Practice another write the function in terms of unit step functions. find the laplace transform of the given function. f(t) = t, 0 ≤ t < 4 0, t ≥ 4

The displacement between t = 0 and t = 3 is 45 meters, so the correct option is d.

The displacement is defined as the difference between the final position and the initial position.

The initial position is what we get when we evaluate in t = 0.

s = 0^3 -18*0^2+60*0 = 0

The initial position is 0 meters.

The initial position is what we get when we evaluate in t = 3.

s = 3^3 -18*3^2+60*3 = 45

The final position is 45 meters.

Then the displacement is:

D = 45m - 0m = 45m

The correct option is d.

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The angle it makes with the positive x axis in the xy plane is 61.3145 degrees.

In this question,

A normal vector to the plane is any vector that starts at a point in the plane and has a direction that is orthogonal (perpendicular) to the surface of the xy plane .

The magnitude of the xy plane, hypotenuse = 25 units

The x component of the xy plane, base = 12 units

Let θ be an angle, then the angle it makes with the positive x axis is

[tex]\theta = cos^{-1}(\frac{base}{hypotenuse} )[/tex]

⇒ [tex]\theta = cos^{-1}(\frac{12}{25} )[/tex]

⇒ [tex]\theta = cos^{-1}(0.48)[/tex]

⇒ [tex]\theta = 61.3145[/tex]

Hence we can conclude that the angle it makes with the positive x axis in the xy plane is 61.3145 degrees.

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The composition of transformation that maps ABCD to EHGF is "(x, y) → (x', -y') → (x' + 6, y' + 3)".

The basic transformation rules are:

The given quadrilateral ABCD has vertices,

A(-5, 2), B(-3, 4), C(-2, 4), and D(-1, 2)

The transformed quadrilateral EHGF has vertices,

E(1, 1), H(3, -1), G(4, -1), and F(5, 1)

In the map ABCD to EHGF, the transformations that took place are:

1) Reflection over x-axis

2) Translation by (x + a, y + b)

Step 1: Reflection over x-axis; (x, y) → (x, -y)

A(-5, 2) → A'(-5, (-2)) = A'(-5, -2)

B(-3, 4) → B'(-3, (-4)) = B'(-3, -4)

C(-2, 4) → C'(-2, (-4)) = C'(-2, -4)

D(-1, 2) → D'(-1, (-2)) = D'(-1, -2)

So, the reflected quadrilateral is A'B'C'D'

Step 2: Translation by (x, y) → (x + a, y + b);

The reflected quadrilateral A'B'C'D' is now translated by

A'B'C'D' → EHGF

So, (for A'(-5, -2) and E(1, 1))

x + a = 1

⇒ -5 + a = 1

⇒ a = 1 + 5

∴ a = 6

and

y + b = 1

⇒ -2 + b = 1

⇒ b = 1 + 2

∴ b = 3

Thus, the translation is (x + 6, y + 3).

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Answer:

15

Step-by-step explanation:

Note: Take note , absolute value will give the magnitude of the value. (Which means ignoring the + / - signs.)

Eg. | - 19 | = 19

Therefore,

[tex] \frac{12(30 - (9 + {4}^{2})) }{10 - | - 6| } \\ = \frac{12(30 - (9 + 16))}{10 - 6} \\ = \frac{12(30 - 25)}{4} \\ = \frac{12(5)}{4} \\ = \frac{60}{4} \\ = 15[/tex]

The coordinates of the vertices of the preimages are A ( 3, 5) , B ( 1, 2) and C ( 7, -1)

It is important to note the following about the 90 degrees rotation about the origin

Note that

A ( x, y) is the coordinates of the preimage

A' ( -y , x) is the coordinates after the said rotation about the origin

Converting the transformed coordinates to the preimage coordinates

For vertex A

A' ( 5, 3)

Compare with A' ( -y, x)

x = 3

y = -5

Substitute the values

A ( 3, 5 )

For vertex B

B' ( -2, 1)

Compare with B' ( -y, x)

x = 1

y = 2

Substitute the values

B ( 1, 2)

For vertex C

C' ( 1, 7)

Compare with C' ( -y, x)

x = 7

y = -1

Substitute the values

C ( 7, -1)

Thus, the coordinates of the vertices of the preimages are A ( 3, 5) , B ( 1, 2) and C ( 7, -1)

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Answer:

Step-by-step explanation:

If Jen ran 34 miles over the last 2 weeks and only 18 miles the second week, she would've had to have run 16 miles the first week.

