Please help with this

Yes, the function x(t) = |6 cos(4t)| can be represented by a Fourier series. The Fourier coefficients are given by cₙ = (1/T) * ∫[x(t) * \(e^(^-^j^n^w^_^0^t^)\))] dt, where T is the period and ω₀ = 2π/T.

To find the Fourier coefficients, we first determine the period T. Since x(t) = |6 cos(4t)|, its period T = π/2. Thus, ω₀ = 2π/T = 4π. Now, we split the function into two cases:

1. When cos(4t) ≥ 0: x(t) = 6 cos(4t)
2. When cos(4t) < 0: x(t) = -6 cos(4t)

We compute the Fourier coefficients cₙ separately for each case and sum the results, considering the half-period due to the absolute value function. We obtain:

cₙ = (1/π) * ∫[6cos(4t) * \(e^(^-^j^n^4^$^\pi$^t^)\)] dt from 0 to π/4, plus
(1/π) * ∫[-6cos(4t) * \(e^(^-^j^n^4^$^\pi$^t^)\)] dt from π/4 to π/2.

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The interest on $5.255 at 12% for 30 days using ordinary interest is approximately $0.0511.

To calculate the interest using ordinary interest, we can use the formula:

Interest = Principal * Rate * Time

Here, the principal (P) is $5.255, the rate (R) is 12% (or 0.12), and the time (T) is 30 days.

Plugging in the values:

Interest = $5.255 * 0.12 * (30/365) = $0.0511 (rounded to four decimal places)

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Answer:

4

Step-by-step explanation:

4/5 - 1/4 = 11/20

(decimals: 0.55)

4

4/5 - 1/4 = 11/20

(I may have used a calculator)

Both a rhombus and a square are parallelograms and quadrilaterals (which means they have four sides with parallel opposite sides). The main difference between the two is that, while a rhombus has two opposite internal angles of equal measure, a square has four right angles with equal measure. A square and a rhombus both have sides equal in length. But square has all its angles equal to 90 degrees, but a rhombus only has its opposite angles equal.

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Answer:

150 cm^2

Step-by-step explanation:

Keep in mind that the dimensions of the cube are identical in 6 directions.  This means that the surface area of the bottom is 5 cm by 5 cm, yielding the area 25 cm^2.  The top has the same area, so considering top and bottom we get a total surface area of 50 cm^2.

Likewise, the total surface area of the sides together is 50 cm^2.  The total surface area of the front and back together is 50 cm^2.

Thus, the total surface area of the entirre cube is 3(50 cm^2), or 150 cm^2

Answer:

225 books

Step-by-step explanation:

you do 15 x 8 and you get 120 then you do 15 x 7 and you get 105 then you add 120 and 105 together and your final answer is 225 books

Answer:

ANswer: 225

Step-by-step explanation:

multiply: 15 x 7 = 105 & 15 x 8 = 120

now add " 105 + 120" together

Total: (See answer above)

Answer: 1 3/5

Step-by-step explanation:

5/5 = 1

There is a remainder of 3/5.

Combine these two pieces to get the whole, 1 3/5.

Answer:

135°

Step-by-step explanation:

Step 1:

100° + 35° + 180° - ? = 180°        Sum of a Δ/Vertical ∠'s

Step 2:

315° - ? = 180°        Combine Like Terms

Step 3:

315° = 180° + ?        Add ? on both sides

Step 4:

315° - 180° = ?     Subtract

Answer:

? = 135°

Hope This Helps :)

The basic annual salary of Martha is R576 000. She is entitled to an annual bonus of 90% of her basic monthly salary. Her employer contributes 8% of her basic salary to her pension fund. She works for 45 hours per week Martha's hourly recovery tariff for 17 March 2022 can be calculated by adding her monthly basic salary, bonus amount, and pension fund contribution, and dividing it by the total number of working hours in a year.

To calculate Martha's remuneration for 17 March 2022. It involves determining her basic monthly salary, annual bonus, pension fund contribution, and the number of working hours on that specific day. By combining these factors and using the given information, the hourly recovery tariff can be calculated.

