look at 7.5 of differential equations 7.1 to 7.5 for Euler's method

Answer:

A=30

Step-by-step explanation:

Answer:

\(a_{n}\) = 5n

Step-by-step explanation:

There is a common difference d between consecutive terms

d = 10 - 5 = 15 - 10 = 20 - 15 = 25 - 20 = 30 - 25 = 5

This indicates the sequence is arithmetic with explicit formula

\(a_{n}\) = a₁ + (n - 1)d

where a₁ is the first term and d the common difference

Here a₁ = 5 and d = 5 , then

\(a_{n}\) = 5 + 5(n - 1) = 5 + 5n - 5 = 5n

The equation of the line that passes through point (8,-5) and perpendicular to y = x - 2 is y = -x + 3.

The formula for equation of line is expressed as;

y = mx + b

Where m is slope and b is y-intercept.

Given that:

y = x - 2

To the equation of the line that passes through the point (8,-5) and is perpendicular to the line.

First, determine the slope of the initial line using the slope intercept-form. y = mx + b

y = x - 2

Slope m = 1

For the equation of line perpendicular to the initial line, its slope must be a negative reciprocal of the initial slope.

Hence, slope of the perpendicular line is;

Slope m = -1/1

Slope m = -1

Next, find the equation of the perpendicular line, by using the point slope formula.

y - y₁ = m( x - x₁ )

Plug in the slope m ( -1 ) and point (8,-5).

y - (-5) = -1( x - 8 )

y + 5 = -x + 8

y = -x + 8 - 5

y = -x + 3

Therefore, the equation of the line is y = -x + 3.

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Answer:

domain is all your x values and range is all your y values

Step-by-step explanation:

-5, -1, 2, 4, 5 are the domain and 3, 5, 2,-5, and -2 are your range.

hope this helps!

-Jules

The dimensions of an open-top rectangular container with a volume of 625 ft^3 are found to minimize total cost. The cost of the bottom is $5 per square foot, and the cost of the sides is $4 per square foot.

Let's assume that the length, width, and height of the open-top rectangular container are L, W, and H, respectively. We are given that the volume of the container is 625 ft^3, so we have: L × W × H = 625.

We want to minimize the cost of making the container, which is given by the sum of the cost of making the bottom and the cost of making the sides. The cost of making the bottom is $5 per square foot, and the area of the bottom is L × W. Therefore, the cost of making the bottom is:

C1 = 5LW

The cost of making the sides is $4 per square foot, and the area of each side is WH (there are two sides with area WH). The other two sides have area LH. Therefore, the cost of making the sides is:

C2 = 4(2WH + 2LH) = 8WH + 8LH

The total cost is the sum of C1 and C2:

C = C1 + C2 = 5LW + 8WH + 8LH

We can use the volume equation to solve for one of the variables in terms of the other two. For example, we can solve for H:

H = 625 / (LW)

Substituting this expression for H into the cost equation, we get: C = 5LW + 8W(625 / LW) + 8L(625 / LW)

Simplifying, we get: C = 5LW + 5000 / W + 5000 / L

To minimize C, we need to find the values of L and W that minimize this expression. To do so, we can take partial derivatives of C with respect to L and W and set them equal to zero:

∂C/∂L = 5W - 5000 / L^2 = 0

∂C/∂W = 5L - 5000 / W^2 = 0

Solving for L and W, we get:

L = 25^(1/3) ≈ 3.18 ft

W = 25^(2/3) ≈ 6.35 ft

Substituting these values into the volume equation, we get:

H = 625 / (LW) ≈ 6.23 ft

Therefore, the dimensions of the container that will minimize total cost are approximately L = 3.18 ft, W = 6.35 ft, and H = 6.23 ft.

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Answer:

Step-by-step explanation:

.2

The given expression is equivalent to option A.

Given expression

\(a^{1/5}\)

We know the \(\sqrt{2} = a ^{1/2}\)

For option A. \(\sqrt[5]{a} = a^{1/5}\)

For option B. \(\sqrt[1/5]{a} = a^{\frac{1}{1/5} }= a^5\)

For option C. \(\frac{1}{(\sqrt{a} )^5} = \frac{1}{a^{1/2\times5}} = a^{5/2}\)

For option D. \(\frac{1}{\sqrt[5]{a} } = a^{-1/5}\)

Therefore, the given expression is equivalent to \(\sqrt[5]{a}\)

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Answer:

0 pars

Step-by-step explanation:

3-3=0

you have a fair die, with six faces containing the numbers 1,2,3,4,5,6. are the two events a and b then A and B are exhaustive.

