(Time limit)

Tell me the domain
Tell me the range
Tell me whether the graph is a function or not
The answer choices are below

The laplace transform is Y(s) = (7 + e^{-s}/s) / (s² - 5s)

The solution y(t) is y(t) = (-e^{5-t} + 2e^{-5} - 6(t-1) + 7u(t-1))/25.

The solution can be expressed as a piecewise-defined function:

y(t) = -e^{5-t}/25 + 2e^{-5}/25 - 6(t-1)/25 + 7/25, t < 1

y(t) = -e^{5-t}/25 + 2e^{-5}/25 - 6(t-1)/25 + 7/25 + (t-1)/25, t ≥ 1

We have,

a.)

To find the Laplace transform of the solution, we first take the Laplace transform of both sides of the differential equation using the initial value theorem, which states that the Laplace transform of the derivative of a function y(t) is sY(s) - y(0):

s²Y(s) - s y(0) - y'(0) - 5(sY(s) - y(0)) = e^{-s}

Simplifying and solving for Y(s), we get:

Y(s) = (7 + e^{-s}/s) / (s² - 5s)

b.)

To obtain the solution y(t), we use partial fraction decomposition to separate Y(s) into two terms:

Y(s) = A/(s-5) + B/s + C/(s-5)^2

Multiplying both sides by the denominator, we get:

7 + e^{-s}/s = A(s-5)² + Bs (s - 5) + C(s)

Setting s = 0, we get:

7 = 25A - 5B + 0C

Setting s = 5, we get:

7 + e^{-5}/5 = 0A + 5B + 5C

Taking the derivative with respect to s and setting s=0, we get:

0 = 10A - B

Solving these equations, we get:

A = -1/25

B = -2/5

C = 6/25

Therefore, the solution y(t) is:

y(t) = (-e^{5-t} + 2e^{-5} - 6(t-1) + 7u(t-1))/25

Where u(t) is the unit step function.

c.)

The solution can be expressed as a piecewise-defined function as follows:

y(t) = -e^{5-t}/25 + 2e^{-5}/25 - 6(t-1)/25 + 7/25, t < 1

y(t) = -e^{5-t}/25 + 2e^{-5}/25 - 6(t-1)/25 + 7/25 + (t-1)/25, t ≥ 1

At t = 1, there is a discontinuity in the first derivative of the solution due to the presence of the delta function in the original differential equation.

This causes a sudden jump in the slope of the graph of the solution.

Thus,

The laplace transform is Y(s) = (7 + e^{-s}/s) / (s² - 5s)

The solution y(t) is y(t) = (-e^{5-t} + 2e^{-5} - 6(t-1) + 7u(t-1))/25.

The solution can be expressed as a piecewise-defined function as:

y(t) = -e^{5-t}/25 + 2e^{-5}/25 - 6(t-1)/25 + 7/25, t < 1

y(t) = -e^{5-t}/25 + 2e^{-5}/25 - 6(t-1)/25 + 7/25 + (t-1)/25, t ≥ 1

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Answer:

x = 3

c(x) = 3x² + 5x + 22

⇒ c(3) = 3(3²) + 5(3) + 22

⇒ c(3) = 3(9) + 15 + 22

⇒ c(3) = 27 + 15 + 22

⇒ c(3) = 64

j(x) = 12x

⇒ j(3) = 12(3)

⇒ j(3) = 36

a(x) = 9x

⇒ a(3) = 9(3)

⇒ a(3) = 27

c(x) = 3x² + 5x + 22 is the function that has the largest value when x = 3.

False. Not all functions are equal at x = 3.

The solution is : the weighted-average accumulated expenditures are $101,269.5.

Explanation:

Calculation to determine the weighted-average accumulated expenditures

Weighted-average accumulated expenditures=$202,539* (3/12 + 2/12 + 1/12)

Weighted-average accumulated expenditures=$202,539*0.5

Weighted-average accumulated expenditures=$101,269.5

Therefore In determining the amount of interest cost to be capitalized, the weighted-average accumulated expenditures are $101,269.5.

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Answer:

8sin²a + cot²a sin²a = 1 is true.