34= 18+x

I hope this helps!

Answer:

(f^−1)′(6)=1/(f'(f^-1(6)))

(f^−1)′(6)=1/(f'(f^-6)))

I hope this helps.

The vertices of the figure after the transformation: T<−5, −2>; 5 units left and 2 units down is X'(-3, -3), V'(-4, 0), E'(-1, -1), K'(0, -5)

Transformation is the movement of a point from its initial location to a new location. Types of transformation are reflection, translation, rotation and dilation.

Rigid transformations are transformation that preserve the shape and size of a figure such are reflection, rotation and translation.

The vertices of the figure after the transformation: T<−5, −2>; 5 units left and 2 units down is X'(-3, -3), V'(-4, 0), E'(-1, -1), K'(0, -5)

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Answer: Option 1

Step-by-step explanation:

The graphs intersect at x=0 and x=2.

The answer that represents the point where f(x) = g(x) is; A: f(2) = g(2) and f(0) = g(0)

A function in math is visualized as a rule, which gives a unique output for every input x. Mapping or transformation is used to denote a function in math.

Given is a graph we need to find the point of intersection where f(x) = g(x)

How to find the coordinates of Intersection :-

From the attached graph, we see that is represents the relationship between the functions f(x) and g(x).

Now, the coordinates of the points where f(x) = g(x) will be the coordinates of the points where both graphs intersect.

The first point of intersection, we see that;

f(0) = g(0) = 4

Second point shows;

f(2) = g(2) = 0

Thus, we can conclude that;

f(2) = g(2) and f(0) = g(0)

Hence, the answer that represents the point where f(x) = g(x) is; A: f(2) = g(2) and f(0) = g(0)

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Answer: 19

Step-by-step explanation:

Multiplying both sides of the equation by [tex]-3[/tex] gives that [tex]x=19[/tex].

The roots of the resulting polynomial equation are [tex](x_{1} ,y_{1} ) = (-2 , -26), (x_{2} ,y_{2} ) = ( 0.11 , 1.94 )[/tex] and [tex]( x_{3} , y_{3} ) = ( 4.39, - -9.81)[/tex] , respectively.

What is a polynomial easy definition?

A mathematical expression of one or more algebraic terms each of which consists of a constant multiplied by one or more variables raised to a nonnegative integral power (such as a + bx + cx2).

Ariana must graph two polynomic expressions:

[tex]f(x) = x^{3} -5 . x^{2} + 2[/tex] and [tex]g(x) = -x^{3} + 17 . x[/tex]

The roots of the resulting polynomial equation are found by means of this formula-

f(x) - g(x) = 0.........................1

Then, we must look for every point so that  f(x) = g(x)

The roots of the resulting polynomial equation are [tex](x_{1} , y_{1} ) = ( -2,-26) , (x_{2} ,y_{2} ) = ( 0.114 , 1.937 )[/tex] and [tex](x_{3},y_{3} ) = ( 4. 386 , -9. 812)[/tex]  respectively.

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Answer:

D

Step-by-step explanation:

Answer:

here is the answer

hope it helps u

happy to help

stay safe and healthy

x=90(being adjacent angle)

now ,

x+30=180(being alternate angle)

x=180-30

x=150#

i think my answer ia wrong sorry -_-

Answer:

x=90

Step-by-step explanation:

x is on a straight line with 90 degrees (given angle measure angle)

you should do 180-90=90 to find that angle x is 90 degrees.

