Let cos(2x) - cos(x) = 0 where 0° < x <180° what are the possible values of x

The dimensions of the garden that minimize the cost is 3.83 and 5.74.

Lets assume the garden has length L and width W and one Length has the brick wall.

L*W = 22 (area constraint)

C = 40 * L + 20 * L + 20 * W + 20 * W

= 60 * L + 40 * W

We need the equation in terms of just one variable, lets use L. We can use the area constraint to do this

W = 22/L (plug this into the C equation)

C(L) = 60*L + 40*(22/L)

= 60*L + 880/L

C(L) = 60*L + 880/L

now take the derivative and get

C'(L) = 60 - 880/L^2

now set that derivative = 0 to find the key L value where the min/max occurs (min in this case)

0 = 60 - 880/L^2

Solve for L,

L = ± (2 sqrt(11/3))

We only need the positive answer as negative length makes no sense here,

L = 3.83 (approximate)

We can now solve for W as well

W = 22/3.83 = 5.74

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The inverse Laplace transform of F(s) is given by f(t) = \(-1/2t^3 - 1/4t^2.\)

To find the inverse Laplace transform of F(s) = \((s^2 + 2s - 8) / (4s),\) we can use the properties and known Laplace transforms. Let's break it down step by step:

1. Rewrite the function:

  F(s) = \((s^2 + 2s - 8) / (4s)\)

       = \((s^2 + 2s - 8) / (4s^2)\)

2. Factorize the numerator:

  F(s) = [(s + 4)(s - 2)] /\((4s^2)\)

3. Split the fraction:

  F(s) = (s + 4) / \((4s^2)\) - 2 / (\(4s^2\))

4. Apply the Laplace transform property for derivative and constant multiplication:

  L{t^n f(t)} =\((-1)^n F^(n)(s),\) where F^(n)(s) denotes the nth derivative of F(s) with respect to s.

  L{(\(t^0\)f(t))'} = -F(s)

  Applying this property to each term, we get:

\(-1/4 * L{(t^0)' / s^2} = -1/4 * (-1) * d/ds[1/s^2]\)

                        \(= 1/4 * d/ds[1/s^2]\)

                        \(= 1/4 * d/ds[s^(-2)]\)

                         \(= 1/4 * (-2s^(-3))\)

                         = -1/2\(s^3\)

  -1/4 * L{(\(t^0\))' / s} = -1/4 * (-1) * d/ds[1/s]

                       = 1/4 * d/ds[1/s]

                       = 1/4 * d/ds\([s^(-1)]\)

                       = 1/4 * \((-1s^(-2))\)

                       = \(-1/4s^2\)

  Therefore, the inverse Laplace transform of F(s) is:

  f(t) = -\(1/2t^3 - 1/4t^2\)

Hence, the inverse Laplace transform of F(s) is given by f(t) = -\(1/2t^3 - 1/4t^2.\)

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The theory behind Euler's equation and the boundary conditions for a column with one fixed end and the other end free. Therefore, the answer to the question is d) 1/2, as x = π/2L = (2(1) - 1)π/2L = (2n - 1)π/2L when n = 1/2.

Euler's equation is derived from the Euler-Bernoulli beam theory, which states that a slender column under axial compression will buckle when the compressive stress exceeds a certain critical value. The buckling load is given by the equation P= xt^2π^2Et, where P is the buckling load, x is a dimensionless factor called the slenderness ratio (the ratio of the column length to its cross-sectional dimensions), t is the thickness of the column wall, E is the modulus of elasticity of the column material, and π is the mathematical constant pi.

For a column with both ends pinned, the value of x is given by x = nπ/L, where n is an integer and L is the length of the column. For a column with one end fixed and the other end free, the value of x is given by x = (2n - 1)π/2L, where n is an integer.  In this case, we have a column with one fixed end and the other end free, so we need to use the equation x = (2n - 1)π/2L to find the value of x. Since n can be any integer, we can choose n = 1 to simplify the equation and get x = π/2L.

Substituting this value of x into Euler's equation, we get P = (π/2L)²π²Et = π²Et/4L². This means that the buckling load for a column with one fixed end and the other end free is proportional to the modulus of elasticity and inversely proportional to the square of the length of the column.

