The sum of a number and its reciprocal is 5/2 Find the number and its reciprocal.

The solution of the system, x' y = t 16x y' = 0 x(0) = 1, y(0) = 3 using laplace transform is

Y(s) = [16 ± sqrt(192s^4 + 256)] / 32

To solve the given system using Laplace transforms, we'll apply the Laplace transform to each equation separately.

1. Taking the Laplace transform of the first equation:
L(x' y) = L(t)
sX(s) - x(0) * y(0) + Y(s) = 1/s^2

2. Taking the Laplace transform of the second equation:
L(16x y') = L(0)
16X(s) * sY(s) - y(0) = 0

Now, we'll substitute the initial conditions into the Laplace transforms:

1. Substituting x(0) = 1 and y(0) = 3 into the first equation:
sX(s) - 1 * 3 + Y(s) = 1/s^2
sX(s) + Y(s) = 1/s^2 + 3

2. Substituting y(0) = 3 into the second equation:
16X(s) * sY(s) - 3 = 0
16X(s) * sY(s) = 3

Now, we'll solve for X(s) and Y(s):

From equation (2), we have:
16X(s) * sY(s) = 3
X(s) = 3 / (16sY(s))

Substituting this into equation (1), we get:
s * (3 / (16sY(s))) + Y(s) = 1/s^2 + 3
3 / (16Y(s)) + Y(s) = 1/s^2 + 3
(3 + 16Y^2(s)) / (16Y(s)) = 1/s^2 + 3
3 + 16Y^2(s) = (16Y(s)) / s^2 + 3s^2
16Y^2(s) - (16Y(s)) / s^2 = 3s^2

Now, we'll solve for Y(s) using quadratic equation:
16Y^2(s) - (16Y(s)) / s^2 - 3s^2 = 0
Multiplying through by s^2:
16Y^2(s) - 16Y(s) - 3s^4 = 0

Using quadratic formula:
Y(s) = [16 ± sqrt((16)^2 - 4 * 16 * (-3s^4))] / (2 * 16)
Y(s) = [16 ± sqrt(256 + 192s^4)] / 32
Y(s) = [16 ± sqrt(192s^4 + 256)] / 32

Therefore, the solution for the Laplace transform of the given system is:
Y(s) = [16 ± sqrt(192s^4 + 256)] / 32

To know more about Laplace transform refer here:

https://brainly.com/question/31689149

#SPJ11

The probability of rolling a five on the first die and a one on the second die is 1/36.

Probability is a measure of the likelihood of an event occurring. It is expressed as a number between 0 and 1, with 0 indicating that the event will not occur and 1 indicating that the event will definitely occur.

There is a 1/6 probability of rolling a 5 on the first die and a 1/6 probability of rolling a 1 on the second die.

The probability of both events occurring is the product of the probabilities of each event.

1/6 × 1/6 = 1/36

Hence, the probability of rolling a 5 on the first die and a 1 on the second die is 1/36. This means there is a 1 in 36 chance of rolling a 5 on the first die and a 1 on the second die if you roll two dice.

Learn more about probability here: https://brainly.com/question/24756209

#SPJ4

Edmond average then was 174.12 , by using the given percentage.

What do you mean by percentage?

A  ratio that may be stated as a fraction of 100 is a percentage. If we need to calculate a percentage of a number, we should divide it by its entirety and then multiply it by 100. The proportion therefore refers to a component per hundred. Per 100 is what the word percent means. The letter "%" stands for it.

It is given that Edmond rushed for an average of 148 yards per game this season.

Let the average of Edmond last year be x

According to question, 148 yards per game is 85% of x

85% of x = 148

85/100 × x = 148

x = 148 ÷ (85/100) = 148 × (100/85) = 14800/85 = 174.12

Thereofore, Edmond average then was 174.12

To learn more about the percentage from the given link.

https://brainly.com/question/24877689

#SPJ1

1) Since R is reflexive, symmetric, and transitive, it is an equivalence relation. 2) here are a total of 8 distinct equivalence classes, which correspond to the 8 possible truth tables for statement forms in three variables.

To prove that the relation R is an equivalence relation, we need to show that it is reflexive, symmetric, and transitive.

1) Reflexive: To show that R is reflexive, we need to prove that every statement form in A has the same truth table as itself. This is true because every statement form is logically equivalent to itself. Therefore, P R P for all P in A.