To calculate Martha's remuneration for 17 March 2022, we need to consider her basic annual salary, annual bonus, pension fund contribution, and the number of working hours on that specific day.

Basic Annual Salary: R576,000

Annual Bonus: 90% of her basic monthly salary

Basic Monthly Salary = Basic Annual Salary / 12

Annual Bonus = Basic Monthly Salary * 90%

Pension Fund Contribution: 8% of her basic salary

Pension Fund Contribution = Basic Annual Salary * 8%

Number of Working Hours on 17 March 2022: Since it is not specified, we'll assume the standard working hours for that day, which is 8 hours.

Now, let's calculate Martha's remuneration for 17 March 2022:

Step 1: Calculate the Basic Monthly Salary

Basic Monthly Salary = Basic Annual Salary / 12

Step 2: Calculate the Annual Bonus

Annual Bonus = Basic Monthly Salary * 90%

Step 3: Calculate the Pension Fund Contribution

Pension Fund Contribution = Basic Annual Salary * 8%

Step 4: Calculate the Hourly Recovery Tariff

Hourly Recovery Tariff = (Basic Monthly Salary + Annual Bonus + Pension Fund Contribution) / (52 weeks * 45 hours per week)

Finally, substitute the calculated values into the formula to find the Hourly Recovery Tariff for Martha's remuneration on 17 March 2022.

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First of all, we need to know what the units are in this problem.

We can see that there is yards, inches, and feet.

(Keep in mind that yd = yard, ft = feet, and in = inches)

1yd = 3ft

1ft = 12in

Let's figure out how many inches are in a yard.

If we know that 3 feet are in every yard, and 12 inches are in every foot, we can make an equation that looks like this:

(1yd × 3ft) × 12 = 36

This means that there are 36 inches in every foot.

Now that we know how many inches are in a yard, lets figure out how many inches are in 10 yards.

36 × 10 = 360

There are 360 inches in 10 yards.

Now, let's figure out how much 360 inches exceeds 192 inches.

360 - 192 = 168

To convert this to feet, we need to use an equation that looks like this:

168 ÷ 12 = 14

Therefore, the amount of feet that the length of the room exceeds the width is 14 feet.

Answer:

3 x -2 or -2 x 3

Step-by-step explanation:

I'm a little confused on what you're asking...

Answer:

system of equation?

Step-by-step explanation:

not sure bout this one

Answer:

10/5 - 4

Step-by-step explanation:

you have to write down what you understand from the sentence.

First, you read it carefully since it says quotient then you will have to put that first and then subtraction. Normally you would put subtraction in front because the sentence is in that order. But since your dealing with division then the subtraction part would go afer.

10/5 - 4

Answer: uhh i think both are correct since the order of operation states that you must do division over subtraction first, it doesn't matter which position 4 is in, but you must do the division first.

Answer:

331 miles

Step-by-step explanation:

$120 - 37.26 =  $82.74

$82.74 = 8274 cents

8274/20 = 330.96 miles

Answer:

The last listed functional expression:

\(\left \{ {x+1\,\,\,\,{x\geq 2} \atop {x+2 \,\,\,\,x<2}} \right.\)

Step-by-step explanation:

It is important to notice that the two linear expressions that render such graph are parallel lines (same slope), and that the one valid for the left part of the domain, crosses the y-axis at the point (0,2), that is y = 2 when x = 0. On the other hand, if you prolong the line that describes the right hand side of the domain, that line will cross the y axis at a lower position than the previous one (0,1), that is y=1 when x = 0. This info gives us what the y-intercepts of the equations should be (the constant number that adds to the term in x in the equations: in the left section of the graph, the equation should have "x+2", while for the right section of the graph, the equation should have x+1.

It is also important to understand that the "solid" dot that is located in the region where the domain changes, (x=2) belongs to the domain on the right hand side of the graph, So, we are looking for a function definition that contains \(x+1\) for the function, for the domain: \(x\geq 2\).