Given

A= { 1,2,4}

B= { 2,3,4,5,6}

C= { 3,4}

D= { 2,4,5}

Solving (a): The mutually exclusive events

These are events that have no common or mutual elements

Events A to D are not mutually exclusive because each of the events have at least 1 common element with one another.

Solving (b): Exhaustive events.

Two events X and Y are said to be exhaustive if:

S= P(X n Y)

i.e. if the sample space equals the intersection of X and Y

For events A to D, we have:

AnB= { 1,2,3,4,5,6}

and the sample space is:

S= {1,2,3,4,5,6}

By comparison;

A n B= S

Hence, A and B are exhaustive.

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The margin of error is a measure of the degree of uncertainty associated with the point estimate of a population parameter. Confidence intervals are constructed to estimate the true value of a population parameter with a certain level of confidence.

The margin of error and the width of the confidence interval are related, in that a larger margin of error implies a wider confidence interval.

When constructing a one-sample z-confidence interval to estimate the population proportion, the margin of error increases as the sample size increases. This is because larger sample sizes provide more information about the population and, as a result, the estimate becomes more precise. Conversely, as the sample size decreases, the margin of error increases, making the estimate less precise.

The margin of error also increases as the population proportion approaches 0.50. This is because when p=0.50, the population is evenly split between the two possible outcomes. As a result, more variability is expected in the sample proportions, leading to a larger margin of error.

Finally, the margin of error decreases as the confidence level (1-a) increases. This is because a higher confidence level requires a wider interval to account for the additional uncertainty associated with a higher level of confidence. In conclusion, the margin of error in one-sample z confidence intervals is affected by sample size, population proportion, and confidence level.

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Kushal's age is 16 years old and Aditee's age is 18 years old.

Kushal and Aditee's current ages are both 18 years old. In 2 years time, Kushal will be 20 years old and Aditee will be 20 years old as well, since 2 years ago, Aditee was 18 years old.
To solve this problem, we can set up a simple equation. Let K = Kushal's age and A = Aditee's age.
K + 2 = A - 2
We know that the sum of both their ages is 36, so we can substitute that into our equation.
K + 2 + A = 36
Now, we can solve for K by subtracting 2 from both sides of the equation.
K + 2 - 2 + A - 2 = 36 - 2
K + A = 34
Therefore, K = 34 - A
Since we know that A = 18, we can substitute that into our equation.
K = 34 - 18
K = 16

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The triangle xyz has three sides and three angles

Neither law can be used to solve the triangle

As a general rule, the law of sines states that:

x/sin(X) = y/sin(Y) = z/sin(Z)

As a general rule, the law of cosines states that:

x^2 = y^2 + z^2 - 2yz cos(X)

From the question, we understand that only the angle measures are given.

The sine and the cosine laws above require at least one side length of the triangle in order to solve the triangle

Since the side lengths are not known, then neither of the laws can be used

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Answer:

I JUST LOVE GETTING POINTS

Step-by-step explanation:

In general, observational studies are more problematic than randomized controlled trials because they can produce spurious relationships.

Observational studies rely on the natural variation in exposures and outcomes that occur in the population, without any intervention or manipulation by the researcher.

This can lead to confounding variables, which are factors that are associated with both the exposure and the outcome and can produce a false association between them.

Randomized controlled trials, on the other hand, assign participants to different exposure groups at random, which reduces the risk of confounding and allows for a more accurate assessment of causality.

Therefore, researchers must be cautious when interpreting observational studies and consider the potential for spurious relationships.

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Answer:

x = 1

Step-by-step explanation:

4(2x + 1) - 3 = - 3(x - 4) ← distribute parenthesis on both sides

8x + 4 - 3 = - 3x + 12

8x + 1 = - 3x + 12 ( add 3x to both sides )

11x + 1 = 12 ( subtract 1 from both sides )

11x = 11 ( divide both sides by 11 )

x = 1

A linear function has an equation of y = mx+b where m = slope and b = y-intercept. The function also has a line graph. By a line graph, the graph must have slope. That means the slope must not equal to 0 or undefined to be a linear function.