Therefore, the answer to the question is d) 1/2, as x = π/2L = (2(1) - 1)π/2L = (2n - 1)π/2L when n = 1/2

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Answer:

4080.01

Step-by-step explanation:

V = 6 A2/3/36 square rooted = 6 × 1532 2/3/36 square rooted = 4080.01042

Therefore, the compound interest of the annuity due of BD 400 paid each 4 months for 6.2 years at a nominal rate of 3% per annum is BD 40,652.17.

Compound interest of an annuity due can be calculated using the formula:A = R * [(1 + i)ⁿ - 1] / i * (1 + i)

whereA = future value of the annuity dueR = regular paymenti = interest raten = number of payments First, we need to calculate the effective rate of interest per period since the nominal rate is given per annum. The effective rate of interest per period is calculated as

:(1 + i/n)^n - 1 = 3/1003/100 = (1 + i/4)^4 - 1

(1 + i/4)^4 = 1.0075i/4 = (1.0075)^(1/4) - 1i = 0.0303So,

the effective rate of interest per 4 months is 3.03%.Next, we can substitute the given values in the formula:

A = BD 400 * [(1 + 0.0303)^(6.2 * 3) - 1] / 0.0303 * (1 + 0.0303)A = BD 400 * [4.227 - 1] / 0.0303 * 1.0303A = BD 400 * 101.63A = BD 40,652.17

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If a bakery sold 328 mocha and 72 chocolate in one day, then the percent of the cupcakes sold that day were mocha is equals to the 21.95% ~ 22%.

Percentage is a way to a number as ratio or fraction where the denominator is 100. We use the percent symbol (%). It is mainly used to represent a portion of a whole or to compare two numbers. The percentage can be calculated by dividing the value by the total value and then multiplying the resultant by 100. The formula used to calculate the percentage is, P = (value/total value)×100%

We have, a bakery sells mocha cupcakes and chocolate cupcakes.

Number of mocha sold by it in one day= 328

Number of chocolate cupcakes sold by it in one day = 72

We have to determine the percent of the cupcakes sold that day were mocha. Using the above percent formula, the percent of the cupcakes sold that day were mocha, P \(=\frac{72}{328}× 100\) = 21.95% ~ 22%

Hence, required percent is 22%.

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3 inch.

the length of the new pieces.

to find the length of the new piece's you'll have to divide 3 by 2.

3/2

= 1.5 inch

so, the length of the new pieces is 1.5 inch.

Answer:

126 was removed.

Step-by-step explanation:

The total before division took place was

Total = mean * 14

mean = 49

Total = 49 * 14

Total = 685

Now you subtract x from the total

685 - x

And divide by 13 [one number is missing]

(685 - x)/13

and the result = 43

(685 - x ) / 13 = 43                Multiply both sides by 13

685 - x  = 43 * 13

685 - x = 559                       Subtract 685 from both sides

- x = - 126                             Multiply by - 1

x = 126

The law of mathematical logic that was used to derive the given conclusion is; Law of Syllogism

The law of syllogism is defined as a type of logical argument using deductive reasoning.

Now, In mathematical logic, the Law of Syllogism states that if the following two statements are true:

(1) If a , then b .

(2) If b , then c .

Then we can derive a third true statement:

(3) If a , then c .

Now, applying that law to our question, we see that;

1) If I'm a student, then I go to school.

2) If I go to school, then I learn.

Then we can derive a third true statement:

3)  If I'm a student, then I learn.

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The expression L^(-1){(s^2 + 2s) e^(-4s^3)} is equal to (t - 4)e^(2(t - 4)^2).

Step 1:

Using the result L{u(t - a)f(t - a)} = e^(-as)L{f(t)}, we can find the inverse Laplace transform of the given expression.

Step 2:

Given L^(-1){(s^2 + 2s) e^(-4s^3)}, we can rewrite it as L^(-1){s(s + 2) e^(-4s^3)}. Now, applying the result L^(-1){s^n F(s)} = (-1)^n d^n/dt^n {F(t)} for F(s) = e^(-4s^3), we get L^(-1){s(s + 2) e^(-4s^3)} = (-1)^2 d^2/dt^2 {e^(-4t^3)}.

To find the second derivative of e^(-4t^3), we differentiate it twice with respect to t. The derivative of e^(-4t^3) with respect to t is -12t^2e^(-4t^3), and differentiating again, we get the second derivative as -12(1 - 12t^6)e^(-4t^3).