2) Symmetric: To show that R is symmetric, we need to prove that if P R Q, then Q R P. This is true because if P and Q have the same truth table, then Q and P must also have the same truth table. Therefore, if P R Q, then Q R P for all P and Q in A.

3) Transitive: To show that R is transitive, we need to prove that if P R Q and Q R S, then P R S. This is true because if P and Q have the same truth table and Q and S have the same truth table, then P and S must also have the same truth table. Therefore, if P R Q and Q R S, then P R S for all P, Q, and S in A.

Since R is reflexive, symmetric, and transitive, it is an equivalence relation.

2) The distinct equivalence classes of R are sets of statement forms that have the same truth table. For example, one equivalence class contains all statement forms that are logically equivalent to p ∧ q ∧ r. Another equivalence class contains all statement forms that are logically equivalent to p ∨ q ∨ r. There are a total of 8 distinct equivalence classes, which correspond to the 8 possible truth tables for statement forms in three variables.

Learn more about equivalence relation here:

https://brainly.com/question/14307463

#SPJ11

You have a bag of 10 marbles. Three of them are red, five are blue, and two are green. The probability of randomly picking a green or blue marble out of the bag is 7/10, 0.7 or 70%.

Given that,

there is a bag containing 10 marbles, out of which 3 are red, 5 are blue and 2 are green, and

we are supposed to find the probability of picking a green or blue marble out of the bag.

Probability is defined as the likelihood of an event occurring out of all the possible outcomes.

It is represented in the form of a fraction, decimal or percentage.

So, in order to find the probability of picking a green or blue marble out of the bag, we need to first find the total number of marbles in the bag, then the number of marbles that are green or blue, and then divide the number of green or blue marbles by the total number of marbles.

Let us calculate the probability of picking a green or blue marble from the bag.

Total number of marbles in the bag = 10

Number of green or blue marbles in the bag

= 5 + 2 = 7

Now,

the probability of picking a green or blue marble out of the bag

= Number of green or blue marbles in the bag / Total number of marbles in the bag= 7 / 10

The probability of picking a green or blue marble out of the bag is 7/10.

This can also be expressed as a decimal value of 0.7 or as a percentage of 70%.

For similar question on probability

https://brainly.com/question/24756209

#SPJ11

Answer:

x = -11/9

Step-by-step explanation:

3(x-4) + 1 = 12x

Step 1: Use distributive property

3*x - 3*4 + 1 = 12x

3x - 12 + 1 = 12x

Step 2: Combine like terms

3x - 11 = 12x

Step 3: Subtract '3x' from both sides

-11 = 12x - 3x

-11 = 9x

Step 4: Divide both sides by 9

-11/9 = x

Answer:

Solve the first part in Parenthese

Step-by-step explanation:

3(X-4)

3x-12+1=12x

         -1   -1

3x-11-12=12x

        -12 -12

3x-11=0x

    -11  -11

3x= -11x

/3      /3

x= -11/9

Answer:

20

Step-by-step explanation:

The small-angle approximation sin(θ) ≈ θ has a 10% error when the value of θ (in radians) is approximately 0.1745 radians or 10 degrees.

The small-angle approximation sin(θ) ≈ θ is commonly used when the angle θ is small, typically measured in radians. To determine the point at which this approximation has a 10% error, we need to find the value of θ that satisfies the condition sin(θ) = 0.1θ.

To solve this equation, we can use numerical methods or approximation techniques. One straightforward approach is to plot the graphs of sin(θ) and 0.1θ and find their intersection point. Alternatively, we can use a calculator or mathematical software to find the value of θ that satisfies the equation.

By performing these calculations, we find that the value of θ at which the small-angle approximation has a 10% error is approximately 0.1745 radians or approximately 10 degrees. Beyond this point, the error between sin(θ) and θ becomes larger and the small-angle approximation is no longer accurate within the 10% error margin.