Further Explanation

A linear function has both domain and range as set of all real numbers because you are able to solve for x-term when inputting any y-value or solve for y-term when inputting any x-value. We can also find the x-intercept by substituting the value of y to 0 and basically solve for x-term. If we want to know the y-intercept, we can substitute x-term to 0 and solve for y. But most people would only look at b-term from y = mx+b because b-term is the y-intercept of function.

From your question, the function is indeed a linear function. The m-term and b-term both are from y = mx+b where m = slope and b = y-intercept.

Therefore, from y=6x+2. The m-value would be 6 and b-value would be 2

The values of the sides are;

41. x = 18√3. Option D

42. x = 6√3. Option A

Using the different trigonometric identities, we have;

41. Using the tangent identity, we have;

tan 60 = 9√2/y

cross multiply the values

y =9√2 ×√3

y = 9√6

Using the sine identity;

sin 45 = y/x

1/√2 = 9√6/x

cross multiply the values, we have;

x = 9√2 ×√3 ×√2

x = 18√3

42. Using the cosine identity

cos 60 = 3√3 /x

cross multiply, we have;

x = 6√3

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Answer:

m ∠ABD = 140°

m ∠DBC = 40°

Step-by-step explanation:

∠ (15x - 4) + ∠(5x - 8) = 180°

15x - 4 + 5x - 8 = 180

20x -1 2 = 180

20x = 180 + 12

x = 9.6

m ∠ABD = 15x - 4 = 140°

m ∠DBC = 5x - 8 = 40°

The APR, given the finance charge, the amount borrowed, and the number of months, is b. 16. 19 %

You can find the APR by using the RATE function on Spreadsheet.

The number of periods = 40 months

The Payment per month was:

= ( Loan amount + Finance charge )

= ( 22, 500 + 6, 743 .25 ) / 40 months

= $ 731.08125

The present value is the loan amount of $ 22, 500

The monthly rate is 1. 13456 %

The APR is:

= 1. 3456 x 12 %

= 16. 19 %

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Answer:

12 cm ,13cm 14cm is the correct answer

The crank angle value when the piston is at Top Dead Center (TDC) is 0 radians or 0 degrees. The maximum ratio of the crank radius to the connected length is 0.3.

The crank angle value refers to the angle between the crankshaft and a reference point when measuring the position of the piston. When the piston is at Top Dead Center (TDC), it is at its highest point in the cylinder. The crankshaft is positioned such that the connecting rod is aligned with the crank radius and the piston is at the topmost position. This corresponds to a crank angle value of 0 radians or 0 degrees.

Regarding the maximum ratio of the crank radius to the connected length, this value is given as 0.3. The crank radius is the distance from the center of the crankshaft to the center of the crank pin, and the connected length is the distance from the center of the crank pin to the center of the piston pin. The maximum ratio of 0.3 indicates that the crank radius is 0.3 times the connected length.

It's important to note that these values are specific to the context of the problem statement provided. Different engines or mechanisms may have different values for the crank angle at TDC and the maximum ratio of crank radius to connected length.

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The measure of the inscribed angle is equal to 90 degrees

The inscribed angle theorem mentions that the angle inscribed inside a circle is always half the measure of the central angle or the intercepted arc that shares the endpoints of the inscribed angle's sides. In a circle, the angle formed by two chords with the common endpoints of a circle is called an inscribed angle and the common endpoint is considered as the vertex of the angle.

In this problem, the side length of the square is 5 which forms 90 degrees to all the other sides.

The measure of the circumscribed angle is 90 degree

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Given a linear system of equations in unknowns x, y, and z with the following augmented matrix:{[1, -1, 0, 0, -7], [-2, 3, 0, 0, 2], [0, 0, 4, -2, 2]}Use Gauss-Jordan elimination to solve the system for x, y, and z.Solution:Step 1. The first step in solving this linear system of equations is to write the matrix in the form of an augmented matrix. In the following, we list the system of equations associated with the augmented matrix: 1x−1y=−72x+3y=24z−y=1  We begin by focusing on the first equation, which is:1x−1y=−7.

