Solve the initial value problem yy' - +ywth y(4) = 3 a To solve this, we should use the substitution ti help (formulas) help (formatas) Enter derivatives using prime notation (0.9. you would enter ytor b. After the substitution from the previous part, we obtain the following linea differential equation in 2, 4, help (equations) c The solution to the original initial value problem is described by the following equation in sy help (equations)

Answer:

The lines t and u are perpendicular.

Step-by-step explanation:

m=(y2-y1)/(x2-x1)

m=(4-11)/(8-3)

m=-7/5

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

m=(y2-y1)/(x2-x1)

m=(9-4)/(8-1)

m=5/7

Perpendicular lines have negative reciprocal slopes.

Answer:

5. c. Every 1 hour

6. c. 4 times

7. b. 3 times

Step-by-step explanation:

The given parameters of the rate of departure of the two vans are;

The rate of departure of Smasher Van bound for Koronadal City = Every 15 minutes

The rate of departure of Nustafa Van= Every 20 minutes

5. The time, 'x', when the two vans leave at the same time is given by the Lowest Common Multiple (LCM) of 15 and 20 as follows;

Multiples of 15 = 15, 30, 45, 60

Multiples of 20 = 20, 40, 60

Therefore, the LCM of 15 and 20 = 60

The time, when the two vans leave at the same time = Every 60 minutes = Every 1 hour

The time, when the two vans leave at the same time = Every 1 hour

6. The number of times the Smasher Van leaves Polomolok so that the two vans leave together is given by the number of multiples 15 minutes in 60 minutes = 60 minutes/(15 minutes) = 4 times

7. The number of times the Nustafa Van leaves Polomolok so that the two vans leave together is given by the number of multiples 20 minutes in 60 minutes = 60 minutes/(20 minutes) = 3 times.

5. c. Every 1 hour

6. c. 4 times

7. b. 3 times  

Let's solve it one by one:

The given parameters of the rate of departure of the two vans are;

The rate of departure of Smasher Van bound for Koronadal City = Every 15 minutes

The rate of departure of Nustafa Van= Every 20 minutes

5. The time, 'x', when the two vans leave at the same time is given by the Least Common Multiple (LCM) of 15 and 20 as follows;

Multiples of 15 = 15, 30, 45, 60

Multiples of 20 = 20, 40, 60

Therefore, the LCM of 15 and 20 = 60

The time, when the two vans leave at the same time = Every 60 minutes = Every 1 hour

The time, when the two vans leave at the same time = Every 1 hour

6. The number of times the Smasher Van leaves Polomolok so that the two vans leave together is given by the number of multiples 15 minutes in 60 minutes = \(\frac{60}{15}=4\text{times}\)

7. The number of times the Nustafa Van leaves Polomolok so that the two vans leave together is given by the number of multiples 20 minutes in 60 minutes = \(\frac{60}{30}=3\text{times}\)

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The length of side of BC is determined as 10.0 m.

option C.

The length of side of BC is calculated from the sum of the length of OB and OC as presented by the diagram.

Congruent triangles are triangles that have the same shape and size, but may be oriented differently or positioned differently in space. In other words, two triangles are considered congruent if their corresponding sides and angles are equal in measure. When two triangles are congruent, they are essentially identical to each other, and they can be superimposed on each other by translations, rotations, and reflections.

if triangle AOB is congruent to triangle BDC, then we can assume the following;

length of side AB = OB = OC = 5 m

BC = 5 m + 5m = 10 m

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Step-by-step explanation:

the reason it's D is because "inelastic" means it doesn't change while the rest of the answers are more dependent on chance, D shows a truck driver doing something consistent and unchanging.

Answer:

-1 < x < 1/3

Step-by-step explanation:

When the graph is decreasing, it means the the graph's slope is negative, or the graph is going towards negative infinity.

We see from the graph that it starts to decrease from -1 to 1/3. Therefore, our answer is -1 < x < 1/3.

Everywhere else on the graph is increasing.

The method that is invoked when an object is created is known as a constructor method.

Constructor in C++ is a special method that is invoked automatically at the time of object creation. It is used to initialize the data members of new objects generally.

The constructor in C++ has the same name as the class or structure. Constructor is invoked at the time of object creation. It constructs the values i.e. provides data for the object which is why it is known as constructors.

Constructor does not have a return value, hence they do not have a return type.