Such definition is the one given last (bottom right) in your answer options.

\(\left \{ {x+1\,\,\,\,{x\geq 2} \atop {x+2 \,\,\,\,x<2}} \right.\\\)

The radian measure of the central angle intercepting an arc of length 10 cm on a circle with a radius of 7 cm is approximately 1.42857 radians.

To find the radian measure of the central angle intercepting an arc of length 10 cm on a circle with a radius of 7 cm, we can use the formula:

θ = s / r,

where θ is the radian measure of the central angle, s is the length of the arc, and r is the radius of the circle.

In this case, the length of the arc (s) is given as 10 cm, and the radius (r) is 7 cm. Plugging these values into the formula, we have:

θ = 10 cm / 7 cm.

Simplifying the expression, we get:

θ ≈ 1.42857 radians.

Therefore, the radian measure of the central angle intercepting an arc of length 10 cm on a circle with a radius of 7 cm is approximately 1.42857 radians.

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Answer:

B

Step-by-step explanation:

Answer:

Lol

Step-by-step explanation:

Please mark me brainleist

Answer:

Reflect over the y-axis, vertically stretch by a factor of 3, and then shift down 1 unit

Step-by-step explanation:

Parent function:  \(f(x)=x\)

The graph of the parent function is a straight line graph that intersects the axes at the origin (0, 0) and has a positive slope of 1 unit.

To determine the sequence of transformations, find the equation of the transformed function in slope--intercept form.

Slope-intercept form of a linear function:  \(f(x)=mx+b\)

(where m is the slope and b is the y-intercept)

To calculate the slope of the transformed function, choose two points on the line and use the slope formula:

\(\implies \sf slope\:(m)=\dfrac{y_2-y_1}{x_2-x_1}=\dfrac{-4-(-1)}{1-0}=-3\)

The y-intercept (where the line crosses the y-axis) of the transformed function is (0, -1).

Therefore the equation of the transformed function is:

\(g(x)=-3x-1\)

Translations

For a > 0

\(f(x+a) \implies f(x) \: \textsf{translated}\:a\:\textsf{units left}\)

\(f(x-a) \implies f(x) \: \textsf{translated}\:a\:\textsf{units right}\)

\(f(x)+a \implies f(x) \: \textsf{translated}\:a\:\textsf{units up}\)

\(f(x)-a \implies f(x) \: \textsf{translated}\:a\:\textsf{units down}\)

\(y=a\:f(x) \implies f(x) \: \textsf{stretched parallel to the y-axis (vertically) by a factor of}\:a\)

\(y=f(ax) \implies f(x) \: \textsf{stretched parallel to the x-axis (horizontally) by a factor of} \: \dfrac{1}{a}\)

\(y=-f(x) \implies f(x) \: \textsf{reflected in the} \: x \textsf{-axis}\)

\(y=f(-x) \implies f(x) \: \textsf{reflected in the} \: y \textsf{-axis}\)

Comparing the transformed function's equation with the parent function:

\(\begin{cases}f(x)=x\\g(x)=-3x-1\end{cases}\)

Transformations

1.  Reflection in the y-axis:

    \(f(-x)=-x\)

2.  Vertically stretched by a factor of 3:

    \(3f(-x)=-3x\)

3.  Shifted 1 unit down:

    \(3f(-x)-1=-3x-1\)

Summary

Reflect over the y-axis, vertically stretch by a factor of 3, and then shift down 1 unit

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Answer:

Step-by-step explanation:

We are given that the factory produces  42,000  computer monitors per day

And the claim is of this amount produces fewer than 660 are defective.

a random sample shows that of 240 monitors 2 are defective

to verify the factory managers claim we need to know how many 240s are there in 42000

=42000/240= 175

Since each 240 will give 2 defective monitors

175 will give= 175*2= 350

350 is less than 660 hence the managers claim is correct

Answer:

x = 8

y = 29

Step-by-step explanation:

