write 2x+xto the power of 3 minus 1 in descending oreder
​

The fraction 1/6 as a decimal is approximately 0.1667.

1. The partial derivative of ∂R/∂R₁ is [tex]R_2^2R_3^2 / (R_1R_2 + R_1R_3 + R_2R_3)^2[/tex]

2.  by symmetry of the problem, ∂R/∂R₂ and ∂R/∂R₃ will be the same expression, but with the roles of the resistances changed. Therefore

∂R/∂R₂ = R₁²R₃² / (R₁R₂ + R₁R₃ + R₂R₃)² and ∂R/∂R₃ = R₁²R₂² / (R₁R₂ + R₁R₃ + R₂R₃)²

The formula for the net resistance R in a parallel circuit is:

R = (R₁R₂R₃) / (R₁R₂ + R₁R₃ + R₂R₃)

The partial derivative ∂R/∂R₁ we can use the quotient rule, which is given by:

(d/dx)[u(x)/v(x)] = [v(x)u'(x) - u(x)v'(x)] / [v(x)]²

u = R₁R₂R₃

v = R₁R₂ + R₁R₃ + R₂R₃,

so u' = R₂R₃

v' = R₂ + R₃ given that the derivative of R₁R₂ and R₁R₃ with respect to R₁ are R₂ and R₃, respectively, and R₂R₃ does not contain R₁, so its derivative is zero.

Applying the quotient rule gives:

∂R/∂R₁ = [R₂R₃(R₁R₂ + R₁R₃ + R₂R₃) - R₁R₂R₃(R₂ + R₃)] / (R₁R₂ + R₁R₃ + R₂R₃)²

= [R₁R₂²R₃ + R₁R₃²R₂ + R₂²R₃² - R₁R₂²R₃ - R₁R₃²R₂] / (R₁R₂ + R₁R₃ + R₂R₃)²

= R₂²R₃² / (R₁R₂ + R₁R₃ + R₂R₃)²

Now, by symmetry of the problem, we can see that ∂R/∂R₂ and ∂R/∂R₃ will be the same expression, but with the roles of the resistances changed. Therefore:

∂R/∂R₂ = R₁²R₃² / (R₁R₂ + R₁R₃ + R₂R₃)²

∂R/∂R₃ = R₁^2R₂^2 / (R₁R₂ + R₁R₃ + R₂R₃)²

The denominators are the same for the partial derivatives with respect to each of the resistances, but the numerators depend on the squares of the other two resistances, not including the one we are differentiating with respect to.

The above answer is based on the full question below;

Suppose that three resistors are in parallel in an electrical circuit. If the resistances are R₁, R₂ and R₃ ohms, respectively, then the net resistance in the circuit equals R =(R₁ R₂ R₃)/(R₁R₂ +R₁R₃ + R₂R₃). Compute the partial differential of ∂R/∂R₁. Given this partial derivative, explain how to quickly write down the partial derivatives ∂R/∂R₂ and ∂R/∂R₃

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Answer:

The correct answer is 7.

Step-by-step explanation:

The sum of 2 and 5 is 7, not 8. Addition is a basic arithmetic operation that combines two numbers to find their total or sum. In this case, when we add 2 and 5 together, we count a total of 7. It's important to carefully perform calculations to ensure accuracy and obtain the correct result.

The final simplified expression: 30 + 20 = 50 the Simplified form of the expression 18 - 9 × (-4) ÷ 3 + 10 × 2 is 50.

The expression 18 - 9 × (-4) ÷ 3 + 10 × 2, we follow the order of operations (also known as PEMDAS: Parentheses, Exponents, Multiplication and Division, and Addition and Subtraction) to perform the operations in the correct order.

First, we simplify the multiplication and division from left to right:

9 × (-4) ÷ 3 = -36 ÷ 3 = -12

Now we have the expression: 18 - (-12) + 10 × 2

Next, we perform the subtraction and addition from left to right:

18 - (-12) = 18 + 12 = 30

Now we have the expression: 30 + 10 × 2

Finally, we perform the multiplication:

10 × 2 = 20

Now we have the final simplified expression: 30 + 20 = 50 the simplified form of the expression 18 - 9 × (-4) ÷ 3 + 10 × 2 is 50.