Step-by-step explanation:

Answer:

[tex]x^2+y^2 = 2x - 2y}[/tex]

Third answer option

Step-by-step explanation:

We are given the polar equation as
[tex]r = 2(\sin \theta - \cos \theta)[/tex]
and asked to convert it into rectangular form

We have the following equations which relate (r, θ) in polar form to (x, y) in rectangular form

[tex]\cos \theta=\dfrac{x}{r} \rightarrow x=r \cos\theta\\\\\sin \theta=\dfrac{y}{r} \rightarrow y=r \sin \theta\\\\[/tex]

[tex]r^2=x^2+y^2[/tex]

Original polar equation:
[tex]r = 2(\sin \theta - \cos \theta)[/tex]

Expand the right side:
[tex]r = 2\sin \theta - 2\cos \theta[/tex]

Substitute for sinθ and cosθ in terms of x and y
[tex]r & = 2\left(\dfrac{y}{r} - \dfrac{x}{r}\right)\\[/tex]

Multiply both sides by r:

[tex]r^2 = 2(x - y)\\r^2 = 2x - 2y\\[/tex]

Substitute [tex]r^2=x^2+y^2[/tex] on the left side:
[tex]\boxed{x^2+y^2 = 2x - 2y}[/tex]

This would be the third answer opton

Answer:

Step 1: Distributive Property

Step 2: Distributive Property

Step 3: Commutative Property

Step-by-step explanation:

Step 1: This is distributing the (x + 4y + z) into the (x - 7y), so each term in the prior expression is multiplied by (x - 7y). Hence, Distributive Property.

Step 2: This is doing the same thing but to each individual term. The x in the first term is multiplied by each term in the (x - 7y), the 4y in the second term is multiplied by each term in the (x - 7y), and the same for z. Hence, Distributive Property.

Step 3: This is reordering the variables in the terms. For example, 4yx is changed to 4xy, and that is possible because of the Commutative Property. zx is also reordered into a xz and 7zy into a 7yz.

Feel free to ask any more questions. Hope this helps!!!

Monthly you should deposit approximately $43 to accumulate ​$76,000 in 4 ​years.

Given that,

f = $76,000

r = 4% = 0.04/12 = 0.0033

n = 4×12 = 48

We know that, a = (f×r)/((1+r)ⁿ⁻¹)

a is the annuity.

f is the future amount.

r is the interest rate per time period.

n is the number of time periods.

Here,

a = (76,000 ×0.0033)/((1.0033)⁴⁸⁻¹)

a = 76,000 ×0.0033×0.17132

a = 42.96

a ≈ $43

Therefore, monthly you should deposit approximately $43 to accumulate ​$76,000 in 4 ​years.

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The solution to the system of equations in this problem is given as follows:

(0.6, 2.4).

The system of equations in the context of this problem is defined as follows:

Equaling the two equations, we can obtain the value of x, as follows:

4x = -x + 3

5x = 3

x = 3/5

x = 0.6.

Substituting the value of x into the second equation, we obtain the value of y as follows:

y = -0.6 + 3

y = 2.4.

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The value of f (-1) by virtue of the given absolute value function graph as required is; 8.

It follows from the task content that the value of the function instance; f (-1) is required to be determined.

On this note, the value of the function instance can be determined as the point of intersection of the line; x = -1 with the given graph.

Ultimately, the value of the instance f (-1) is; 8.

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The ratio of the sides of the medium box to the small box is 3:1, the ratio of the area of the bases is 9:1, and the ratio of the volumes is 27:1 and the volume of the medium box is 5832 cubic inches.

Let's denote the side length of the small cube as "s". Since it is a cube, all sides are equal.

Given that the volume of the small box is 216 cubic inches, we can set up the equation;

Volume of small box = s³ = 216

Taking the cube root of both sides, we get;

s = ∛216 = 6 inches

So, the side length of the small cube is 6 inches.

For the medium box, the length, width, and height are all tripled, so the new side length of the medium cube is 3 times the side length of the small cube:

Side length of medium cube = 3s = 3 × 6 = 18 inches

Now, let's calculate the ratio of the sides, area of the bases, and volumes of the small and medium boxes;

Ratio of sides: Side length of medium cube / Side length of small cube = 18 / 6 = 3

Ratio of area of bases: (Side length of medium cube)² / (Side length of small cube)² = (18)² / (6)² = 9

Ratio of volumes: (Volume of medium box) / (Volume of small box) = (Side length of medium cube)³ / (Side length of small cube)³ = (18)³ / (6)³ = 27

So, the ratio of the sides of the medium box to the small box is 3:1, the ratio of the area of the bases is 9:1, and the ratio of the volumes is 27:1.

The volume of the medium box is given by;

Volume of medium box = (Side length of medium cube)³ = 18³

= 5832 cubic inches

Therefore, the volume of the medium box is 5832 cubic inches.

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The area of the triangle with base of 5 ​inches and a height of 10 inches is 25 square inches. The correct answer is C.

The formula for the area of a triangle is A = 1/2 * b * h, where A is the area, b is the base, and h is the height. Using this formula, we can calculate the area of the triangle in question.

Given that the base of the triangle is 5 inches and the height is 10 inches, we can plug these values into the formula and solve for A:

A = 1/2 * b * h

A = 1/2 * 5 * 10

A = 25

Therefore, correct answer is C.

The height of a triangle is the perpendicular distance between the base and the opposite vertex. The base is the side of the triangle on which the height is measured.