Answer:67 wins, 26 losses

Step-by-step explanation: They played 93 games. Let L = their losses and w = their wins. They won 15 more than twice as many games they lost so w =  2L + 15. So, 93 = 3L + 15. 93 - 15 = 78. 78 divided by 3 is 26 so they lost 26 games and won the rest of them or 93-26 = 67 wins and 26 losses.

The length of the longest piece of the cut rope is; 105 cm

We are given that;

Length of rope = 245 cm

We need to make the ratio of second piece equal in both the ratio to find the ratio of all three pieces.

2:3

4:5

Multiply 1st ratio by 4 and 2nd ratio by 3:

Now, the ratio becomes: 8:12 and 12:15

And the ratio of three pieces can be represented as:

8: 12: 15, this ratio is the first piece: second piece: third piece

Thus;

8x + 12x + 15x = 245

35x = 245

x = 245/35

So, the pieces lengths will be;

First piece = 8 * 7 = 56 cm

Second piece = 12 * 7 = 84 cm

Third piece = 15 * 7 = 105 cm

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Answer:

x²y³

Step-by-step explanation:

(x²) (y³) = x²y³

Hope it helps!

Have a nice day:)

❄ Hi there,

let us find the product of the square of x and the cube of y.

[tex]\sf{The \ square \ of \ x: \ x^2}\\\sf{The \ cube \ of \ y: y^3}\\\sf{The \ product \ of \ the \ two: x^2y^3}[/tex]

The square of x means: x times x, or, as I said earlier, x².

The cube of y means: y times y times y, or, as I said earlier, [tex]\sf{y^3}[/tex].

The product means: you multiply x² times y³.

❄

Answer:

3. 125

4. 115

5. m<1 = 70, m<2 = 55, m<3 = 55

6. m<2 = 50, m<3 = 50, m<4 = 80, m<6 = 130

The double reflection generates the following three points: A''(x, y) = (1, - 1), B''(x, y) = (2, 2) and C''(x, y) = (5, 2).

In this problem we must apply two rigid transformations to find three points. The formula for reflection over an axis parallel to the y-axis is defined below:

P'(x, y) = (x', k) - [P(x, y) - (x', k)]     (1)

Where:

If we know that A(x, y) = (1, - 5), k = - 1 and k' =  1, then the resulting points are:

Point A

A'(x, y) = (1, - 1) - [(1, - 5) - (1, - 1)]

A'(x, y) = (1, - 1) - (0, - 4)

A'(x, y) = (1, 3)

A''(x, y) = (1, 1) - [(1, 3) - (1, 1)]

A''(x, y) = (1, 1) - (0, 2)

A''(x, y) = (1, - 1)

Point B

B'(x, y) = (2, - 1) - [(2, - 2) - (2, - 1)]

B'(x, y) = (2, - 1) - (0, - 1)

B'(x, y) = (2, 0)

B''(x, y) = (2, 1) - [(2, 0) - (2, 1)]

B''(x, y) = (2, 1) - (0, - 1)

B''(x, y) = (2, 2)

Point C

C'(x, y) = (5, - 1) - [(5, - 2) - (5, - 1)]

C'(x, y) = (5, - 1) - (0, - 1)

C'(x, y) = (5, 0)

C''(x, y) = (5, 1) - [(5, 0) - (5, 1)]

C''(x, y) = (5, 1) - (0, - 1)

C''(x, y) = (5, 2)

The double reflection generates the following three points: A''(x, y) = (1, - 1), B''(x, y) = (2, 2) and C''(x, y) = (5, 2).

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Answer:

68

Step By Step Explanation:

Evaluate for a=3,b=2

(5)(3)(2)+(4)(2)+(10)(3)

(5)(3)(2)+(4)(2)+(10)(3)

=68

Answer:

The solution is 68

Step-by-step explanation:

a = 3 and b = 2

5ab+4b+10a

= 5(3)(2)+4(2)+10(3)

= 5(6)+8+30

= 30+8+30

= 38+30

= 68

Answer: E. 10,000,000 cubic millimeters

Step-by-step explanation: To find out any result from cubic centimeters to cubic millimeters, you multiply the cubic centimeters' value by 1000 to get the cubic millimeters' value.

