.198008

Therefore, the velocity of the particle is 0.198008 m/s.

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Answer:

Infinitely many solutions

Explanation:

1) subtract “1” from both sides to get y by itself

Y=-2x-1

2) 4y+8x=-4 share a gcf of “4” so you can divide the whole equation by 4

y+2y=-1

Now substitute “-2x-1” as y

(-2x-1)+2x=-1

-2x and 2x cancel each other and so does -1 and -1

Hence, this system has infinitely many solutions

Answer:

x = 0, y = 1.

Step-by-step explanation:

We can solve for the variables x and y by using substitution. Let's start by solving the first equation for one of the variables:

-1 = 2x - y

y = 2x + 1

Next, we'll substitute y = 2x + 1 into the second equation:

8x - 4y = -4

8x - 4(2x + 1) = -4

Expanding the second equation:

8x - 8x - 4 = -4

-8x - 4 = -4

-8x = 0

x = 0

Finally, we can use one of the equations to find y:

y = 2x + 1

y = 2(0) + 1

y = 1

So, the solution is x = 0, y = 1.

Minimum surface area of rectangular bin with 62,500 cm^3 volume and square base is 31250 cm^2.

What is rectangle ?

A rectangle is a two - dimensional shape with four sides, where each pair of opposite sides are equal in length and parallel to each other

Let's say the length, width and height of the rectangular bin are l, w and h respectively. The volume of the bin can be expressed as:

V = l * w * h = 62500 cm^3 (Given)

Since the base is a square, have w = l. Therefore,

V = l^2 * h

h = V / l^2 = 62500 / l^2

The surface area of the bin can be expressed as:

A = 2lw + 2lh + 2wh

Substituting the value of w = l and h = V / l^2, get:

A = 2l^2 + 2l * (V / l^2) + 2l * l = 2l^2 + 2V / l + 2l^2 = 4l^2 + 2V / l

To minimize the surface area, differentiate A with respect to l and set it to zero:

dA/dl = 8l + 2V / l^2 = 0

4l^3 = V

l^3 = V / 4

Taking the cube root of both sides,

l = (V / 4)^(1/3)

Substituting the value of V,

l = (62500 / 4)^(1/3) = (15625)^(1/3) = 125 cm

Since w = l,

w = 125 cm

h = V / l^2 = 62500 / (125)^2 = 250 cm

The minimum surface area is then given by,

A = 2lw + 2lh + 2wh = 2 * 125 * 125 + 2 * 125 * 250 + 2 * 125 * 125 = 31250 cm^2

Minimum surface area of rectangular bin with 62,500 cm^3 volume and square base is 31250 cm^2.

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Minimum surface area of rectangular bin with 62,500 cm³ volume and square base is 31250 cm^2.

A rectangle is a two - dimensional shape with four sides, where each pair of opposite sides are equal in length and parallel to each other

Let's say the length, width and height of the rectangular bin are l, w and h respectively. The volume of the bin can be expressed as:

V = l * w * h = 62500 cm³ (Given)

Since the base is a square, have w = l. Therefore,

V = l² * h

h = V / l² = 62500 / l²

The surface area of the bin can be expressed as:

A = 2lw + 2lh + 2wh

Substituting the value of w = l and h = V / l^2, get:

A = 2l² + 2l * (V / l²) + 2l * l = 2l²+ 2V / l + 2l² = 4l² + 2V / l

To minimize the surface area, differentiate A with respect to l and set it to zero:

dA/dl = 8l + 2V / l² = 0

4l³ = V

l³ = V / 4

Taking the cube root of both sides,

l = (V / 4)^(1/3)

Substituting the value of V,

l = (62500 / 4)^(1/3) = (15625)^(1/3) = 125 cm

Since w = l,

w = 125 cm

h = V / l² = 62500 / (125)²= 250 cm

The minimum surface area is then given by,

A = 2lw + 2lh + 2wh = 2 * 125 * 125 + 2 * 125 * 250 + 2 * 125 * 125 = 31250 cm²

Minimum surface area of rectangular bin with 62,500 cm^3 volume and square base is 31250 cm².

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Hey there!

|2x + 1| < -4

Since you have an absolute value that is LESS than 0, we can say that it doesn’t have any solutions.

Thus, your answer should be:

NO SOLUTIONS

REMEMBER: If your absolute value is smaller/less than 0, you would NOT have any solutions to the particular equation (like this one you have provided just now)

Good luck on your assignment & enjoy your day!

