1288) Determine the Inverse Laplace Transform of F(s)-204/(s^2+144). The form of the answer is f(t)-Asin(wt). Give your answers as: A, W ans: 2

Answer:

20 cm²

Step-by-step explanation:

1/2 ( 5 x 8 ) = 1/2 ( 40 ) = 20

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-Chetan K

An assumption or concept is given as a hypothesis for the purpose of debating it and testing if it might be true.

hence,sample test of means one-sample test of proportions one-sample test of variances two-sample test of means (independent samples) two-sample test of means (paired samples) two-sample test of proportions two-sample test of variances.

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Answer:For the given figure the value of x is 14

Step-by-step explanation:

Given  a regular polygon

A regular polygon is a polygon which has all sides equal and each side  subtends equal interior angle at the center.

According to the figure

We are given a regular polygon with 10 sides

The angle subtended  at the center is given as

(10x + 4)°

The Sum of interior angles =  ( 10-2) = 1440°

So the angle subtended by one side at the center is given as follows

1440°/ 10 = 144°

Since the angle subtended at the center = 144° = (10x + 4)°

so by solving this we can get

140 = 10x

x = 14  

Answer:

x ≥ 15/2 im pretty sure

Step-by-step explanation:

reduce the fraction: -7 ≤ x + 1/2. move the terms: -x ≤ 1/2 + 7 calculate the sum: -x ≤ 1/2 + 7 = -x ≤ 15/2 and change the signs: x ≥- 15/2.

Answer:the answer is A

Step-by-step explanation:

The step is

Real number - rational(irrational)_ - integer - whole - then natural

The true statement regarding number sets are b. all irrational numbers are real numbers.

Irrational numbers are those numbers which have a non-repeating, non-terminating pattern after decimal place.

According to the given statements we have to determine which is true.

a. all integers are not whole numbers as 0 contains in the set of whole numbers but not in the set of integers.

b. all irrational numbers are real numbers this is a true statement because all the real numbers consist of rational and irrational numbers.

We don't need to check other options because we have been asked which of the following is true not which of the following is/are true.

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The polynomial has two local minima and two local maxima when graphed using a graphing calculator.

Given polynomial: y = 1.2x⁵ + 3.75x⁴ - 5x³ - 14x² + 19x

To determine the local maxima and minima of the given polynomial, we need to find its derivative.

dy/dx = 6x⁴ + 15x³ - 15x² - 28x + 19To find the critical points of the function, we need to solve the above equation for dy/dx = 0. 6x⁴ + 15x³ - 15x² - 28x + 19 = 0

The above equation can be solved using a graphing calculator to find its roots.

Upon solving the above equation using a graphing calculator, we get:x ≈ -2.188x ≈ -1.255x ≈ 0.388x ≈ 1.055

We can now use the first derivative test to determine whether these critical points are the local maxima or minima.

If dy/dx changes sign from negative to positive, the critical point is a local minimum.

If dy/dx changes sign from positive to negative, the critical point is a local maximum.

Hence, the graph of the polynomial has:

One local maximum at x ≈ -2.188Two local minima at x ≈ -1.255 and x ≈ 0.388One local maximum at x ≈ 1.055

Therefore, the polynomial has two local minima and two local maxima when graphed using a graphing calculator.

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Answer:

it is a reflection

Answer:

reflection y=x

Step-by-step explanation:

Answer:

No

Step-by-step explanation:

Answer:

By using the pythsgorean theorem! simple

Answer:\(\sqrt{155}\)

Step-by-step explanation:

Oh god pythagorean triples got thrown out the window for this one. This will be a bit ugly.

First, we find the other side length of the rectangle using the pythagorean theorem.

Then, we use that side length in ANOTHER pythagorean theorem to get our answer.

Well, we know that the side length is \(\sqrt{5^{2}+9^{2} }\)

We'll use whatever that number is, let's call it x for now, in our other expression:

\(\sqrt{x^{2}+7^{2}}\)

So we can do this in one clean equation by substituting our first equation as x in the second one.

Or do them separately. Your choice.

Anyways, try to solve this one now that you know what to do. If you need more help then message.

If xn>0 for all nN, and lim (xn)=0, then lim(√(xn))=0

We know that the limit of a sequence is unique. Since lim(xn) = 0, we have that for every ε > 0, there exists an N ∈ ℕ such that for all n ≥ N, we have |xn - 0| < ε, which implies xn < ε. Now, consider the sequence √(xn). Since xn > 0 for all n ∈ ℕ, we can take the square root of both sides of the inequality xn < ε. This gives us:
√(xn) < √(ε).
Since ε > 0 can be arbitrarily small, it's clear that lim(√(xn)) = 0, as for every ε > 0, there exists an N such that for all n ≥ N, we have √(xn) < √(ε).