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Answer:

180

Step-by-step explanation:

The area of a parallelogram is given by the formula A = b × h, where b is the base and h is the height. In this case, the base is 10 and the height is 18. Therefore, the area is:

A=10×18

A=180

The area of the parallelogram is 180 square units

The linear combination of the standard unit vectors i and j for the given initial and terminal points is 9i + 20j.

To find the linear combination of the standard unit vectors i and j, we need to determine the components of the vector that connects the initial point to the terminal point.

Given:

Initial Point: (0, -8)

Terminal Point: (9, 12)

To find the linear combination, we subtract the coordinates of the initial point from the coordinates of the terminal point:

So, Terminal Point - Initial Point

= (9, 12) - (0, -8)

= (9 - 0, 12 - (-8))

= (9, 20)

Therefore, the linear combination of the standard unit vectors i and j for the given initial and terminal points is 9i + 20j.

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The value of 'c' that satisfies the  Expression √(3 * 5^2 - c) = -12 is c = -69.

The given expression √(3 * 5^2 - c) = -12, we can solve for the value of 'c'. Let's break down the problem step by step.

1. Start with the given expression: √(3 * 5^2 - c) = -12.

2. Square both sides of the equation to eliminate the square root:

  3 * 5^2 - c = (-12)^2.

3. Simplify the equation:

  3 * 25 - c = 144.

4. Multiply 3 by 25:

  75 - c = 144.

5. Subtract 75 from both sides of the equation:

  -c = 144 - 75.

6. Simplify the right side of the equation:

  -c = 69.

7. Multiply both sides of the equation by -1 to solve for 'c':

  c = -69.

Therefore, the value of 'c' that satisfies the given expression √(3 * 5^2 - c) = -12 is c = -69.

It's important to note that when evaluating an equation, we need to ensure that the solution satisfies the original equation. In this case, if we substitute c = -69 back into the original equation, we can verify that both sides of the equation are equal:

√(3 * 5^2 - (-69)) = √(75 + 69) = √144 = 12 = -12 (as given).

Therefore, the solution c = -69 is valid.

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Answer:

0.63

Step-by-step explanation:

We have the following information:

The probability of a student being male is 0.45.

The probability of a student having a job off-campus is 0.33.

The probability of a student being male and having a job off-campus is 0.15.

Now, we want to find the probability that a student is either male or has an off-campus job.

To do this, we add the probability of being male (0.45) to the probability of having an off-campus job (0.33). However, we need to be careful not to count the students who are both male and have an off-campus job twice. So, we subtract the probability of being male and having an off-campus job (0.15) once.

By doing this, we account for all the possible cases and get the probability that a student is either male or has an off-campus job.

Calculating the values:

P(Male or Off-campus job) = P(Male) + P(Off-campus job) - P(Male and Off-campus job)

= 0.45 + 0.33 - 0.15

= 0.63

Therefore, the probability that a student chosen at random from the college is male or has an off-campus job is 0.63.

Hope this helps!

Answer: 5.4

Step-by-step explanation:

First, start with adding the two given sides, then take that sum and subtract it from the perimeter, then after that, divide by two

1 + 3.8= 4.8  

15.6 - 4.8=10.8

10.8 / 2 = 5.4

The solution is: The arc length SR is 52.12ft.

We have,

Arc length is the distance between two points along a section of a curve. An arc is a cut out section of a circumference of a circle.

The arc angle = sector angle in the diagram

The length of an arc is expressed as;

l = tetha/360 × 2πr

where r is the radius and tetha is the angle between the two radii.

l = 332/360 × 2 × 9 × 3.14

l = 1042.48 × 18/360

l = 18764.64/360

l = 52.12( nearest hundredth)

therefore the length of the arc is 52.12 ft

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I'm not pretty sure about your question but hope this can help:

To find the roots of the equation 2x = 3sin(x) + 5 using the bisection method, we need to follow these steps:

Step 1: Define the function

Let's define the function f(x) = 2x - 3sin(x) - 5.

Step 2: Choose an initial interval

We need to choose an interval [a, b] such that f(a) and f(b) have opposite signs. Based on the graph or estimation, we can select an interval that contains the root. Let's choose [a, b] = [0, 2] as an example.