~Amphitrite1040:)

Answer:

Step-by-step explanation:

13)  5.38  Slightly off

14)  10.4   Correct

15)  Can't read the numbers

16)  11.7  slightly off

17)  Can't read (be careful with which side goes where in the Pythagorean Theorem calculation.  a^2 + b^2 = c^2 where a and b are the two sides and c is the hypotenuse (across from the right angle).  

18)   16.46

19)  10.57

20)  7.04

21)   4.87    It seems that the hypotenuse is given as 7.2, so the equation should be 5.3^2 + x^2 = 7.2^2

22)   Same as in 21:  2.7^2 + x^2 = 6.5^2  x = 5.91

[But I'm having difficulty reading the problems due to fuzziness]

The solution is , The equation of g(x) is g(x) = 2*x^(1/2).

Function, in mathematics, an expression, rule, or law that defines a relationship between one variable (the independent variable) and another variable.

here, we have,

given that,

The original function f(x) is defined

as f(x) = x^(1/2)

which is the square root of x.

When the function is stretched horizontally by a factor of 2,

the x term becomes 2x.

So the new function g(x) is defined

as g(x) = 2*x^(1/2)

Hence, The solution is , The equation of g(x) is g(x) = 2*x^(1/2).

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Non-Euclidean geometries provide a different and more general view of geometry that can help better understand the nature of space and the relationships between objects in the world .

Non-Euclidean geometry is a branch of mathematics that studies the properties and characteristics of geometries that are different from Euclidean geometry, which is the traditional study of geometry and the one most people are familiar with .

Non-Euclidean geometries differ from Euclidean geometry in that they have different postulates , or basic assumptions , about the relationships between points, lines, and angles .

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Answer:

Step-by-step explanation:

x=8

The length of the side AD that needed to be replaced is D. 5.1

A triangle is a three-sided closed-plane figure formed by joining three noncolinear points. Based on the side property triangles are of three types they are Equilateral triangle, Scalene triangle, and Isosceles triangle.

We know, tan = opposite/adjacent.

tan30° = DB/12.

DB = 12×tan30°.

DB = 6.93.

Now, m∠BCA = 30° + 15° = 45°.

Therefore,

tan45° = (AD + DB)/12.

AD + DB = 12.

AD = 12 - 6.93.

AD = 5.1.

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Answer:

5.1

Step-by-step explanation: got right on test

Different Quadrilateral Types

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The perimeter of this rectangular field is equal to 1,100 meters.

Mathematically, the area of a rectangle can be calculated by using this formula:

A = LW

Where:

Note: Area = 6 × 10,000 = 60,000 m^2.

Next, we would determine the width of this rectangle:

60,000 = 400W

W = 60,000 /400

Width, W = 150 m.

Mathematically, the perimeter of a rectangle can be calculated by using this mathematical expression;

Perimeter of a rectangle = 2(L + W)

Perimeter of a rectangle = 2(400 + 150)

Perimeter of a rectangle = 2(550)

Perimeter of a rectangle = 1,100 meters.

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The perimeter of the rectangular field with an area of 6 hectares and length of 400m is 1100 meters.

The perimeter of a rectangle is expressed as;

P = 2( length + width )

Given the data in the question;

First, we determine the width of the field using the area formula.

Area = Length × width

Plug in the values and solve for width

60,000m² = 400m × width

60,000m² / 400m = Width

Width = 150m

Now, the perimeter will be;

P = 2( 400 + 150 )

P = 2( 550 )

P = 1100 meters.

Therefore, the perimeter is 1100 meters.

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Her rate at the end of the summer is 20 miles per hour.

We can define the rate in this case as the change in position as a function of the time.

So, the rate would be something like a speed (exactly a speed, actually).

Initially, the camper travles at a rate of 10mi/h in 2 hours, so the total distance is:

d = (10mi/h)*2h = 20mi

And at the end of the sumer, the camper travels that distance in one hour, so the rate at the end of the summer is:

R = 20mi/1h = 20mi/h

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Answer:

ladder has to be at least 13 ft long

Step-by-step explanation:

l = length of the ladder

12.6² + 3.2² = l²

l² = 158.76 + 10.24 = 169

√l² = l = √169 = 13

The ladder is the hypotenuse of a right triangle with sides 12.6 and 3.2

The result will be the x value when the difference between the values of f(x) and g(x) is less than 0.1, which will be the positive solution to the nearest tenth of f(x)=g(x).

To find the positive solution, to the nearest tenth, of f(x)=g(x) using Cora's process, the steps are as follows:

Input the initial value of x, for example x=0.

Calculate f(x) and g(x):

If f(x) is less than g(x), then x should be increased and vice versa.

Increase or decrease x accordingly and calculate the new values of f(x) and g(x).

Keep repeating steps 3 and 4 until the difference between the values of f(x) and g(x) is less than 0.1.