Given the conditions that xn > 0 for all n ∈ N and lim(xn) = 0, we have shown that lim(√(xn)) = 0.

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Answer:

(13.5)/4 = 3.375

step-by-step explanation

In a triangle, The value of x is, 40°

And, The value of y is, 50°

A triangle is a three sided polygon, which has three vertices and three angles which has the sum 180 degrees.

We have to given that;

The triangle is show in figure.

We know that;

In a triangle, the pair of two opposite sides are equal then there corresponding angles are also equal.

Now, By figure we can formulate;

⇒ x + x + 100 = 180

Solve for x;

⇒ 2x + 100 = 180

⇒ 2x = 180 - 100

⇒ 2x = 80

⇒ x = 40

Thus, The value of x = 40°

And, We get;

⇒ x° + y° + 90° = 180°

⇒ 40 + y + 90 = 180

⇒ y + 130 = 180

⇒ y = 180 - 130

⇒ y = 50°

Thus, The value of y = 50°

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The point where the cost equals the revenue is at 40 thousand batteries, where the cost and revenue are both 48,000.

The profit from producing 100 thousand batteries is 48,000.

1:Determine the point where the cost equals the revenue.

Cost = Revenue

0.4x + 32 = 1.2x

Solve for x by subtracting 0.4x from both sides:0.8x + 32 = 0

Divide both sides by 0.8:x = 40

Plug in x = 40 to either the cost or revenue equation to find the value of y:

Cost at x = 40: 0.4(40) + 32 = 48

Revenue at x = 40: 1.2(40) = 48

2: The point where the cost equals the revenue is at 40 thousand batteries, where the cost and revenue are both 48,000. This means that if the company produces 40 thousand batteries, they will break even - their revenue will equal their cost. Producing more than 40 thousand batteries will result in a profit, while producing less than 40 thousand batteries will result in a loss.

3: The point (40, 48) corresponds with the graph, as this is where the red cost line and blue revenue line intersect.

4: Profit is found by subtracting cost from revenue. Let P be the profit, then:

P = R - C

Substitute the revenue and cost equations into the profit equation:

P = 1.2x - 0.4x - 32

P = 0.8x - 32

5: To find the profit from producing 100 thousand batteries, substitute x = 100 into the profit equation:

P = 0.8x - 32

P = 0.8(100) - 32

P = 48,000

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The happening in the graph is that the speed of the roller skater increases and decreases with time

From the question, we have the following parameters that can be used in our computation:

The graph

On the graph, we have the following axes

x-axis = Time

y-axis = Speed

The x-axis is continually increasing while the y-axis decreases and increases (as in a sine function)

This means that the speed increases and decreases with time

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The interest rate for the savings account is 5% after 4 years, $20,000 deposited in a savings account with simple interest earned $800 in interest.

We can use the formula for simple interest to solve the problem:

Simple interest = (Principal * Rate * Time) / 100

where Principal is the initial amount deposited, Rate is the interest rate, and Time is the time period for which the interest is calculated.

We know that the Principal is $20,000 and the time period is 4 years. We are also given that the interest earned is $800. So we can plug in these values and solve for the interest rate:

$800 = (20,000 * Rate * 4) / 100

Multiplying both sides by 100 and dividing by 20,000 * 4, we get:

Rate = $800 / (20,000 * 4 / 100) = 0.05 or 5%

Therefore, the interest rate for the savings account is 5%.

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Answer:

For 1 copy it takes 5 seconds, for 2 copy it takes 7 seconds, and for 3 copy it takes 9 seconds.

For each copy, it takes 2 seconds more.

Step-by-step explanation:

A teacher is making multiple copies of a 1-page homework assignment. The time it takes her in seconds is 2 times the number of copies she makes plus 3. What is the total number of seconds it takes for the teacher to make 1 copy? 2 copies? 3 copies? By how many seconds does the total time increase for each copy?

Let the number of copies represented by x and y is the time taken.

The time It takes her in seconds is 2 times the number of copies she makes plus 3.

So the required equation is \(y=2x+3\).

To calculate the time taken for the first copy put x=1 in the above equation.

\(y=2(1)+3\)

\(y=5\)

To calculate the time taken for the first copy put x=2 in the above equation.