The prototype of Constructors is as follows:

<class-name> (list-of-parameters);

Constructors can be defined inside or outside the class declaration:-

The syntax for defining the constructor within the class:

<class-name> (list-of-parameters) { // constructor definition }

The syntax for defining the constructor outside the class:

<class-name>: :<class-name> (list-of-parameters){ // constructor definition}

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The required probability is 0.4408.

The operating characteristics of the loading gate problem are:

L = λ/ (μ - λ)

W = 1/ (μ - λ)

Lq = λ^2 / μ (μ - λ)

Wq = λ / μ (μ - λ)

ρ = λ / μ

P0 = 1 - λ / μ

Where, L represents the average number of cars either being loaded or waiting.

W represents the average time a car spends either being loaded or waiting.

Lq represents the average number of cars waiting.

Wq represents the average waiting time of a car.

ρ represents the utilization factor.

ρ = λ / μ represents the ratio of time the worker spends loading cars to the total time the system is busy.

P0 represents the probability that the system is empty.

The probability that there will be more than six cars either being loaded or waiting is to be determined. That is,

P (n > 6) = 1 - P (n ≤ 6)

Now, the probability of having less than or equal to six cars in the system at a given time,

P (n ≤ 6) = Σn = 0^6 [λ^n / n! * (μ - λ)^n]

Putting the values of λ and μ, we get,

P (n ≤ 6) = Σn = 0^6 [(6/ 48)^n / n! * (8/ 48)^n]

P (n ≤ 6) = [(6/ 48)^0 / 0! * (8/ 48)^0] + [(6/ 48)^1 / 1! * (8/ 48)^1] + [(6/ 48)^2 / 2! * (8/ 48)^2] + [(6/ 48)^3 / 3! * (8/ 48)^3] + [(6/ 48)^4 / 4! * (8/ 48)^4] + [(6/ 48)^5 / 5! * (8/ 48)^5] + [(6/ 48)^6 / 6! * (8/ 48)^6]P (n ≤ 6) = 0.5592

Now, P (n > 6) = 1 - P (n ≤ 6) = 1 - 0.5592 = 0.4408

Therefore, the required probability is 0.4408.

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Answer:

C,D

Step-by-step explanation:

Answer:

4.02m

Step-by-step explanation:

carry  1   1  

1 . 2 8

+  2 . 7 4

 4 . 0 2

just add the two given numbers

Answer:

3.62 meters

Step-by-step explanation:

Hope this helps!

Answer:

35/12 or 2 11/12

Step-by-step explanation:

1 1/6=7/6

2 1/2=5/2

7*5=35

6*2=12

3*12=36 so 35/12=2 11/12

An ordinal scale provides more information than a nominal scale since values linked with an ordinal variable will be in natural order, whereas values connected with the nominal variable won't.

Ordinal variables as well as nominal variables are the two categories of variables listed here. This sort of variable cannot be submitted to the same forms of statistical tests as interval and ratio variables, hence it is crucial to be able to recognize them accurately. Both of these variables fall within the qualitative category. This contrasts with interval as well as rate variables, both of which are categorized as quantitative.

An illustration of an ordinal variable is a Likert scale with words for mood (such as joyful, neutral, or sad). An illustration of a nominal variable is the names of cities in the Canadian province of Alberta.

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As x approaches 0, the limit of p(x) does not exist.

To determine the limit of p(x) as x approaches 0, we can evaluate the behavior of the function from both sides of x = 0.

If we approach from the left side (negative values of x), the expression cos²2(x)/sin(2x) approaches positive infinity as sin(2x) approaches 0 and cos²(x) remains positive.

However, if we approach from the right side (positive values of x), the expression cos²(x)/sin(2x) approaches negative infinity as sin(2x) approaches 0 and cos²(x) remains positive.

Since the function has different limits from the left and right sides, the limit of p(x) as x approaches 0 does not exist.

Therefore, the statement "As x approaches 0, the limit of p(x) does not exist" accurately describes the behavior of the function.

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Answer:

the answer is x=2

Step-by-step explanation:

4x+2x=9+3

6x=12

x=2

There are 12 identical marbles in a bag, and Suzy is going to select 9 marbles from the bag at random.

The problem asks how many possible outcomes there are.

To begin with, we need to understand the concept of combinations. A combination is a way to select a subset of objects from a larger set, without regard to the order of the objects. For example, if we have four marbles (A, B, C, and D), there are six possible combinations of two marbles: AB, AC, AD, BC, BD, and CD.