The result will be the x value when the difference between the values of f(x) and g(x) is less than 0.1, which will be the positive solution to the nearest tenth of f(x)=g(x).

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Simplifying the given expression can be rewritten as:  [tex](512m^9n^3)[/tex].

The main power rules are presented below.

For simplifying the given expression, it is necessary to apply the presented power rules previously.

The given expression is (-4mn)³*(-2m²)³. Thus,

       (-64m³n³) * [tex](-8m^6)[/tex]

        Note that the rule should be apply in numbers and letters.

      [tex](512m^9n^3)[/tex]

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Answer:4

Step-by-step explanation:

3

The value of the variable x in the given right angle expression is; x = 11

We know that a right angle simply means an angle that is equal to 90 degrees.

Now, we see that the sum total of the angle in the diagram is 90 degrees and as such the sum of the two internal angles will be 90 degrees.

Thus;

5x + 35 = 90

Subtract 35 from both sides to get;

5x = 55

x = 55/5

x = 11

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The best approximation to a solution of the system of equations is x = -11 and y = 22.

A system of equations is a collection of two or more equations with the same variables. Solving a system of equations means finding the values of the variables that satisfy all the equations in the system.

In this case, you have a system of two equations:

4x + 2y = 0 and x + y = 11.

To find the best approximation to a solution of the system, we can use substitution or elimination methods.

First, we can isolate one of the variables in one of the equations.

=> 4x + 2y = 0.

Dividing both sides by 2, we get:

=> 2x + y = 0.

Now we have one equation in terms of one variable, which is y.

Next, we can substitute the expression for y from this equation into the second equation:

=> x + y = 11.

Replace y with -2x

=> x + (-2x) = 11.

=> -x = 11.

=> x = -11.

Finally, we can substitute the value for x back into one of the original equations to find the value of y.

Let's substitute x = -11 into the first equation:

=>  4(-11) + 2y = 0.

=> -44 + 2y = 0.

=> 2y = 44.

=> y = 22.

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As side EG is the largest side at 15, and the greatest angle is the opposite side's angle,  ∠F.

Given that it consists of sides and three vertices, a triangle qualifies as a polygon. It connects to the fundamental geometric shapes. Triangle ABC is the term used to refer to such a triangle with the points A, B, and C. When the three points are not collinear, a unique plane and triangle in Geometric forms are discovered. Triangles are polygons because they have three sections and three corners. The points where the four structures of the triangle converge are referenced to as the triangle's corners. Three triangle angles are multiplied to yield 180 degrees.

given

Find the smallest angle by finding the angle opposite the smallest side, then the medium-sized angle by finding the angle opposite the medium-sized side .

Then the greatest angle by finding the angle opposite the largest side when there are three side lengths available.

As side FG is the smallest side at 7, and the smallest angle is the one across from it, ∠ E.

The opposing angle,  ∠G, is the medium-sized angle, just as side EF is a medium-sized side as measured by 12.39.

As side EG is the largest side at 15, and the greatest angle is the opposite side's angle,  ∠F.

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The complete question is :-

a) Order the angle measures m∠E , m∠F and m∠EGF from least to greatest ad well as side length .

Therefore, using the discriminant approach, the two values of the roots of the equation X2-5x+2=0 are 4.56 and 0.44.

When use the formula to solve a problem, the "discriminant" is the value that helps in recognizing the various sorts of solutions. In a mathematical formula (a quadratic equation), it is a special function of a cross that reveals information out about bases of the equation. The "b" term must be square-rooted before the "a" term and "c" term may be isolated by four times to calculate the discriminant. It has a (delta) next to the letter "D" that stands for discrimination. Positive discriminant describes a quadratic equation with two unique real number solutions. Repeated positive integer solutions exist for a quadratic equation with a characteristic of zero. A negative discriminant reveals that none of the solutions is a real number.

given

x2 - 5x + 2 = 0

the roots of the equation

x = -b ±[tex]\frac{\sqrt{b^{2} - 4ac} }{2a}[/tex]

x = 5 ± [tex]\sqrt{17} / 2[/tex]

Therefore, using the discriminant approach, the two values of the roots of the equation X2-5x+2=0 are 4.56 and 0.44.

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Answer:

-1+p<15

=-1+1+p<15+1

=p<16

Answer:56

Step-by-step explanation:

You divide 14kg by 2kg and get 7kg. So then you times 7kg by 8 seeds.

Hope this helps :)

The horizontal distance of a raindrop that falls from the end of the roof to the center of the base of the house, obtained from the linear equation for the height of the roof is; x = 18 feet

A linear equation is an equation that has one as the highest index, and which when graphed, forms a straight line.