By multiplying the base and the height and dividing the result by 2, we can find the area of a triangle. This formula works for all types of triangles, regardless of their size or shape.

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Complete question is:

Find the area of a triangle with base of 5 ​inches and a height of 10 inches.

A 100 square inches

B 50 square inches

C 25 square inches

D 12.5 square inches

The value of area of the figure is,

⇒ 10√10 units²

We have to given that;

To find the area of figure.

Here, We have to find length of AD and AB for area of figure.

Coordinate of A = (- 2, 2)

Coordinate of B = (- 4, -4)

Coordinate of D = (3, 2)

Since, The distance between two points (x₁ , y₁) and (x₂, y₂) is,

⇒ d = √ (x₂ - x₁)² + (y₂ - y₁)²

Hence, Length of AD;

AD = √ (-2 - 3)² + (2 - 2)²

AD = √25

AD = 5

Length of AB;

AB = √ (- 2 + 4)² + (2 + 4)²

AB = √4 + 36

AB = √40

AB = 2√10

Thus, The value of area of the figure is,

⇒ AD x AB

⇒ 5 × 2√10

⇒ 10√10

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Answer:2.71

0.43 are correct

Step-by-step explanation:We can solve this quadratic equation in sin(θ) by using the substitution u = sin(θ):

-u^2 - 2u + 1 = 0

Multiplying both sides by -1, we get:

u^2 + 2u - 1 = 0

We can use the quadratic formula to solve for u:

u = (-b ± sqrt(b^2 - 4ac)) / 2a

where a = 1, b = 2, and c = -1. Substituting these values, we get:

u = (-2 ± sqrt(4 + 4)) / 2

u = (-2 ± 2sqrt(2)) / 2

Therefore, either:

Step-by-step explanation:

5 (4x^8) ^(-1/2)    -   2 x^-3

p ^(1/2)

r ^5/3  

A function of the form y= A sin (Bx-C)+D that has period 8, phase shift -2, and the range -12 ≤y≤-4 is y = 4 sin (π/4 x + π/2) - 8

To write a function of the form y = A sin (Bx - C) + D that has a period of 8 and phase shift of -2, we can use the general formula:

y = A sin [(2π/P)(x - C)] + D

where P is the period, C is the phase shift, and D is the vertical shift. In this case, P = 8 and C = -2, so we have:

y = A sin [(2π/8)(x + 2)] + D

Simplifying the equation, we get:

y = A sin (π/4 x + π/2) + D

To find the amplitude A and vertical shift D that satisfy the range -12 ≤ y ≤ -4, we can use the fact that the sine function oscillates between -1 and 1. If we set A = 4, then the maximum value of y is 4 + D, and the minimum value of y is -4 + D. To ensure that the range is -12 ≤ y ≤ -4, we need to choose D such that:

4 + D ≤ -4 and -4 + D ≥ -12

Solving these inequalities, we get:

-8 ≤ D ≤ 0

Therefore, a function that satisfies the given conditions is:

y = 4 sin (π/4 x + π/2) - 8

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Answer:

Since the disease doubles every 7 days, the number of cases on day 21 will be 2^3 times the number of cases on day 14, which will be 2^2 times the number of cases on day 7, which will be 2^1 times the number of cases on day 1.

Starting with 3 cases on day 1, we can use the formula:

N = 3 * 2^(t/7)

where N is the number of cases after t days.

Plugging in t = 21, we get:

N = 3 * 2^(21/7) = 3 * 2^3 = 24

Therefore, there will be 24 cases by the end of day 21.

Step-by-step explanation:

To draw the graph of y = g(-x), we need to replace x with -x in the original function.

If y = g(x) is given by the following graph:

(see attachment labeled "Attachment1")

Then y = g(-x) can be obtained by reflecting the graph of y = g(x) about the y-axis:

(see attachment labeled "Attachment 2")

Therefore, the graph of y = g(-x) is the reflection of the graph of y = g(x) about the y-axis.

I hope this helps you! Mark brainliest if you can :D

Answer:

Step-by-step explanation:

Answer:

where is the question.

send it so I'll answer it

The area of the following composite figures is 78 square units.

The area of the square is computed as 36 (length x width) or 2(Length).

The area of the triangle is computed as (base x height) ÷ 2.

The areas of the composite figures are added to determine the total area.

Line AD = 6

Line DC = 6

Line AB = 20

Base of the triangle = 14 (20 - 6)

Area of triangle = (h x b) ÷ 2

= (6 x 14) ÷ 2

= 42

Area of square portion = 36 (6 x 6)

Total area = 78 square units

Thus, we can conclude that the area of the composite figures are 78 square units.

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The composite functions are (f · g) (x) = (x + 2)² and (f / g) (x) = 1, whose domains are all real numbers. The value of each function at x = 2 is listed below:

In this problem we must determine and analyze composite functions. Composite functions can be found by combining two simpler functions thanks to operators. There are four operators to make composite functions:

The domain of a function is the set of all possible of x-values.