\(y=2(2)+3\)

\(y=7\)

To calculate the time taken for the first copy put x=3 in the above equation.

\(y=2(3)+3\)

\(y=9\)

Hence, For each copy, it takes 2 seconds more.

Answer: A:500-300=4n and C:4n+300=500

Step-by-step explanation:

Answer:

x=29

Step-by-step explanation:

4x-18+5x-71=180

9x=269

x=29

The limit doesn't exist.

The value that a function (or sequence) approaches when the input (or index) gets closer to a particular value is known as a limit. Calculus and mathematical analysis are impossible without limits, which are also required to determine continuity, derivatives, and integrals.

In addition to being closely related to limit and direct limit in category theory, the idea of a limit of a sequence is further generalized to include the concept of a limit of a topological net.

A function's limit is typically expressed in formulas as

\(\lim_{x \to c } F(x) = L\)

It is typically used to assign values to specific functions at locations where none are defined while maintaining consistency with existing values.

\(F(x) = -x+8 ,x\leq 0\)

\(F(x) = 4x+9 , if x > 0\)

\(\lim_{x \to 0^{+} } F(x) = \lim_{n \to 0^{+} } (4x+9) = 9\)

\(\lim_{x \to 0^{-} } F(x) = \lim_{x \to 0^{-} } (-x+8) =8\)

\(\lim_{x \to 0^{+} } F(x) \neq \lim_{x \to 0^{-} } F(x)\)

So limit doesn't exist

For limit to exist

\(\lim_{x \to 0^{+} } F(x) = \lim_{x \to 0^{-} } F(x) = \lim_{x \to 0} f(x)\)

must be satisfied

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Answers:

Length = 270 feet

Width = 45 feet

========================================================

Work Shown:

x = width

6x = length, since it is 6 times the width

P = perimeter of rectangle

P = 2*(Length + Width)

P = 2*(6x + x)

P = 2*(7x)

P = 14x

Plug in the given perimeter P = 630 and solve for x.

P = 14x

14x = P

14x = 630

x = 630/14

x = 45

The width is 45 feet.

The length must be 6x = 6*45 = 270 feet.

The required length and width of the lawn is given as Length = 270 feet and Width = 45 feet.

Given that,
A landscaper buried a water line around a rectangular lawn to serve as a supply line for a sprinkler system. The length of the lawn is 6 times its width. If 630 feet of pipe was used to do the job, what is the length and the width of the lawn is to be determined.

Perimeter is the measure of the figure on its circumference.

Here,
let the length be l and the width be w,
According to the question,
l = 6w
and
Perimeter of the lawn = 630
2 [l + w] = 630
2 [6w + w] = 630
14w = 630
w = 45
Now,
l = 45[6] = 270

Thus, the required length and width of the lawn is given as Length = 270 feet and Width = 45 feet.

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The value of X= 132.

A point where two lines meet produces an angle.

The breadth of the "opening" between these two rays is referred to as a "angle". It is depicted by the figure.

Radians, a unit of circularity or rotation, and degrees are two common units used to describe angles.

By connecting two rays at their ends, one can make an angle in geometry. The sides or limbs of the angle are what are meant by these rays.

The limbs and the vertex are the two main parts of an angle.

The common terminal of the two beams is the shared vertex.

According to our question-

the sum of angles of triangle = 180

12+16+20+x=180

x=132

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The number of freshmen that are students is 738

Let y represent the number of students that are freshmen

The freshmen class is made up of 480 female students

This number represents 65% of the freshmen class

Therefore the total number of students that are freshmen can be calculated as follows

y × 65/100= 480

65y/100= 480

Cross multiply both sides

65y= 480 × 100

65y= 48000

y= 48000/65

y= 738.4

≅ 738

Hence 738 students are freshmen

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Answer:

y=-2(x-1)+6

Step-by-step explanation:

y=m(x-h)+k

y=-2(x-1)+6

The pair of 1st line is vertical opposite angle and 2nd one is adjacent angles.

What is vertical opposite angle ?

When 2 lines meet one another, then the other angles, shaped thanks to intersection ar known as vertical angles or vertically opposite angles. A try of vertically opposite angles ar continuously adequate to one another. Also, a angle and its adjacent angle are supplementary angles, i.e., they add up to a hundred and eighty degrees.

Main body:

1st pair of line intersect each other , so ∠1 = ∠2 by using vertical opposite angle.

2nd pair of line also intersect each other , so ∠3 ,∠4 are adjacent angles.

Hence ,pair of 1st line is vertical opposite angle and 2nd one is adjacent angles.

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