Step 3:

Therefore, the expression L^(-1){(s^2 + 2s) e^(-4s^3)} simplifies to (-1)^2 d^2/dt^2 {e^(-4t^3)} = d^2/dt^2 {(t - 4)e^(2(t - 4)^2)}. This means the inverse Laplace transform of (s^2 + 2s) e^(-4s^3) is (t - 4)e^(2(t - 4)^2).

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Answer:

Otion 3

I posted a question pls if u know help me answer it

To find the lower quartile of a set of numbers, we need to determine the value that separates the lowest 25% of the data from the rest. In the given set of numbers, the lower quartile can be found by arranging the data in ascending order and identifying the value at the 25th percentile.

First, let's arrange the data in ascending order: 1 5 6 6 7 7 8 8 8 8 9 9 18 20 20 20 20 20 24 32 50 50 68 100.

To find the lower quartile, we need to determine the position of the 25th percentile. Since there are 23 data points, the 25th percentile corresponds to the value at the (25/100) * 23 = 5.75th position.

Since the position is not a whole number, we need to find the value between the fifth and sixth data points. The fifth data point is 7, and the sixth data point is also 7. Therefore, the lower quartile is 7.

The lower quartile represents the value below which 25% of the data lies. In this case, 25% of the data points are less than or equal to 7. It indicates that a quarter of the values in the dataset are smaller than or equal to 7, while the remaining 75% are larger.

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Answer: 36 ft

Step-by-step explanation:

To determine which pair of events are independent, we need to check if the probability of their intersection is equal to the product of their individual probabilities. If the two probabilities are equal, the events are independent; otherwise, they are dependent.

Using the probabilities given, we can calculate the probabilities of the individual events:

P(a) = 0.4

P(b) = 0.3

P(c) = 0.2

P(d) = 0.1

We can also calculate the probabilities of the intersections of the events:

P(a ∩ b) = 0.1

P(a ∩ c) = 0.1

P(a ∩ d) = 0.1

P(b ∩ c) = 0.05

P(b ∩ d) = 0.05

P(c ∩ d) = 0.01

Now, we can check the pairs of events for independence:

1. Events a and b:

P(a) * P(b) = 0.4 * 0.3 = 0.12

P(a ∩ b) = 0.1

Since P(a ∩ b) is not equal to P(a) * P(b), events a and b are dependent.

2. Events a and c:

P(a) * P(c) = 0.4 * 0.2 = 0.08

P(a ∩ c) = 0.1

Since P(a ∩ c) is greater than P(a) * P(c), events a and c are dependent.

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3. Events a and d:

P(a) * P(d) = 0.4 * 0.1 = 0.04

P(a ∩ d) = 0.1

Since P(a ∩ d) is greater than P(a) * P(d), events a and d are dependent.

4. Events b and c:

P(b) * P(c) = 0.3 * 0.2 = 0.06

P(b ∩ c) = 0.05

Since P(b ∩ c) is not equal to P(b) * P(c), events b and c are dependent.

5. Events b and d:

P(b) * P(d) = 0.3 * 0.1 = 0.03

P(b ∩ d) = 0.05

Since P(b ∩ d) is not equal to P(b) * P(d), events b and d are dependent.

6. Events c and d:

P(c) * P(d) = 0.2 * 0.1 = 0.02

P(c ∩ d) = 0.01

Since P(c ∩ d) is not equal to P(c) * P(d), events c and d are dependent.

Therefore, none of the pairs of events are independent.

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Regarding the proportional relationships in each problem, the measures are given as follows:

5. The rate of change is of 4.5 miles per hour.

6. The slope is of -2.

7. The hourly charge for the services is of $75.

8. A proportional relationship is graphed, and it has a constant of 7.5.

9. He can make 18 hats in four and a half hours.

The general format of an equation representing a proportional relationship is presented below, in which the output variable y is given by the multiplication of the input variable x and the constant of proportionality k:

y = kx.

For item 5, the rate of change is represented by the constant, which is calculated as follows:

k = 18/4 = 4.5 miles per hour.

For item 6, given two points, the slope is given by the change in y divided by the change in x, hence:

m = (8 - (-12))/(7 - 17) = 20/-10 = -2.