The linear function for the height of the roof is, h(x) = -|x| + 34

Where;

h(x) = The height of the roof

x = The horizontal distance from the center of the roof

The minimum height of the roof, obtained from the diagram = 16 feet

Therefore, we get, when h(x) 16, substituting the value h(x) = 16, in the function for the height of the roof, we get;

h(x) = -|x| + 34

h(x) = 16

Therefore, 16 = -|x| + 34 (substitution property)

|x| = 34 - 16 = 18

The distance from the center of the house, which corresponds to the least height of the roof, which is the end of the roof and the location at which the raindrop falls is; x = 18 feet

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The reaccepts 10 integers from the user using an array and a loop is explained below.

To start, you need to declare an array variable that can store 10 integers. For example, you can declare an array variable called "numbers" as follows:

int numbers[10];

Next, you will use a loop to repeatedly ask the user to input an integer. The loop will run 10 times to receive 10 integers. You can use the for loop for this purpose.

Here is an example:

for (int i = 0; i < 10; i++) {

 printf("Enter integer %d: ", i + 1);

 scanf("%d", &numbers[i]);

}

In this code, the for loop starts with the value of i being 0. It runs until i is less than 10. After each iteration, i is incremented by 1.

After the loop finishes, all 10 integers received from the user are stored in the numbers array. You can access them using the index of the array.

In conclusion, to receive 10 integers from the user using an array and a loop, you need to declare an array variable, use a for loop to repeatedly ask the user for input, and store the input in the array using the scanf function.

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If a = [tex]\left[\begin{array}{ccc}1&0&-4\\0&3&-2\\-2&6&3\end{array}\right][/tex] , b = [tex]\left[\begin{array}{ccc}4\\1\\-4\end{array}\right][/tex] and we denote the columns of A by a₁, a₂, a₃, and let W = Span {a₁, a₂, a₃,} , then b is not in {a₁, a₂, a₃} .

The Span of set of vectors is set of all linear combinations of those vectors. In other words, it's the set of all possible vectors that can be created by taking a weighted sum of the original vectors.

The span of a set of vectors is a subspace of the vector space in which the vectors lie, and it's the smallest subspace that contains all of the original vectors.

The vector b is not in {a₁,a₂,a₃} because "b" is not equal to any of the column vectors of A. Clearly, there are only 3 vectors in {a₁,a₂,a₃}.

The given question is incomplete , the complete question is

a = [tex]\left[\begin{array}{ccc}1&0&-4\\0&3&-2\\-2&6&3\end{array}\right][/tex] , b = [tex]\left[\begin{array}{ccc}4\\1\\-4\end{array}\right][/tex] . Denote the columns of A by a₁, a₂, a₃, and let W = Span {a₁, a₂, a₃,}.  Is b in {a₁, a₂, a₃} ?

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Answer:

$538

Step-by-step explanation:

The minimum payment in the first month would be:

Minimum payment = 1.5% * $19,500 + 3% * $19,500 = $292.25

At the end of the first month, the balance would be:

Balance = $19,500 + $19,500 * 1.5% - $292.25 = $19,318.375

In the second month, the minimum payment would be:

Minimum payment = 1.5% * $19,318.375 + 3% * $19,318.375 = $291.26

At the end of the second month, the balance would be:

Balance = $19,318.375 + $19,318.375 * 1.5% - $291.27 = $19,138.89

In the third month, the minimum payment would be:

Minimum payment = 1.5% * $19,138.89 + 3% * $19,138.89 = $290.26

At the end of the third month, the balance would be:

Balance = $19,138.89 + $19,138.89 * 1.5% - $290.26 = $18,961.62

So, Ellen would have paid off $19,500 - $18,961.62 = $538.38. The answer rounded to the nearest cent is $538

Answer:

x=33

Step-by-step explanation:

[tex]180=2x-24+4x+6[/tex]

[tex]180=6x-18[/tex]

[tex]198=6x[/tex]

[tex]x=33[/tex]

A rectangular prism has 6 faces, 8 vertices and 12 edges.

What is rectangular prism?

A rectangular prism is a three-dimensional shape, that has six faces (two at the top and bottom and four are lateral faces). All the faces of the prism are rectangular in shape. Hence, there are three pairs of identical faces here. Due to its shape, a rectangular prism is also called a cuboid. A rectangular prism is a three-dimensional solid shape with six faces that including rectangular bases. A cuboid is also a rectangular prism. The cross-section of a cuboid and a rectangular prism is the same.

If all the faces of the prism are squares then the rectangular prism is a cube. The volume of a rectangular prism is a measure of the space inside the prism.

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