10,000 * 1,000 = 10,000,000 cubic millimeters.

Hope this helped!

Step-by-step explanation:

The correct answer is E 10,000,00

Answer:

11/20

Step-by-step explanation:

You could turn them all into equivalent fractions, but the common denominator would be 1,763,580.  Yuck.

Look at the relationship for the numerators to the denominators.  The only numerator that is more than half of its denominator is 11/20.  Half of 20 would be 10 and 11 has a larger value than 10, so as a decimal, it would be more than .5.  All of the other numerators are less than half, so that they have to less than .5.

If you changed all of the numbers to decimals, you would see that 11/20 has the largest value.

The solution to the systems if equation y = 4x - 5, y = 2x + 3 is (x, y) = (4, 11)

y = 4x - 5

y = 2x + 3

4x - 5 = 2x + 3

4x - 2x = 3 + 5

2x = 8

x = 8/2

x = 4

y = 4x - 5

= 4(4) - 5

= 16 - 5

y = 11

Therefore, the solution to the system of be equation is x = 4 and y = 11

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Answer:

3,360

Step-by-step explanation:

so, to start with, there are 8 over 5 permutations (the sequence of the picked beads matters, but no repetitions of beads are possible) to pick 5 items out of 8 available ones.

that is

8! / ((8-5)!) = 8! / 3! = 8×7×6×5×4 = 6,720

rotations and reflections are the same thing here for a 1- dimensional sequence.

1 2 3 4 5 rotated around the middle (3) is

5 4 3 2 1

a reflection is again

5 4 3 2 1

so, we need to consider that instead of 8 beads for the first choice we have only 4 beads to choose from to leave the other 4 beads as choices for the last position.

once we have this established, it is sure that the first and the last position cannot have mirrored beads in any permutation. and therefore rotational or reflectional permutations are impossible.

in other words, half of the possible permutations would be rotations/reflections, and we need to eliminate them.

so, the calculation is

4×7×6×5×4 = 8×7×6×5×4/2 = 6,720/2 = 3,360

Answer:

∠S = 66°

Step-by-step explanation:

A parallelogram's 4 angles always add up to 360°, and opposite angles are the same. (∠S = ∠U; ∠T = ∠V)

So, ∠S + ∠T = 180°.

180° = (2x + 4x + 12 + 6)°

180° = (6x + 18)°

162° = (6x)°

27° = x°

(2x + 12)° = ∠S

(2(27) + 12)° = ∠S

(54 + 12)° = ∠S

66° = ∠S

It is accurate. In the phrase “two more hours than Nandini,” n + 2 are correct translations. Then the correct option is A.

Algebra is used to analyze mathematical symbols, and logic is used to manipulate those symbols.

As an example, Kelley models the sentence "Xander studied two more hours than Nandini" using the equation n + 2.

Consequently, the following will describe Kelley's expression's accuracy the best:

It is precise. Since "two" is translated as "2," "more" as "+," and "Nandini's study time is unknown or "n," 2 + n or n + 2 are the appropriate translations for the sentence "two more hours than Nandini."

So, option A is the best choice.

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I understand that the question you are looking for is :

Kelley writes the expression n + 2 to model the phrase “Xander studied two more hours than Nandini.” Which best explains the accuracy of Kelley’s expression?

It is accurate. In the phrase “two more hours than Nandini,” “two” is “2,” “more” is “+,” and Nandini’s study time is unknown or “n,” so 2 + n or n + 2 are correct translations.

It is inaccurate. In the phrase “two more hours than Nandini,” “two” is “2,” “more” is “+,” and Nandini’s study time is unknown or “n,” so 2 + n is the correct translation.

It is inaccurate. In the phrase “two more hours than Nandini,” “two” is “2,” “more than” is “>,” and Nandini’s study time is unknown or “n,” so 2 greater-than n is the correct translation.

It is inaccurate. In the phrase “two more hours than Nandini,” “two” is “2,” “more than” is “<,” and Nandini’s study time is unknown or “n,” so 2 less-than n is the correct translation.

Solutions of the equation are 22.5°, 30°.

The given equation is sin(5θ) - sin(3θ) = cos(4θ)

We take left side of the equation

sin(5θ) - sin(3θ) = 2cos ((5θ+3θ)/2) (sin(5θ-3θ)/2)

=2cos4θsinθ  [From sum-product identity]

Now we can write the equation as

2cos(4θ)sin(θ) = cos(4θ)

2cos(4θ)sinθ - cos(4θ) = 0

cos(4θ)[2sinθ - 1] = 0

cos(4θ) = 0

4θ = 90°

θ = 90/4

θ = 22.5°

and (2sinθ - 1) = 0

sinθ = 1/2

θ = 30°

Therefore, solutions of the equation are 22.5°, 30°

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The equations with tangents at (0,0) are [tex]y = \frac{4}{7} x[/tex] and

[tex]y = -\frac{4}{7} x[/tex].

In this question,

The curves are x = 7 cos(t), y = 4 sin(t) cos(t)

Two tangents at (0, 0)

In this case, the parametric derivative of x and y are expressed in terms of t.

The first derivative dy/dx can be expressed as

[tex]\frac{dy}{dx}=\frac{\frac{dy}{dt} }{\frac{dx}{dt} }[/tex]

Now, dy/dt is obtained by differentiate y with respect to t,

[tex]\frac{dy}{dt}= 4[cos(t)(cos(t))+sin(t)(-sin(t))][/tex]

⇒ [tex]\frac{dy}{dt}= 4[cos^{2} (t)-sin^{2} (t)][/tex]

Now, dx/dt is obtained by differentiate x with respect to t,

[tex]\frac{dx}{dt} =7(-sin(t))[/tex]

⇒ [tex]\frac{dx}{dt} =-7sin(t)[/tex]

Thus, [tex]\frac{dy}{dx}=\frac{4[cos^{2}(t)-sin^{2}(t ) ]}{-7sin(t)}[/tex]

At (0,0) x = 0 and y = 0, Then

0 = 7 cos(t)

0 = 4 sin(t) cos(t)

and

cos(t) = 0

sin(t) cos(t) = 0

There are two values between -π and π which satisfy these equations simultaneously are

t = π/2

t = -π/2

The equation of a straight line given a point and its slope is

y-y₀ = m(x-x₀)

The two tangents lies at (0,0), so the equation becomes

y = mx

Then the two straight lines will be

y = m₁x  and

y = m₂x

For t = π/2,

[tex]m_1=\frac{dy}{dx}=\frac{4[cos^{2}(\frac{\pi }{2} )-sin^{2}(\frac{\pi }{2} ) ]}{-7sin(\frac{\pi }{2} )}[/tex]

⇒ [tex]m_1=-\frac{4[0-1]}{7(1)}[/tex]

⇒ [tex]m_1=\frac{4}{7}[/tex]

For t = -π/2,

[tex]m_2=\frac{dy}{dx}=\frac{4[cos^{2}(-\frac{\pi }{2} )-sin^{2}(-\frac{\pi }{2} ) ]}{-7sin(-\frac{\pi }{2} )}[/tex]

⇒ [tex]m_2=-\frac{4[0-1]}{-7(1)}[/tex]

⇒ [tex]m_2=-\frac{4}{7}[/tex]

Thus the equations with tangents at (0,0) are [tex]y = \frac{4}{7} x[/tex] and

[tex]y = -\frac{4}{7} x[/tex].

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The transformation that maps quadrilateral 1 onto quadrilateral 2 is a translation followed by a dilation with a scale factor of 2.

A transformation can be defined as the movement of a point on a cartesian coordinate from its original (initial) position to a new location.

In Geometry, there are different types of transformation and these include the following:

Based on similarity transformation of both quadrilateral 1 and quadrilateral 2, we can infer and logically deduce that the transformation which directly maps quadrilateral 1 onto quadrilateral 2 is a translation followed by a dilation with a scale factor of 2, as shown in the image attached below.

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