2. Solve by Laplace Transforms: y" +5y' - 14y = 0 subject to y(0) = 11 and y'(0) = -5.

An example of two nonlinear functions that don't dominate each other is the sin function (f(x) = sin(x)) and the exponential function (g(x) = e^x).

For any given value of x, the sin function oscillates between -1 and 1, taking on both positive and negative values. It has a periodic nature and does not grow or decay exponentially as x increases or decreases.

On the other hand, the exponential function grows or decays exponentially as x increases or decreases. It is characterized by a constant positive growth rate. The exponential function increases rapidly when x is positive and approaches zero as x approaches negative infinity.

The key characteristic here is that the sine function oscillates while the exponential function grows or decays exponentially.

Due to their fundamentally different natures, neither function dominates the other over their entire domains.

Learn more about nonlinear functions from the given link:

https://brainly.com/question/17604622

Answer:

is this a trick question?  the value of 2+2 = 4

if you are asking what a^2 + b^2  is then ... 1/a^2 + 45a^2 + 61

Step-by-step explanation:

The bases of a pentagonal prism are two identical pentagons. It features five rectangle-shaped faces. The prism has ten vertices and fifteen edges.

A pentagonal prism is a prism with five rectangular sides and two top and bottom pentagonal bases. With 7 faces, 10 vertices, and 15 edges, it is a particular form of heptahedron. A pentagonal prism can have five sides due to its pentagonal bases. The pentagonal prism is also called Five-sided polygon prism in other name.

The pentagonal prism is a prism with five rectangular sides and two pentagonal base

To know more about prism, visit,

https://brainly.com/question/23963432

#SPJ4

Answer:

The bases of a pentagonal prism are two identical pentagons. It features five rectangle-shaped faces. The prism has ten vertices and fifteen edges.

Step-by-step explanation:

hope this helped!

one of the angles measures greater than 90 degrees (110.01 degrees), this is an obtuse triangle.

An obtuse triangle is a triangle that has one angle which measures greater than 90 degrees. In order to determine if a triangle is an obtuse triangle, we need to calculate its angles.

To calculate the angles of the triangle, we can use the following formula:

Angle 1 = arccos ( (b2 + c2 - a2) / 2bc )

Angle 2 = arccos ( (a2 + c2 - b2) / 2ac )

Angle 3 = arccos ( (a2 + b2 - c2) / 2ab )

In this case, a = 6cm, b = 10cm, and c = 13cm. Substituting these values into the formula, we get:

Angle 1 = arccos ( (102 + 132 - 62) / 2 x 10 x 13 ) = 89.99 degrees

Angle 2 = arccos ( (62 + 132 - 102) / 2 x 6 x 13 ) = 110.01 degrees

Angle 3 = arccos ( (62 + 102 - 132) / 2 x 6 x 10 ) = 89.99 degrees

Since one of the angles measures greater than 90 degrees (110.01 degrees), this is an obtuse triangle.

Learn more about angle here

https://brainly.com/question/28451077

#SPJ4

Solving for D & C

---------------------------------

(3c + d) + (-d) = 60 + (-d)

3c + d - d = 60 - d

3c= -d + 60

3c/3 =-d+60/3

c= -d+60/3

--------------------------------------

(3c+d)+(-3c)=60+(-3c)

d = -3c + 60

Answer:

∠ A = 42° , ∠ G = 85°

Step-by-step explanation:

the measure of an inscribed angle is half the measure of its intercepted arc.

(3)

∠ A is an inscribed angle , so

∠ A = \(\frac{1}{2}\) BC = \(\frac{1}{2}\) × 84° = 42°

(4)

∠ G is an inscribed angle but we require arc DF

the sum of the arcs in a circle = 360°

FG + GD + FD = 360°

70° + 120° + FD = 360°

190° + FD = 360° ( subtract 190° from both sides )

FD = 170°

Then

∠ G = \(\frac{1}{2}\) DF = \(\frac{1}{2}\) × 170° = 85°

Answer:

84 squared units.

Step-by-step explanation:

In order to find the surface area of the pyramid, you use the following formula:

\(S=b^2+\frac{1}{2}ps\)           (1)

b: base of the pyramid = 6

p: perimeter of the base = 6*4 = 24

s: slant height

Then, you first calculate the slant height, by using the Pythagoras' theorem:

\(s=\sqrt{(5)^2-(\frac{6}{2})^2}=4\)

Thus, you replace the values of b, p and s in the equation (1):

\(S=(6)^2+\frac{1}{2}(24)(4)=84\)

The surface area of the pyramid is 84 squared units.