Learn more about radians here:

https://brainly.com/question/30472288

#SPJ11

Answer:

35

Step-by-step explanation:

Here is the full steps:

Distribute

-7(x+10)=7(5-x)

-7x-70=7(5-x)

Distribute

-7x-70 = 35-7x            → Answer for the attachment "35"

Add 70  to both sides of the equation

-7x-70+70=-7x+35+70

Simplify

-7x=-7x+105

Add 7x  to both sides of the equation

-7x+7x=-7x+105+7x

0 = 105

[RevyBreeze]

__________________________________________________________
Hello! In this question, we will be plugging in values to fit the simplification process of the expression.
__________________________________________________________

Explanation:

We were given the expression: -7(x + 10) = 7(5 - x)

In order to simplify the expression, we would use the distributive property.

Solve:

-7(x + 10) = 7(5 - x)

Distribute the "7" to the terms inside the parenthesis (x + 10).

-7x + (-70) = 7(5 - x)

Distribute the other "7" to the terms inside the parenthesis (5 - x).

7x + (-70) = 35 - 7x

Since we are only looking for the values in the simplification process, the answer for the first box would be -70 and the second box would be 35.
__________________________________________________________
Answer:
1. -70

2. 35

__________________________________________________________

The total area of the rectangles are:

a. Area = 15a

b. Area = 2x

c. Area = 3r

d. Area = 24p

e. Area = 14m

f. Area = 15x + 40

Th area of a rectangle is given by the formula: length × width

a. width = 3

Length = 5 + a = 5a

Area = 5a × 3 = 15a

b. width = 1/3

length = 6x

Area = 6x × 1/3 = 2x

c. width = r

length = 3

Area = 3 × r = 3r

d. width = 6

length = 4p

Area = 4p × 6 = 24p

e. width = m

length = 6 + 8 = 14

Area = 14 × m = 14m

f. width = 5

length = 3x + 8

Area = (3x + 8)5 = 15x + 40

Learn more about area of rectangle on:

https://brainly.com/question/25292087

Answer:

36.656

Step-by-step explanation:

Calculate using trigonometry, Calculator may be required

Ok, so it's actually pretty easy

First of all, we know that all triangles' angles add up to 180 degrees

Here we can tell that we have one 90 degree angle and another 45 degree angle

Now, we can subtract both of these angles to then finalize that, the missing angle is equal to 45 degrees

Hope this helps :)

Step-by-step explanation:

See below

Answer:

\( \frac{5}{n + 3} \)

Step-by-step explanation:

\(1. \: 5 \times \frac{1}{n + 3} \\ 2. \: \frac{5}{n + 3} \)

Each time X increases, there is a perfectly predictable increase in Y  is indicated by a Pearson correlation of r= +1.00 between X and Y

A Pearson correlation coefficient of +1.00 indicates a perfect positive linear relationship between the variables X and Y. It means that as X increases, Y increases in a perfectly predictable manner. The correlation coefficient of +1.00 indicates a strong and direct relationship between the two variables, where the values of Y can be precisely determined based on the values of X.

Know more about Pearson correlation here:

https://brainly.com/question/30916205

#SPJ11

The value of DF = 20.

Two objects are similar if they have the same shape, or one has the same shape as the mirror image of the other.

Given:

Using theorem

If two triangles are similar, then the ratio of the area of both triangles is proportional to the square of the ratio of their corresponding sides.

ΔSDF/Δ RTY = (SD/RT)= (DF/TY)=  (FS/ YR)

ar ΔSDF² / ar  ΔRTY² = 16/81

SD/ RT = 4/9

SD = 4x,  RT= 9x

SD= 8

4x = 8

x = 2

So,

RT=  9*2 = 18

SF = RT -2

SF = 16

(SD/RT)= (FS/ YR)

8 / 18 = 16/ YR

YR= 36

TY= 9 +RY = 45

(DF/TY)=  (FS/ YR)

DF / 45= 16/ 36

DF=20

Learn more about similarity here:

brainly.com/question/25882965

#SPJ1

Answer:

a. Letting m represent the number of additional miles driven, we have .35m.

b. Devon paid $43 for additional mileage.

Step-by-step explanation:

For part b: $421 - ($54 × 7)

= $421 - $378 = $43

The algebraic expression to represent the amount Devon paid for additional mileage only is 0.35m and Devon pays for additional mileage if he paid a total of $421 for the rental car is $43.

It is defined as the relation between two variables, if we plot the graph of the linear equation we will get a straight line.

If in the linear equation, one variable is present, then the equation is known as the linear equation in one variable.