Step 3: Apply the bisection method

Now we can apply the bisection method to find the root within the chosen interval. The steps are as follows:

1. Calculate the midpoint of the interval: c = (a + b) / 2.

2. Evaluate f(c).

3. If f(c) is very close to zero (i.e., |f(c)| < tolerance), then c is the root. Stop the process.

4. If f(a) and f(c) have opposite signs, set b = c. Otherwise, set a = c.

5. Repeat steps 1-4 until you find a root within the desired tolerance.

Step 4: Choose a tolerance

You need to choose a tolerance level, which determines how close to zero the function value needs to be to consider it a root. Let's choose a tolerance of 0.0001 as an example.

Now, let's apply the bisection method step by step:

Step 1: Define the function: f(x) = 2x - 3sin(x) - 5

Step 2: Choose an initial interval: [a, b] = [0, 2]

Step 3: Apply the bisection method:

1. Calculate the midpoint of the interval: c = (0 + 2) / 2 = 1.

2. Evaluate f(c): f(1) = 2(1) - 3sin(1) - 5 ≈ -5.42.

3. Since f(1) is not very close to zero, we proceed to the next step.

4. f(0) = 2(0) - 3sin(0) - 5 = -5, and f(1) = -5.42 have opposite signs.

  Therefore, we update the interval to [a, b] = [0, 1].

5. Repeat steps 1-4.

1. Calculate the midpoint of the interval: c = (0 + 1) / 2 = 0.5.

2. Evaluate f(c): f(0.5) = 2(0.5) - 3sin(0.5) - 5 ≈ -4.11.

3. Since f(0.5) is not very close to zero, we proceed to the next step.

4. f(0) = -5 and f(0.5) ≈ -4.11 have opposite signs.

  Therefore, we update the interval to [a, b] = [0, 0.5].

5. Repeat steps 1-4.

Continue this process until you reach a root within the desired tolerance of 0.0001.

Please note that the bisection method is an iterative process, and it may take several iterations to converge to the root depending on the chosen interval and tolerance level.

The root lies approximately between 1.40625 and 1.4375.

To find the roots of the equation 2x = 3sin(x) + 5 using the bisection method, we need to locate the interval in which the root lies and then iteratively narrow down the interval until we get a root within a desired level of accuracy. The bisection method requires that the function changes sign within the interval we consider.

Let's first rearrange the equation to get it in the form f(x) = 0:

f(x) = 2x - 3sin(x) - 5

Now, we will perform the bisection method:

Step 1: Choose an interval [a, b] where the function changes sign. Let's start with [a, b] = [0, 2] since we can observe a sign change within this interval (f(0) < 0 and f(2) > 0).

Step 2: Calculate the midpoint of the interval: c = (a + b) / 2.

Step 3: Evaluate the function at the midpoint: f(c).

Step 4: If f(c) is close to zero (within the desired level of accuracy), then c is an approximation to the root, and we can stop the iteration.

Step 5: If f(c) has the same sign as f(a), replace a with c; otherwise, replace b with c.

Step 6: Repeat steps 2 to 5 until the desired level of accuracy is achieved.

Let's perform a few iterations to find the root:

Iteration 1:

[a, b] = [0, 2]

c = (0 + 2) / 2 = 1

f(c) ≈ 21 - 3sin(1) - 5 ≈ -5.42 (negative, replace a with c)

Iteration 2:

[a, b] = [1, 2]

c = (1 + 2) / 2 = 1.5

f(c) ≈ 21.5 - 3sin(1.5) - 5 ≈ 1.03 (positive, replace b with c)

Iteration 3:

[a, b] = [1, 1.5]

c = (1 + 1.5) / 2 = 1.25

f(c) ≈ 21.25 - 3sin(1.25) - 5 ≈ -2.07 (negative, replace a with c)

Iteration 4:

[a, b] = [1.25, 1.5]

c = (1.25 + 1.5) / 2 = 1.375

f(c) ≈ 21.375 - 3sin(1.375) - 5 ≈ -0.55 (negative, replace a with c)

Iteration 5:

[a, b] = [1.375, 1.5]

c = (1.375 + 1.5) / 2 = 1.4375

f(c) ≈ 21.4375 - 3sin(1.4375) - 5 ≈ 0.26 (positive, replace b with c)

Iteration 6:

[a, b] = [1.375, 1.4375]

c = (1.375 + 1.4375) / 2 = 1.40625

f(c) ≈ 21.40625 - 3sin(1.40625) - 5 ≈ -0.145 (negative, replace a with c)

Continue the iterations until you achieve the desired level of accuracy. After enough iterations, you'll approximate the root of the equation to a desired precision. In this example, the root lies approximately between 1.40625 and 1.4375.