Answer:

Step-by-step explanation:

wrong

The coefficient of (3y² + 9)5 is 15.

A polynomial is of the form a₀xⁿ + a₁xⁿ⁻¹ + a₂xⁿ⁻² + ... + aₙ₋₁x + aₙ.

Here, x is the variable, aₙ is the constant term, and a₀, a₁, a₂, ..., and aₙ₋₁, are the coefficients.

a₀ is the leading coefficient.

In the question, we are asked to identify the coefficient of (3y² + 9)5.

First, we expand the given expression:

(3y² + 9)5

= 15y² + 45.

Comparing this to the standard form of a polynomial, a₀xⁿ + a₁xⁿ⁻¹ + a₂xⁿ⁻² + ... + aₙ₋₁x + aₙ, we can say that y is the variable, 15 is the coefficient, and 45 is the constant term.

Thus, the coefficient of (3y² + 9)5 is 15.

Learn more about the coefficients of a polynomial at

https://brainly.com/question/9071229

#SPJ1

Answer:

First we need to write this in proper form:

\(\frac{f(x)}{g(x)} =\frac{x^{2}-6x-7}{x+1} \\Factor f(x)\\\\f(x)=(x-7)(x+1)\\\\\frac{f(x)}{g(x)} =\frac{(x-7)(x+1)}{x+1} \\\\\\X+1 cancels out\\\\\frac{f(x)}{g(x)} =x-7\)

Correct answer is B, f/g(x) = x-7

---------------

#Team Trees #Team Seas #PAW #Spread_Positivity

I hope this helps,

-Oceanbreeze24

The magnitude of the x-component of this vector is 9.05m.

The angle of inclination of the vector is calculated as;

θ = 90 ⁰ - 48.4 ⁰

θ = 41.6 ⁰

The magnitude of the x-component of the vector is calculated as;

Vx = 12.1 m x cos ( 41.6 )

Vx = 9.05 m

A vector can be represented by an ordered set of numbers, called components, that indicate the magnitude and direction of the vector in a particular coordinate system. The components of a vector can be added or subtracted using vector addition and subtraction, and multiplied by a scalar (a real number) using scalar multiplication.

Vectors can be visualized as arrows in a two- or three-dimensional space, where the length of the arrow represents the magnitude of the vector, and the direction of the arrow represents the direction of the vector. Vectors can also be represented as matrices, which can be used to perform various operations on vectors, such as dot product and cross product.

To learn more about Vector visit here:

brainly.com/question/29740341

#SPJ4

Complete Question:-

The missing sides of the special right triangles are listed below:

Case 1: y = √2 · 13, x = 13

Case 2: x = y = 15√2

Case 3: x = 6, y = 3√3

Case 4: x = 17√3, y = 17

Case 5: x = y = 10

Case 6: x = 50, y = 25

Case 7: x = y = 4√7

Case 8: x = 16√3, y = 8√3

Case 9: x = 11√3, y = 33

Case 10: x = 3√2, y = 2√6

Case 11: x = √10, y = 2√5

Case 12: x = 4√7, y = 8√21

Herein we find twelve cases of special right triangles whose missing sides must be determined by using the following rules:

45 - 90 - 45 Right triangle

r = √2 · x = √2 · y

30 - 60 - 90 Right triangle

x = (1 / 2) · r

y = (√3 / 2) · r = √3 · x

Where:

Case 1

y = √2 · 13

x = 13

Case 2

x = y = 15√2

Case 3

x = 3 / (1 / 2)

x = 6

y = 3√3

Case 4

x = 34 · (√3 / 2)

x = 17√3

y = 34 · (1 / 2)

y = 17

Case 5

x = y = 10

Case 6

x = 25√3 / (√3 / 2)

x = 50

y = 25√3 / √3

y = 25

Case 7

x = y = 2√14 · √2 = 2√28 = 4√7

Case 8

x = 24 / (√3 / 2)

x = 48 / √3

x = 16√3

y = 24 / √3

y = 8√3

Case 9

x = 22√3 · (1 / 2)

x = 11√3

y = 22√3 · (√3 / 2)

y = 33

Case 10

x = √18

x = 3√2

y = √6 / (1 / 2)

y = 2√6

Case 11

x = √10

y = √20

y = 2√5

Case 12

x = 4√21 / √3

x = 4√7

y = 4√21 / (1 / 2)

y = 8√21

To learn more on special right triangles: https://brainly.com/question/14373781

#SPJ1

Answer: Plane

Step-by-step explanation: A plane is a flat surface that has no thickness.

Think of a plane as a wall or a floor of a room.

Another important characteristic of a plane is that it has no edges.

So it extends forever in all directions.