It is given that:

During a long weekend, Devon paid a total of x dollars for a rental car so he could visit his family. He rented the car for 7 days at a rate of $54 per day.

For part (a):

Write an algebraic expression to represent the amount Devon paid for additional mileage only.

The amount Devon paid for additional mileage only = 0.35m

For part (b):

Devon pays for additional mileage if he paid a total of $421 for the car rental is:

= $421 - ($54 × 7)

= $43

Thus, the algebraic expression to represent the amount Devon paid for additional mileage only is 0.35m and Devon pays for additional mileage if he paid a total of $421 for the rental car is $43.

Learn more about the linear equation here:

brainly.com/question/11897796

#SPJ2

Answer:

  72 square units

Step-by-step explanation:

The area is given by the formula ...

  A = 1/2ab·sin(C)

  A = 1/2(12)(24)sin(30°) = 1/2(12)(24)(1/2) = 72 . . . square units

Here's the LaTeX representation of the given explanation:

To determine the values of \(\( p \)\) for which the series converges, we can use the alternating series test and the integral test.

First, let's apply the alternating series test. For the series \(\( \sum(-1)^{n-1} \cdot 6n(\ln(n))^p \)\) , we need to check the conditions:

1. The sequence \(\( \{6n(\ln(n))^p\} \)\) is decreasing.

2. The limit of the terms as \(\( n \)\) approaches infinity is zero.

For the first condition, let's consider the ratio of consecutive terms:

\(\( a_n = 6n(\ln(n))^p \)\( a_{n+1} = 6(n+1)(\ln(n+1))^p \)\)

We can calculate the ratio:

\(\( \frac{a_{n+1}}{a_n} = \frac{6(n+1)(\ln(n+1))^p}{6n(\ln(n))^p} \)\( = (n+1) \left(\frac{\ln(n+1)}{\ln(n)}\right)^p \)\)

Now, if \(\( p > 0 \), \( \frac{\ln(n+1)}{\ln(n)} > 1 \) for all \( n \)\) , and the ratio is greater than 1 for all \(\( n \).\) Therefore, the series does not satisfy the condition of a decreasing sequence for \(\( p > 0 \).\)

Next, let's apply the integral test. We need to check if the integral of the absolute value of the series converges. Consider the integral:

\(\( \int_{2}^{\infty} |(-1)^{n-1} \cdot 6n(\ln(n))^p| \, dn \)\)

Let's split the integral into two parts based on the sign of the series:

\(\( \int_{2}^{\infty} 6n(\ln(n))^p \, dn - \int_{2}^{\infty} 6n(\ln(n))^p \, dn \)\)

We can evaluate the first integral as follows:

\(\( \int_{2}^{\infty} 6n(\ln(n))^p \, dn = 6\int_{2}^{\infty} n(\ln(n))^p \, dn \)\)

Now, for \(\( p > -1 \)\) , we can use the integral test to determine the convergence of the series by evaluating the integral. If the integral converges, the series also converges.

However, for \(\( p \leq -1 \)\) , the integral \(\( \int 6n(\ln(n))^p \, dn \)\) diverges.

Therefore, the series converges for \(\( p > -1 \)\) and diverges for \(\( p \leq -1 \)\).

In interval notation, the values of \(\( p \)\) for which the series converges are given by \(\( (-1, \infty) \).\)

To know more about converges visit-

brainly.com/question/32579520

#SPJ11

Answer:

7/8

Step-by-step explanation:

turn 1/4 denominator into 8 and by doing that, u multiply by 2.

whatever you do to the bottom, u do to the top. so 1/4= 2/8

5/8+2/8= 7/8

5/8  +  1/4 = 37/20

37/20=1 y 17/20

Respuesta:

A.) BA = 12 m

Explicación paso a paso:

Usando triángulos similares:

BA / AC = DE / EC

BA = x; AC = 20; DE = 3; EC = 5

POR ESO ; TENEMOS :

x / 20 = 3/5

Multiplicar en cruz:

5 * x = 20 * 3

5 veces = 60

5x / 5 = 60/5

x = 12

The midpoint has coordinates (19,19) as per the midpoint formula.

The statement is false.

The statement is false. The midpoint of the segment joining two points is determined by taking the average of their x-coordinates and the average of their y-coordinates. In this case, the two given points are (0,0) and (38,38).