To get rid of the x-coefficient, we add one time the first equation to the second equation. This operation is written as follows:{[1, -1, 0, 0, -7], [-2, 3, 0, 0, 2], [0, 0, 4, -2, 2]}We add row1 to row2. -2r1 + r2 = r2{-2, 2, 0, 0, 14}r3 = r3This gives us the new augmented matrix.{[1, -1, 0, 0, -7], [0, 1, 0, 0, -5], [0, 0, 4, -2, 2]}Step 2Next, we focus on the second equation:0x+1y=−5.

The y-variable is isolated, and we now look at the third equation.4z−2y=1We can isolate the variable z by dividing the entire equation by 4 as follows:z−0.5y=0.25In order to eliminate y in the third row, we add 0.5 times the second row to the third row. This operation is written as follows:{[1, -1, 0, 0, -7], [0, 1, 0, 0, -5], [0, 0, 4, -2, 2]}We add 0.5 r2 to r3. r3 + 0.5r2 = r3{[1, -1, 0, 0, -7], [0, 1, 0, 0, -5], [0, 0, 4, -1, -1]}Step 3We can now solve for z using the third equation:4z−1y=−1z = (-1 + y) / 4.

Substituting this into the second equation gives:-2((1 - y) / 4) + 3y = 2y - 1 = 2y - 1Thus, y = 1/2.Substituting the value of y = 1/2 into the first equation gives:x - (1/2) = -7, so x = -13/2.Finally, we can substitute the values of x and y into the third equation to get the value of z: 4z - 1(1/2) = -1, so z = -3/2.The solution to the system of linear equations is: x = -13/2, y = 1/2, and z = -3/2.

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The maximum profit is achieved when approximately 312.5 units of lab equipment are sold.

The revenue function R(x) represents the amount of money the company earns from selling x units of lab equipment. It is given by the equation:

R(x) = -0.32x^2 + 270x

The costs function C(x) represents the expenses incurred by the company for producing and selling x units of lab equipment. It is given by the equation:

C(x) = 70x + 52

To determine the company's profit, we subtract the costs from the revenue:

Profit = Revenue - Costs

P(x) = R(x) - C(x)

Substituting the given revenue and costs functions:

P(x) = (\(-0.32x^2 + 270x)\) - (70x + 52)

Simplifying the equation:

P(x) = -0.32x^2 + 270x - 70x - 52

P(x) = -\(0.32x^2\)+ 200x - 52

The profit function P(x) represents the amount of money the company makes from selling x units of lab equipment after deducting the costs. It is a quadratic function with a negative coefficient for the x^2 term, indicating a downward-opening parabola. The vertex of the parabola represents the maximum profit the company can achieve.

To find the maximum profit and the corresponding number of units sold, we can use the vertex formula:

x = -b / (2a)

For the profit function P(x) = -\(0.32x^2 + 200x\)- 52, a = -0.32 and b = 200.

x = -200 / (2 * -0.32)

x = 312.5

Therefore, the maximum profit is achieved when approximately 312.5 units of lab equipment are sold.

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price per house : $250,000

number of houses: 9

To find how much he will earn (y) we have to multiply the price per house by the number of houses (x).

y = 250,000 x

Where x is the independent variable (number of houses) and y is the dependent variable (earnings)

Replacing x by the number of houses:

y = 250,000 ( 9) = $2,250,000

Answer:

y=1

Step-by-step explanation:

6=2(y+2)

6=2y+4

2=2y

y=1

Answer:

y=1

Step-by-step explanation:

The largest number of fence post that can possibly be cut from the log is 23.8( nearest tenth)

A word problem in math is a math question written as one sentence or more. This statements are interpreted into mathematical equation or expression.

For us to know the number of fence post that can be obtained from the log, we need to convert the length of the log into cm

Therefore;

1m = 100cm

16m = 16× 100 = 1600 cm

Therefore the maximum number of fence post that can be obtained is

1600/70 = 160/7

= 23.8 ( nearest tenth)

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Answer:2

Step-by-step explanation: