Trigonometry Question:
Find all solutions on the interval [0,2π)
12sin^2(x)+cos(x)-6=0

For starters,

[tex]\cos(6t+\pi) = \cos(6t) \cos(\pi) - \sin(6t) \sin(\pi) = -\cos(6t)[/tex]

Now by the fundamental theorem of calculus, integrating both sides gives

[tex]\displaystyle \frac{ds}{dt} = s'(0) + \int_0^t 36 \cos(6u) \, du = 100 + 6 \sin(6t)[/tex]

Integrating again, we get

[tex]\displaystyle s(t) = s(0) + \int_0^t (100 + 6\sin(6u)) \, du = \boxed{100t - \cos(6t) + 1}[/tex]

Alternatively, you can work with antiderivatives, then find the particular constants of integration later using the initial values.

[tex]\displaystyle \int \frac{d^2s}{dt^2} \, dt = \int 36\cos(6t) \, dt \implies \frac{ds}{dt} = 6\sin(6t) + C_1[/tex]

[tex]\displaystyle \int \frac{ds}{dt} \, dt = \int (6\sin(6t) + C_1) \, dt \implies s(t) = -\cos(6t) + C_1t + C_2[/tex]

Now,

[tex]s(0) = 0 \implies 0 = -1 + C_2 \implies C_2 = 1[/tex]

and

[tex]s'(0) = 100 \implies 100 = 0 + C_1 \implies C_1 = 100[/tex]

Then the particular solution to the IVP is

[tex]s(t) = -\cos(6t) + 100t + 1[/tex]

just as before.

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!

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:

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

The expectancy theory that could be phrased as the above question is based on the element called expectancy.

In this question,

Expectancy theory proposes that an individual will behave or act in a certain way because they are motivated to select a specific behavior over others due to what they expect the result of that selected behavior will be.

To make the connection between motivation, effort and performance, expectancy theory has three variables: Expectancy, Instrumentality and Valence.

Expectancy theory consists of three basic components:

(1) The employee's expectancy that working hard will lead to his or her desired level of performance;

(2) The employee's expectancy that working hard will thus ensure that rewards will follow; and

(3) Whether or not the employee's perception that the outcome of working hard is worth the effort or value associated with hard work.

VIE expectancy theory is often formulated using the equation MF (motivational forces) = V (valence) x I (instrumentality) x E (expectancy).

From the definition, the probability that, "if i do a good job, that there will be some kind of outcome in it for me" is comes under the element expectancy(E).

Hence we can conclude that the expectancy theory that could be phrased as the above question is based on the element called expectancy.

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The answer choices which represents the slope of the line described by the points, (1,-1) and (5,-7) is; Choice A; -3/2.

The line in discuss as described in the task content is passing through the points; (1,-1) and (5,-7).

Hence, it follows conventionally from the slope formula that the slope of the line is;

slope, m = (-7-(-1))/(5-1)

m = -6/4

m = -3/2.

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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.

❄

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:

b

Step-by-step explanation:

the opposite sides of a parallelogram are parallel and congruent

thus option b is the correct one

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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The expression [tex]$-500 \times 18+15000=-9000+15000=6000[/tex] which best fit exists in the Linear model.

Given: Monthly Rate = $20

Number of customers = 5000

If there exists a decrease of $1 in the monthly rate, the number of customers increases by 500.

Let us decrease the monthly rate by $1.

Monthly Rate = $20 - $1 = $19

Number of customers = 5000 + 500 = 5500

Let us decrease the monthly rate by $1 more.

Monthly Rate = $19 - $1 = $18

Number of customers = 5500 + 500 = 6000

Linear change in the number of customers whenever there exists a decrease in the monthly rate.

We have 2 pairs of values here,

x = 20, y = 5000

x = 19, y = 5500

The equation in slope-intercept form: y = mx + c

The slope of a function: [tex]$&m=\frac{y_{2}-y_{1}}{x_{2}-x_{1}} \\[/tex]

[tex]$&m=\frac{5500-5000}{19-20} \\[/tex]

[tex]$&\Rightarrow-500[/tex]

So, the equation is y = -500x + c

Putting x = 20, y = 5000:

[tex]$&5000=-500 \times 20+c \\[/tex]

[tex]$&\Rightarrow c=5000+10000=15000 \\[/tex]

[tex]$&\Rightarrow \mathbf{y}=-500 \mathbf{x}+15000[/tex]

Whether (18,6000) satisfies it.

Putting x = 18

[tex]$-500 \times 18+15000=-9000+15000=6000[/tex]

Therefore, the expression [tex]$-500 \times 18+15000=-9000+15000=6000[/tex] which best fits exist Linear model.

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Answer:

68.54

Step-by-step explanation:

w + (w – 12 ÷ 22 • 3) • 7

10 + (10 – 12 ÷ 22 • 3) • 7

Parentheses first

(10 – 12 ÷ 22 • 3)

(10 – 36 ÷ 22)

(10 – 1.636)

(8.364)

-------

10 + (8.364) • 7

10 + 58.54

68.54

The value of the expression will be equal to 66.54. The correct option is  B.

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

Numbers (constants), variables, operations, functions, brackets, punctuation, and grouping can all be represented by mathematical symbols, which can also be used to indicate the logical syntax's order of operations and other features.

Given that the expression is w + (w – 12 ÷ 2^ 2• 3) • 7 and the value of w is 10.

By substituting the value of w equal to 10 the value of the expression is,

E = w + (w – 12 ÷ 22 • 3) • 7

E = 10 + (10 – 12 ÷ 22 • 3) • 7

Solve the Parentheses first.

P = (10 – 12 ÷ 22 • 3)

P = (10 – 36 ÷ 22)

P = (10 – 1.636)

P = (8.364)

Solve further to get the final value.

E = 10 + (8.364) • 7

E = 10 + 56.54

E = 66.54.

Therefore, the value of the expression will be equal to 66.54.

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Using a linear function, it is found that they will have 405 MB of free space when they first have the same amount of space left.

A linear function is modeled by:

y = mx + b

In which:

The free space for each of Nereo and Azeneth can be modeled by a linear function, in which the slope is negative with the amount that each second of video takes and the y-intercept is the initial free space. Her the functions for the amount of free space after x seconds are given by:

They will have the same amount of free space when:

N(x) = A(x)

1000 - 7x = 1255 - 10x

3x = 255

x = 255/3

x = 85.

The space will be of:

N(85) = 1000 - 7 x 85 = 405 MB.

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A regular hexagon inscribed in a circle is the construction that requires both endpoints of the diameter and the points where the arcs intersect the circle to be connected, in order, by line segments. Option D. This is further explained below.

Generally, any of the pieces into which something may be separated or which naturally separates over time. a section that is removed from a figure (such as a circle) using a line or plane as the cutting tool. a segment of a straight line that includes the territory between two points.

In conclusion, For the construction of a regular hexagon that is inscribed inside a circle, it is necessary for the ends of the diameter as well as the locations at which the arcs meet the circle to be linked, in the correct sequence, by line segments.

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Complete Question

Which construction requires both endpoints of the diameter and the points where the arcs intersect the circle to be connected, in order, by line segments?

The correct choices based on the integers are: 1a, 2b, 3d, and 4c.

In the question, we are asked to match the scenarios to their corresponding boundaries.

Thus, the correct choices based on the integers are: 1a, 2b, 3d, and 4c.

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Answer:

B. 126 [tex]\pi[/tex]

Step-by-step explanation:

The volume for a cylinder is: Area of the base x Height

The base is a circle with a diameter of 6cm.

The formula to find the area of the base is: radius x radius x pi

In this case, the radius is 3 (6/2) so the area will be 9pi.

Now that we know that area of the base, all we need to do is multiply the height, which is 14cm.

9 pi x 14 = 126 pi

So B. 126 pi is the correct answer!

Answer:

126π

option B is the correct answer

Answer:

Wayne used 2/5 more flour than sugar

Step-by-step explanation:

If you add 2/5 to 2/5 you get 4/5

1) The Inequalities for Tammy and Keith are respectively; For Tammy: 10x + 5y > 200 and for Keith: 12x + 3y > 180

2) The possible combination of the number of lawns they could have each mowed and the number of yards they could have raked are;

(11, 17), (14, 5), (16, 0), (18, 2)

Tammy earns $10 for each lawn mowed.

Tammy earns $5 for each yard raked.

We are told that She wants to earn more than $200 from her part-time jobs. Thus, the inequality for Tammys would be;

10x + 5y > 200

Keith earns $12 for each lawn mowed

Keith earns $3 for each yard raked.

We are told that Keith wants to earn more than $180 for each part time job. Thus, the inequality is;

12x + 3y > 180

B) To know the possible combination of the number of lawns they could have each mowed and the number of yards they could have raked, i have drawn a graph of both inequalities and the possible points from there are;

(11, 17), (14, 5), (16, 0), (18, 2)

The complete question is;

Tammy and Keith each work two part-time jobs in the summer mowing lawns andraking yards . Tammy earns $10 for each lawn she mows and $5 for each yard sherakes . She wants to earn more than $200 from her part-time jobs . Keith earns $12 for each lawn he mows and $3 for each yard he rakes. He wants to earn more than $180 for each part time job.

A) Write a system of Inequalities to model the number of lawns they each mow (x) and the number of yards they each rake.

B.) What is a possible combination of the number of lawns they could have each mowed and the number of yards they could have raked? Explain how you chose the combination and why you know that combination is correct.

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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:

39C7 or 15380937

Step-by-step explanation:

There are 13 clubs in a 52 card deck. We can remove these from the possibilities. 52-13=39. The rest is simple, choose 7 from 39 using the choose function is 39!/(32!*7!)=15380937. Or just say 39C7 as your answer.

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: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 general term for the arithmetic sequence; -13, -11, -9, -7 is Tn = -15 - 2n.

-13, -11, -9, -7

Common difference, d = Second term - first term

= -11 - (-13)

= -11 + 13

= 2

Therefore,

Tn = a + (n - 1)d

Where,

Tn = a + (n - 1)d

= -13 + (n - 1)2

= -13 - 2n - 2

Tn = -15 - 2n

So therefore, the general term for the arithmetic sequence; -13, -11, -9, -7 is Tn = -15 - 2n.

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Answer:

See Below.

Explanation:

Quadratic Form:

[tex]a {x}^{2} + bx + c[/tex]

Quadratic Formula:

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

Based on the information given from the question, we can deduce:

a = 1

b = 6

c = -5

Now we can substitute all these values into the formula to find x.

[tex]x = \frac{ - 6 + - \sqrt{ {6}^{2} - 4(1)( - 5)} }{2(1)} \\ = - 3 + \sqrt{14} \: or \: - 3 - \sqrt{14} [/tex]

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

50,400 different anagrams can be made from the letters in the word statistics.

Given word : STATISTICS

Anagrams are words formed by jumbling the positions of the letters given in the word.

For such problems we do factorial of number of words and divide by the repeated letters factorials.

Total number of letters = 10

They can be permutated among themselves in 10! ways.

Some letters are repeated in word STATISTICS

Since, there are 3 S's and 3 T's and 2 I's

So, Number of anagrams = [tex]\frac{10!}{3!.3!.2!}[/tex]

= [tex]\frac{10 \times 9 \times 8 \times 7 \times 6 \times 5 \times 4 \times 3!}{3! \times 3 \times 2 \times 1 \times 2 \times 1}[/tex]

= [tex]\frac{10 \times 9 \times 8 \times 7 \times 6 \times 5 \times 4}{3 \times 2 \times 2}[/tex]

= 10 × 9 × 8 × 7 × 2 × 5

= 50,400

50,400 different anagrams can be made from the letters in the word statistics.

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The factor of [tex]$a^{2} b+2 a^{2}+3 b+6$[/tex] exists [tex]$\left(a^{2}+3\right)(b+2)$$[/tex].

Let the given factor be [tex]$a^{2} b+2 a^{2}+3 b+6$[/tex]

To factor this we use the grouping method

We group the first two terms and last two terms then we factor out the greatest common factor (GCF) from each group.

[tex]$\left(a^{2} b+2 a^{2}\right)+(3 b+6)$$[/tex]

Take out GCF from each group

[tex]$a^{2}(b+2)+3(b+2)$$[/tex]

Now factor out b+2, we get

[tex]$\left(a^{2}+3\right)(b+2)$$[/tex]

The factor of [tex]$a^{2} b+2 a^{2}+3 b+6$[/tex] exists [tex]$\left(a^{2}+3\right)(b+2)$$[/tex].

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