For item 7, the hourly charge is also given by the slope, hence:

m = (165 - 15)/(2 - 0) = $75 an hour.

For item 8, a proportional relationship is graphed, as it is a linear function with an intercept of 0, and the constant is given as follows:

k = 30/4 = 7.5.

For item 9, the equation is:

y = 4x.

Hence in 4.5 hours, the number of hats is calculated as follows:

y = 4 x 4.5 = 18 hats.

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Answer:

13

Step-by-step explanation:

To find the distance between two points in a coordinate plane, we can use the distance formula:

d = sqrt((x2 - x1)^2 + (y2 - y1)^2)

where (x1, y1) and (x2, y2) are the coordinates of the two points.

Using this formula, we can find the distance between the points (-3, 6) and (-8, -6) as follows:

d = sqrt((-8 - (-3))^2 + (-6 - 6)^2)

= sqrt((-5)^2 + (-12)^2)

= sqrt(25 + 144)

= sqrt(169)

= 13

Therefore, the distance between the two points in simplest radical form is 13.

Step-by-step explanation:

the option that you've chose.

it's the correct answer!

have a good day :)

Answer:

The answer is D. number 4.

Answer:

C

Step-by-step explanation:

It can't be B or D, because there is only a difference in the X axis (Meaning it goes either left or right)

It can't be A because 2 is less than 11, so (2, -1) would be left 9 units in relation to (11, -1)

The y-intercept of the line of fit is 80, which means that a student who studies for 0 hours is predicted to earn 80% on the test.

This means that even if a student does not study at all, they are predicted to earn a grade of 80% on the test based on the relationship between the amount of time spent studying and the grades earned on the test. This y-intercept value is also the predicted grade if the student did not study at all.

However, it is important to note that this prediction is based solely on the linear relationship observed in the given data and may not necessarily hold true for all cases or situations.

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The exact value of y is π/4, which is approximately 0.7854 radians or 45 degrees.

To find the exact value of the real number y using y = arctan(-1), we can evaluate the arctan function at -1.

The arctan function gives us the angle whose tangent is a given value. In this case, we want to find the angle whose tangent is -1.

Since the tangent of π/4 is equal to 1, we can write -1 as -tan(π/4).

Therefore, y = arctan(-1) = arctan(-tan(π/4)).

Now, arctan and -tan are inverse functions, so they cancel each other out, resulting in:

y = π/4.

Therefore, the exact value of y is π/4, which is approximately 0.7854 radians or 45 degrees.

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Answer:

big area/small area = (big length/small length)^2

24/small area = (6/3)^2

24/sa = 4

sa= 6

Hello!

\(\large\boxed{-16}\)

Use PEMDAS (order of operations) to solve:

-4 · [3 + (-5)²] ÷ 7

Square -5:

-4 · [3 + 25] ÷ 7

Add the numbers inside of the parenthesis:

-4 · [28] ÷ 7

Multiply -4 and 28:

-112 ÷ 7

Divide:

= -16.

Answer:

Q1 (-2,-5)(0,3)(4,19)(7,31)

Step-by-step explanation:

Using sampling concepts, it is found that the most representative sample of the population of interest is given by:

50 randomly selected employees at the company.

It is a common statistics practice, when we want to study something from a population, we find a sample of this population, which has to involve all groups in the population.

In this problem, all employees have to be considered, no matter their department or experience on the company, hence the most representative sample of the population of interest is given by:

50 randomly selected employees at the company.

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Answer:

Step-by-step explanation:

\(2.4\times\:10\\\)

Multiply without the decimal points then put the decimal point in the answer

\(24\times\:10=240\\\)

2.4 has 1 decimal place

10 has 0 decimal places

Therefore, the answer has 1 decimal place

\(\\=24.0\\\\=24\)

The value product of 2.4 × 10 will be 24.

To multiply means to add a number to itself a particular number of times. Multiplication can be viewed as a process of repeated addition.

Given that;

The expression is,

⇒ 2.4 × 10

Now,

Since, The expression is,

⇒ 2.4 × 10

After multiply, we get;

⇒ 2.4 × 10 = 24

Thus, The value = 24

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Answer:

(0,1) , (2,4) , (4,7)

Explanation:

convert the equation into slope-intercept form (this would be y=3/2x+1)

now plug in random numbers for x and solve for y by multiplying them by 3/2 and adding 1.