In this problem, we have 12 marbles and we are choosing 9 of them. To find the total number of combinations, we can use the formula for combinations:

nCr = n! / r!(n-r)!

where n is the total number of objects, r is the number of objects we are choosing, and ! represents factorial (i.e. multiplying a number by all the positive integers less than it).

So, plugging in our numbers:

12C9 = 12! / 9!(12-9)! = 12! / 9!3! = (121110) / (321) = 220

Therefore, there are 220 possible outcomes if Suzy selects 9 marbles at random from a bag containing 12 identical marbles.

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A measurable part of a line that consists of two points, called endpoints, and all of the points between them are called Line sigments.

Geometry is a branch of mathematics that deals with how objects can be expressed as relationships of points, lines, planes, surfaces, and dimensions. When we draw lines in geometry, we use an arrow at each end to show that it expands infinitely. A line is a path between two points that can be measured. Since line segments have a defined length, they can form the sides of any polygon. The figure below shows the line AB, where the length of the line AB is related to the distance between its endpoints, A and B. The symbol for the line is named after its two endpoints, e.g.

\( \bar{AB}\)

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Answer:

Step-by-step explanation:

X<= 2

Which is x is less than or equal to 2.

Answer:

\(n\leq 2\)

Step-by-step explanation:

The answer is (B) 1/e.

To find the absolute maximum value of f(x) = ln(x)/x, we need to find the critical points and endpoints of the function and then evaluate f(x) at these points to determine the maximum value.

First, we find the derivative of f(x):

f'(x) = (1/\(x^2\)) * (xln(x) - 1)

Setting f'(x) = 0, we get:

xln(x) - 1 = 0

Solving for x, we get:

x = 1/e

Since f(x) is only defined for x > 0, the only critical point is x = 1/e.

Next, we evaluate f(x) at the critical point and at the endpoints of the domain of the function:

f(1/e) = ln(1/e)/(1/e) = -1/e

f(0+) = lim(x→0+) ln(x)/x = lim(x→0+) (1/x) / 1 = ∞

f(∞) = lim(x→∞) ln(x)/x = lim(x→∞) (1/x) / (1/x) = 1

Since f(x) approaches infinity as x approaches 0+, and f(x) approaches 1 as x approaches infinity, the absolute maximum value of f(x) occurs at x = 1/e, and the maximum value is f(1/e) = -1/e.

Therefore, the answer is (B) 1/e.

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The amount of feet of border that she needs to purchase is given as follows:

20 feet.

The perimeter of a square of side length s is given by the multiplication of four and the side length s, as follows:

P = 4s.

All the sides measure 5 feet, hence the parameter s is given as follows:

s = 5.

Then the perimeter of the square plot is given as follows:

P = 4 x 5

P = 20 feet.

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Answer:

Irrational

Step-by-step explanation:

Answer:

Rational

Step-by-step explanation:

The number 35 is a rational number if 35 can be expressed as a ratio, as in RATIOnal. A quotient is the result you get when you divide one number by another number. For 35 to be a rational number, the quotient of two integers must equal 35

Answer:

area= x^2+8x+7

Step-by-step explanation:

a=l*w

l=x+7

w=x+1

a=(x+7)(x+1)

a= x^2+8x+7

Answer:

b = -2.7

Step-by-step explanation:

Isolate the variable, b

-5 = b - 2.3

add 2.3 to both sides (to isolate variable b)

-5 + 2.3 = b - 2.3 + 2.3

-2.7 = b + 0

-2.7 = b

Check work:

-5 = -2.7 - 2.3

-5 = -5

Correct

Among the provided answer options, the closest value to -0.555 is -0.55, which is option c. Therefore, option c (-0.55) is the value of c that satisfies P(Z ? c) = 0.71.

The notation P(Z ? c) represents the probability that a standard normal random variable Z is less than or equal to c. To find the value of c that corresponds to P(Z ? c) = 0.71, we need to determine the Z-score associated with this probability.

Using a standard normal distribution table or a calculator, we can find that a Z-score of approximately 0.555 corresponds to a cumulative probability of 0.71. However, since we are looking for the value of c in P(Z ? c), we need to consider the opposite inequality.

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The formula for the function g is g(x) = x^2 - 9x + 9.

To find a formula for the function g, we can analyze the given equation. The equation g(x) = x^2 - 9x + 9 represents a quadratic function.