To find the x-coordinate of the midpoint, we take the average of the x-coordinates of the two points:

(x1 + x2) / 2

= (0 + 38) / 2

= 38 / 2

= 19

Therefore, the x-coordinate of the midpoint is 19, which matches the statement. However, to determine if the statement is true or false, we also need to check the y-coordinate.

To find the y-coordinate of the midpoint, we take the average of the y-coordinates of the two points:

(y1 + y2) / 2

= (0 + 38) / 2

= 38 / 2

= 19

The y-coordinate of the midpoint is also 19. Therefore, the coordinates of the midpoint are (19,19), not 19 as stated in the statement. Since the midpoint has coordinates (19,19), the statement is false.

To learn more about the midpoint;

https://brainly.com/question/28224145

#SPJ4

Orange is a reflection of green because they have the same points. The difference is one has all positive and the other has one negative.

Not actual points just an example:

Orange (5,5), (5,5), (5,5)

Green (-5,5), (-5,5), (-5,5)

They are the same shape but Orange is a reflection of green

The degree of the polynomial is 8, which is the highest exponent of the variable x.

The leading coefficient is -1.

To find the maximum number of real zeros, we can use Descartes' rule of signs. First, we count the number of sign changes in the coefficients of the polynomial.

- from -1x⁸ to -3x⁷ (change from negative to negative)

- from -3x⁷ to +3x⁵ (change from negative to positive)

- from +3x⁵ to -4 (change from positive to negative)

Therefore, there are either 3 or 1 positive real zeros.

Next, we count the number of sign changes in the coefficients of f(-x), which is the polynomial with its terms reversed in order.

- from -1(-x)⁸ to -3(-x)⁷ (change from negative to negative)

- from -3(-x)⁷ to +3(-x)⁵ (change from negative to positive)

Therefore, there are either 2 or 0 negative real zeros.

Since the number of positive real zeros is either 3 or 1, and the number of negative real zeros is either 2 or 0, the maximum number of real zeros is 3.

To learn more about polynomial visit:

https://brainly.com/question/11536910

#SPJ4

The total area of the kite is : 40 x 108

A kite is a quadrilateral with four sides and four angles.

Two sides of the quadrilateral are equal.

Analysis:

Area of 2 top triangles with 40cm base and 33 cm height = 1/2bh + 1/2bh

= bh

where b = base = 40cm  h = height = 33cm

Area of 2 top triangles = 40cm x 33cm

Area of two bottom triangles with 40cm base and 75cm height

= 40cm x 75cm

= 40cm x 75cm + 40cm x 33cm

= 40cm( 75 + 33) = 40 x 108

in conclusion, the area of the kite is 40 x 108.

Learn more about kite : brainly.com/question/23279609

#SPJ4

Answer:

(40)(108) & (40)(33)+(40)(75)

Option 1 & 3

Correct Answer 100%. Pls, give me brainliest. Thank You.

Answer:

5 percent of 120,000 is 6,000 than 6,000*25 the years is going to be 150,000 than add that with 120,000 you get 270,000

Answer:

\(\frac{2}{5}\)

Step-by-step explanation:

the rate of change is calculated as\(\frac{y_{2}-y_{1} }{x_{2}-x_{1} }\)

where (x₁, y₁ ) and (x₂, y₂ ) are any 2 ordered pairs from the table

using (x₁, y₁ ) = (20, 16 ) and (x₂, y₂ ) = (10, 12 ) , then

rate of change = \(\frac{12-16}{10-20}\) = \(\frac{-4}{-10}\) = \(\frac{4}{10}\) = \(\frac{2}{5}\)

The relationship has a constant of proportionality of 37

From the graph, we have the following points

x = 1 and y = 37

These points can be represented:

x = 1

y = 37

The above parameters can be represented as the following points

(x, y) = (1, 37)

The constant of proportionality of the points is then calculated as

k = y/x

Substitute the known values in the above equation

So, we have the following equation

k = 37/1

Evaluate the quotient

So, we have

k = 37

Hence, the constant of proportionality is 37

Read more about constant of proportionality at

brainly.com/question/28413384

#SPJ1

Answer:

15-(2×X)

Step-by-step explanation:

hope this is what you need

Answer:

Step-by-step explanation:

i can't see the expressions, but your answer will be 2x-15