Answer:

x = -5

Step-by-step explanation:

4 -2(x+7) = 3(x+5)

Use the distributive property to simplify.

4 - 2x - 14 = 3x + 15

Combine like terms.

-10 - 2x = 3x + 15

Subtract 15 on both times,

-25 - 2x = 3x

Add 2x on both sides.

-25=5x

Divide 5 on both sides.

x=-5

As a result, the quadrilateral's perimeter is 6s, where s is one of its lesser sides' lengths.

The entire distance encircling the perimeter of a two-dimensional shape is known as the perimeter. The lengths of all the shape's edges are added up to determine it. The formula P = 2l + 2w, where P seems to be the perimeter, l is the length, and w seems to be the width of the rectangle, can be used to determine the perimeter of a rectangle, for instance, which is the sum of the distances of all four edges.

given

The perimeter can be expressed as follows if the quadrilateral's corners are designated as A, B, C, and D, where A and D are the ends of the longer sides (because a = 2b):

perimeter: DA, AB, BC, CD, and DA

Because an Equals 2b, AB = CD = 2s.

Because x = y, BC = DA = s.

With these numbers entered into the perimeter formula, we obtain:

circumference is equal to AB + BC + CD + DA = 2 + 2 + 2 + s = 6

As a result, the quadrilateral's perimeter is 6s, where s is one of its lesser sides' lengths.

To know more about perimeter visit:

https://brainly.com/question/6465134

#SPJ1

Answer: SAS stands for side angle side and it means triangles are congruent by having the same side, angle, and side

Explanation: Let's say, two triangles both have the same angle, say 90 degrees. They also share two side lengths. Both triangles have a side length of 9 and another side length of 8.

The two triangles, sharing all these properties, must be congruent. This congruency is proven by SAS.

However, you must not get confused with other ways to prove congruency like ASA (Angle-Side-Angle)

Convenience purchase: Coca-Cola. Shopping purchase: Apple iPhone. Specialty purchase: Rolex. These brand name products correspond to their respective purchase types based on convenience, shopping involvement, and specialty appeal in the consumer marketplace.

Convenience purchases refer to low-involvement purchases made by consumers for everyday items that are readily available and require minimal effort to obtain. These purchases are typically driven by convenience and habit rather than extensive consideration or brand loyalty.

Shopping purchases involve higher involvement and more deliberate decision-making. Consumers invest time and effort in comparing options, seeking the best value or quality, and may consider multiple brands before making a purchase. These purchases often involve durable goods or products that require more consideration.

Specialty purchases are distinct and unique purchases that cater to specific interests, preferences, or hobbies. These purchases are driven by passion, expertise, and a desire for premium or specialized products. Consumers are often willing to invest more in these purchases due to their unique features, quality, or exclusivity.

Three specific brand name products in the consumer marketplace that correspond to these types of purchases are

Convenience Purchase: Coca-Cola (Soft Drink)

Coca-Cola is a widely recognized brand in the beverage industry. It is readily available in various sizes and formats, making it a convenient choice for consumers seeking a refreshing drink on the go.

With its widespread availability and strong brand presence, consumers often make convenience purchases of Coca-Cola without much thought or consideration.

Shopping Purchase: Apple iPhone (Smartphone)

The Apple iPhone is a popular choice for consumers when it comes to shopping purchases. People invest time researching and comparing features, pricing, and user reviews before making a decision.

The shopping process involves considering various smartphone brands and models to ensure they select a product that meets their specific needs and preferences.

Specialty Purchase: Rolex (Luxury Watches)

Rolex is a well-known brand in the luxury watch industry and represents specialty purchases. These watches are associated with high-quality craftsmanship, precision, and exclusivity.

Consumers who are passionate about luxury watches and seek a premium product often consider Rolex due to its reputation, heritage, and unique features. The decision to purchase a Rolex involves a significant investment and is driven by the desire for a prestigious timepiece.

These examples illustrate how different types of purchases align with specific brand name products in the consumer marketplace, ranging from convenience-driven choices to more involved shopping decisions and specialty purchases driven by passion and exclusivity.

To know more about Convenience purchases:

https://brainly.com/question/30247858

#SPJ4

Answer:

-3/5

Step-by-step explanation:

There is a formula that is used to find the gradient of a line.

The numerator consists of the y-values and the denominator consists of the x-values.