The general form of a quadratic function is f(x) = ax^2 + bx + c, where a, b, and c are constants.

Comparing the given equation to the general form, we can determine the values of a, b, and c.

From the given equation, we have a = 1, b = -9, and c = 9. Therefore, the formula for the function g is:

g(x) = x^2 - 9x + 9

So, the formula for the function g is g(x) = x^2 - 9x + 9.

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Question-

The graphs of ( f ) and ( g ) are given. Find a formula for the function ( g )

Answer:

f(x) = 24/6x relates to

Step-by-step explanation:

graph of the parent functions

Answer:

The graph of g(x) is stretched vertically by a factor of 5/3

Step-by-step explanation:

Answer:

your answer should be a

Step-by-step explanation:

Answer:

c

Step-by-step explanation:

To find h'(2), we need to use the chain rule. Let's consider each option:

for option (a), h(x) = 5f(x) − 2g(x)
Using the product rule, we have:
                  h'(x) = 5f'(x) - 2g'(x)

Therefore, at x=2:
h'(2) = 5f'(2) - 2g'(2) = 5(-1) - 2(5) = -15

for option (b), h(x) = f(x)g(x)
Using the product rule again, we have:
                h'(x) = f'(x)g(x) + f(x)g'(x)

Therefore, at x=2:
h'(2) = f'(2)g(2) + f(2)g'(2) = (-1)(3) + (-4)(5) = -23

for option (c), h(x) = f(x)/g(x)
Using the quotient rule, we have:
h'(x) = [f'(x)g(x) - f(x)g'(x)] / [g(x)]^2

Therefore, at x=2:
h'(2) = [f'(2)g(2) - f(2)g'(2)] / [g(2)]^2 = [(-1)(3) - (-4)(5)] / 3^2 = 23/9

for option (d), h(x) = g(x)/ (1+f(x))
Using the quotient rule again, we have:
h'(x) = [(1+f(x))g'(x) - g(x)f'(x)] / [(1+f(x))^2]

Therefore, at x=2:
h'(2) = [(1+f(2))g'(2) - g(2)f'(2)] / [(1+f(2))^2] = [(1-4)(5) - 3(-1)] / (1-4)^2 = -8/9

Therefore, the answer is (d) h(x) = g(x)/ (1+f(x)) and h'(2) = -8/9.

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The product M' × M results in the identity matrix, which confirms that we have found the correct inverse matrix M'.

To find M', we need to compute the inverse of M. To do this, we can use the formula for the inverse of a 2x2 matrix:

M^-1 = 1/((3*5) - (2*7)) * [5 -2; -7 3]

Simplifying, we get:

M^-1 = 1/-1 * [5 -2; -7 3]

M^-1 = [-5 2; 7 -3]

Now, to verify that \(M' = M^-1\), we need to compute M' × M and see if we get the identity matrix:

M' × M = [-5 2; 7 -3] × [3 2; 7 5]

M' × M = [(-5*3) + (2*7) (-5*2) + (2*5); (7*3) + (-3*7) (7*2) + (-3*5)]

M' × M = [-1 0; 0 -1]

Since we got the identity matrix, we know that M' = M^-1, which means that we have correctly found the inverse of the encoding matrix.
Hi there! To help you with your question, we need to find the inverse matrix (M') of the given encoding matrix M and verify by computing the product M' × M.

The given matrix M is:
[ 3 2 ]
[ 7 5 ]

To find the inverse matrix M', we first calculate the determinant of M:
det(M) = (3 × 5) - (2 × 7) = 15 - 14 = 1

Since the determinant is non-zero, M' exists. Now, let's find M':
M' = (1/det(M)) × adjoint(M)

Adjoint of M is obtained by swapping the diagonal elements and changing the sign of the off-diagonal elements:
adjoint(M) = [ 5 -2 ]
                    [ -7  3 ]

Now, let's find M':
M' = (1/1) × [ 5 -2 ]
                  [ -7  3 ]
M' = [ 5 -2 ]
      [ -7  3 ]

Finally, let's verify by computing the product M' × M:
[ 5 -2 ] × [ 3 2 ] = [ (5×3) + (-2×7)   (5×2) + (-2×5) ]
[ -7  3 ]   [ 7 5 ]   [ (-7×3) + (3×7)   (-7×2) + (3×5) ]

= [ 1  0 ]
  [ 0  1 ]

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