First, we determine the two composite functions: f(x) = g(x) = x + 2.

Case A:  

(f · g) (x) = (x + 2)²

Case B:

(f / g) (x) = 1

Second, determine the domain for each case:

Case A:

All real numbers.

Case B:

All real numbers.

Third, evaluate each case at x = 2:

Case A:

(f · g) (2) = (2 + 2)² = 4² = 16

Case B:

(f / g) (2) = 1

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Some questions that can be asked on the Expenditures and Consumptions behaviours and attitudes of polytechnic Students in a questionnaire are:

One must carefully consider the purpose of a questionnaire, as well as the information required before starting to design it. Also crucial are factors such as the target audience, number and type of questions (i.e., multiple-choice or open-ended), and its format (e.g., Likert scale).

The way in which questions are organized plays an important role, such that people can easily comprehend them and respond accurately while finishing the survey as fast as needed. Concludingly, logical sequencing of questions should be ensured for the overall design to make sense from beginning to end.

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Answer:

To calculate the height of the large bottle, we can use proportions. We know that the small bottle has a width of 5.5 cm and a height of 10 cm. We also know that the large bottle has a width of 9.9 cm. If we set up a proportion with the widths and heights of the two bottles, we can solve for the height of the large bottle.

5.5 cm / 10 cm = 9.9 cm / h

Multiplying both sides by h, we get:

5.5 cm * h = 10 cm * 9.9 cm

Dividing both sides by 5.5 cm, we get:

h = (10 cm * 9.9 cm) / 5.5 cm

h = 18 cm

Therefore, the height of the large bottle is 18 cm.

Step-by-step explanation:

Few families can survive on a single salary is true statement

Many families rely on dual incomes to make ends meet, especially in areas with high living costs.

However, there are still many families that rely on a single salary to support themselves.

While it may be challenging to make ends meet on a single salary, it is still possible for families to survive and even thrive in these circumstances.

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The area of the given triangle is expressed as: 25.6 in²

We are only given two sides of the triangle and an angle and so we must find the length of the third side to be able to find the area. The length of the third side is gotten from cosine rule to get:

a = √(14.1² + 7.2² - 2(14.1 * 7.2)*cos 30.3)

a = 8.68 in

In order for us to calculate the area of triangle which has 3 sides, we will have to utilize the Heron's Formula.

From the formula, the area of a triangle (A) that has 3 sides a, b, and c is calculated via the formula:

A = √[s(s - a)(s - b)(s - c)]

where:

s denotes the semi-perimeter of the specific triangle given by the formula: s = (a + b + c)/2.

s = (8.68 + 14.1 + 7.2)/2

s = 14.99 in

Thus:

Area = √[14.99(14.99 - 8.68)(14.99 - 14.1)(14.99 - 7.2)]

Area = 25.6 in²

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Since we can't have a fractional number of lines, Citywide can sign up for a maximum of 1 line and still stay within their budget.

Let's start by calculating the total amount Citywide pays for their telephone costs without the federal excise tax. We can do this by subtracting the 3% tax from the total budget:

$190 / 1.03 = $184.47

The $96 budget plan includes 4,000 minutes, which means that each minute costs:

$96 / 4,000 = $0.024

If Citywide wants to stay within their budget, they need to make sure that the total cost of the lines they sign up for plus the federal excise tax is less than or equal to $190.

Let's represent the number of lines Citywide signs up for as "n". The total cost of the lines plus tax can then be represented as:

n * $96 * 1.03

Setting this expression less than or equal to $190, we get:

n * $96 * 1.03 <= $190

Simplifying, we get:

n <= $190 / ($96 * 1.03)

n <= 1.945

Thus, Citywide can sign up for a maximum of 1 line and still stay within their budget.

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Answer:

Step-by-step explanation: mark me brainliest

Using inverse variation, the value of x = -19.2

Inverse variation is when a quantity varies inversely as the other.

Given: y varies inversely with x.

If y=-24 when x =36, what is the value of x when y = 45.

To splve this, we proceed as follows

Since y varies inversely with x, we have that

y ∝ 1/x

y = k/x where k = constant of proportionality

So, making k subject of the formula, we have that

k = yx

Now, If y=-24 when x =36, we have that

k = - 24 × 36

= -864

So, substituting k into y, we have that

y = k/x

= -864/x

So, to find the value of x when y = 45, making x subject of the formula, we have that

x = -864/y

So, substituting y into the equation, we have that

x = -864/y

= -864/45

= -19.2

So, the value of x = -19.2

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Without additional information about the model house, it is impossible to accurately describe the surface that Molly does not need to paint. It could be any surface that will not be visible when the model house is displayed, such as the underside of a roof, the back of a wall, or the bottom of a floor.