The answer when you simplify would be -3/5

Answer:

12y

Step-by-step explanation:

Answer:

Step-by-step explanation:

lim x -> +oo    -2x³ - 13x² + 8x + 52

x³ (-2 -13/x + 8/x² + 52/x³)

+oo³ (-2 - 13/+oo + 8/+oo² + 52/oo³)

+oo(-2 + 0 + 0 + 0)

-oo

lim x -> -oo    -2x³ - 13x² + 8x + 52

x³ (-2 -13/x + 8/x² + 52/x³)

-oo³ (-2 - 13/-oo + 8/-oo² + 52/-oo³)

-oo(-2 + 0 + 0 + 0)

+oo

Answer: John walks a total of 360 yards from school.

Step-by-step explanation:

Let's represent the total distance John walks from school as "x".

According to the problem, John has already walked 15% of the way, which can be written as:

0.15x

We also know that he has walked 54 yards so far, which means:

0.15x = 54

To find the total distance John walks from school, we can solve for "x" by dividing both sides of the equation by 0.15:

x = 54 ÷ 0.15

x = 360

Therefore, John walks a total of 360 yards from school.

To know more about total distance refer here

https://brainly.com/question/6516113#

#SPJ11

Answer:

-209

Step-by-step explanation:

The value of 3 in 6300 is 10 times the value of 3 in 530.

6300 AND 530 are integers. Integers are whole numbers. It is a number without a fraction or decimal component. Integers can either be positive, negative or zero.

The value of each number in 6300:

The value of each number in 530:

3 in 6300 has a value of 100

3 in 530 has a value of 10

100 / 10 = 10

To learn more about integers, please check: https://brainly.com/question/21493341

#SPJ1

The number of cases per batch that should be produced to minimize cost is: 300 units

The number of cases per batch that should be produced to minimize cost can be found by using the Economic Order Quantity.

The Economic Order Quantity (EOQ) is a calculation performed by a business that represents the ideal order size that allows the business to meet demand without overspending. The inventory manager calculates her EOQ to minimize storage costs and excess inventory.  

Thus:

Number of cases per batch = √((2 * Setup costs * annual demand)/ holding costs for the year)

Solving gives:

√((2 * 30 * 15000)/10)

= √90000

= 300 units

Read more about Economic Order Quantity at: https://brainly.com/question/26814787

#SPJ1

Step-by-step explanation:

(4^3)×(5^2)

that is the answer

(2^6)•(5^2) is correct

The probability of P(x < 4) is 0.6922 or approximately 69.22%.

The exponential distribution is often used to model the time between events that occur randomly and independently at a constant rate over time. The probability density function of the exponential distribution with parameter λ is given by f(x) = λe^(-λx) for x ≥ 0.

In this case, X ~ Exp(0.75) means that the parameter λ is 0.75. To find P(x < 4), we need to calculate the area under the curve of the probability density function to the left of 4. This can be done by integrating the function from 0 to 4 as follows

P(x < 4) = ∫₀⁴ λe^(-λx) dx

= [-e^(-λx)]₀⁴

= -e^(-0.75 * 4) + 1

= 0.6922

Therefore, the probability that X is less than 4 is 0.6922 or approximately 69.22%.

To know more about probability here

https://brainly.com/question/31493532

#SPJ4

Answer:

true

Step-by-step explanation:

(a) The probability that the entire system works is  0.3136

(b) The probability that the component a is not working is 0.3

Probability is a scale between 0 and 1 that represents the possibility of an event happening. An event with probability 1 is guaranteed to happen, while an event with probability 0 is impossible. The number of favorable outcomes divided by the total number of potential outcomes in the sample space yields the probability of an event A, commonly denoted as P(A). The sample space, for a fair six-sided die, is the set of all potential outcomes, such as 1, 2, 3, 4, 5, and 6. The probability of rolling a 4 is 1/6. Numerous disciplines employ probability to make predictions, deduce conclusions, and make judgments in the face of uncertainty.

(a) To find the probability that the entire system works, we need to find the product of the probabilities of the individual components working.

For the components connected in series, A and B, the probability that both work is equal to the product of their individual probabilities:

P(A and B) = P(A) * P(B) = 0.7 * 0.8 = 0.56

For the components connected in series-parallel, C, D, and E, the probability that all three work is equal to the product of their individual probabilities:

P(C and D and E) = P(C) * P(D) * P(E) = 0.8 * 0.8 * 0.9 = 0.576

To find the probability of the entire system working, we need to find the product of the probability of A and B working and the probability of C, D, and E working:

P(system works) = P(A and B) * P(C and D and E) = 0.56 * 0.576 = 0.3136

(b) Given that the system works, the probability that component A is not working would be equal to 1 minus the probability that component A is working:

P(A not working | system works) = 1 - P(A working | system works) = 1 - 0.7 = 0.3

To know more about outcomes visit:

brainly.com/question/19916581

#SPJ4

The complete question is