8x - 11 = 9x - 19

x - 19 = -11

x = 8

2y - 5 = 9x - 19

2y - 5 = 9(8) - 19

2y - 5 = 72 -19

2y - 5 = 53

2y = 58

y = 29

Answer:

k = - \(\frac{1}{4}\)

Step-by-step explanation:

Given that x varies directly with y then the equation relating them is

x = ky ← k is the constant of variation

To find k use the condition x = - 3 when y = 12

- 3 = 12k ( divide both sides by 12 )

\(\frac{-3}{12}\) = k , that is

k = - \(\frac{1}{4}\)

Answer:

B

Step-by-step explanation:

To go from B' to B , perform the inverse operation

That is the translation rule is (x - 4, y - 5 ) , then

B'(7, - 4 ) → B (7 - 4, - 4 - 5 ) → B (3, - 9 ) → option B

The most inaccurate version of pi in history was likely that of the ancient Egyptians, around 1650 BCE.

The value they used was approximately 3.125, which is quite different from the true value of pi (approximately 3.14159).

Explanation of how this value was derived and its context in history:
1. The ancient Egyptians were known for their achievements in mathematics, especially in the field of geometry.

They used their knowledge to construct monumental structures like the pyramids.
2. To calculate the area of a circle, the Egyptians used a formula that approximated pi as the ratio of the circumference to the diameter of the circle.

They likely derived this value from their observations and measurements of circular objects.
3. The value they used for pi, approximately 3.125, can be found in the Rhind Mathematical Papyrus, an ancient Egyptian mathematical document dating back to around 1650 BCE.

This document contains several mathematical problems and solutions, including those related to geometry.
4. Although the ancient Egyptians' approximation of pi was inaccurate compared to the true value, it served their purposes at the time and was an impressive achievement considering the tools and knowledge available to them.
5. Over time, mathematicians continued to refine the value of pi, with more accurate approximations being developed by scholars like Archimedes (circa 287-212 BCE), who calculated pi to be between 3.1408 and 3.1429.
In summary, the most inaccurate version of pi in history was likely that of the ancient Egyptians, who used a value of approximately 3.125 around 1650 BCE.

This value, though far from the true value of pi, was still a significant achievement for their time.

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Answer:

18m+2

Step-by-step explanation:

multiply 6m by 3 and add 2

f(6m)=18m+2

9514 1404 393

Answer:

  B = 13

Step-by-step explanation:

The tangent and cotangent are equal when the angles are complementary.

  (3B +35) +(2B -10) = 90

  5B = 65

  B = 13

___

Check

For B=13, the angles are 3B+35 = 39+35 = 74, and 2B-10 = 26-10 = 16. Both are acute angles.

Answer:

D) -5 +4i

Step-by-step explanation:

Subtract the complex number:

 Add/subtract the real part with real part and imaginary part with imaginary part.

11 - 7i -(16- 11i) = 11 - 7i - 16 + 11i

                      = 11 - 16 - 7i + 11i

                      = -5 + 4i

Donna deposits $700 into an account that pays simple interest at a rate of 2% per year. Donna will be paid $28 in interest in the first 2 years.

To calculate the interest, we use the formula:

Interest = Principal × Rate × Time.

In this case, the principal (initial deposit) is $700, the rate is 2% (or 0.02), and the time is 2 years.

Plugging these values into the formula, we get:

Interest = $700 × 0.02 × 2 = $28.

Therefore, Donna will earn $28 in interest in the first 2 years.

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The statement "If x = -10, then x² = 100" is false. When we square -10, we get 100, so the correct statement would be "If x = -10, then x² = 100."

The statement that is NOT true is:

If x = -10, then x² = 100.

The other three statements are all true:

If x² = 100, then x = 10.This is true because the square root of 100 is ±10, and when we take the square root, we consider the positive square root, which is 10.

If x = 10, then x² = 100. This is also true because when we square 10, we get 100.The statement x² = 100 if and only if x = 10 or x = -10 is true.

This statement is based on the fact that the square root of 100 is ±10, so when we square either 10 or -10, we get 100.

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