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To find the range, we subtract the smallest value from the largest value:

Range = 31 - 10 = 21

To find the mean, we add up all the values and divide by the total number of values:

Mean = (10 + 21 + 16 + 22 + 31) ÷ 5 = 20

To find the median, we need to arrange the values in order from smallest to largest:

10, 16, 21, 22, 31

The median is the middle value when the values are arranged in order. Since there are an odd number of values, the median is the middle value of the sequence, which is 21.

To find the mode, we need to find the value that occurs most frequently in the sequence. In this case, there is no mode because no value occurs more than once in the sequence.

The Profit of selling 850 gallons of gasoline is S/. 221.

The profit of selling 850 gallons of gasoline,  the difference between the selling price and the cost price per gallon, and then multiply that by the number of gallons sold.

Given:

Cost price per gallon = S/. 12.89

Selling price per gallon = S/. 13.15

Number of gallons sold = 850

Profit per gallon = Selling price per gallon - Cost price per gallon

Profit per gallon = S/. 13.15 - S/. 12.89

Profit per gallon = S/. 0.26

Total profit = Profit per gallon * Number of gallons sold

Total profit = S/. 0.26 * 850

Total profit = S/. 221

Therefore, the profit of selling 850 gallons of gasoline is S/. 221.

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The length of the third side of the triangle must be less than the sum of the two other sides given.

k < 10 cm.

The possible lengths of the triangle is determined from the rules of length of a triangle.

The rule of lengths of triangle states that the length of one side of a triangle must be greater than the difference and less than the sum of the lengths of the other two sides.

Let the third side of the triangle = k

The possible values of k is determined as;

k < ( 3 cm + 7 cm)

k < 10 cm

Thus, the length of the third side of the triangle must be less than the sum of the two other sides given.

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The value of x is 15.

Given,

Circle with secant RBA and tangent RG.

Secant RBA is divided into two parts RB and BA.

Tangent is RG.

Theorem on circles:
If a secant RBA intersects circle at two points B and A and RG be the tangent to the circle at G, then

RG² = RB × RA

Substitute the values,

RG = Tangent = x

RB = 9cm

RA = RB + BA = 9 + 16 = 25 cm

x² = 9 × 25

x = 15.

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Answer:

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

Let it be x years after that Jack's mother will be 3 times as old as Jack.

Set up equation and solve for x:

After 15 years Jack will be 20 and his mother will be 60 years old.

Answer:

The statement that is NOT always true about matrices A, B, and C is:

C. If A is singular, then its transpose is also singular.

Step-by-step explanation:

A matrix A is singular if and only if its determinant is zero. However, the transpose of a matrix does not necessarily have the same determinant as the original matrix. So, it is possible for a matrix A to be singular while its transpose is non-singular. Therefore, statement C is not always true.

The scale factor of the perimeters from figure A to figure B is 1.5. Scale factor is the ratio of any two corresponding lengths in two similar figures.

Here, the two figures are similar, that is why we can find the scale factor by dividing corresponding sides of one figure by the corresponding sides of another figure. We will find the scale factor for the perimeter of figures A and B below:Perimeter of figure A = 12 + 10 + 18 = 40 unitsPerimeter of figure B = 15 + 15 + 15 = 45 unitsTo find the scale factor of the perimeters, we divide the perimeter of figure B by the perimeter of figure

A:Scale factor of the perimeters = (Perimeter of figure B)/(Perimeter of figure A) = 45/40 = 1.125To simplify any fractional answer, we have to convert it to the lowest terms, which is 9/8. The decimal answer 1.125, when rounded to the nearest tenth is 1.1. Therefore, the scale factor of the perimeters from figure A to figure B is 1.5.

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Answer:

Step-by-step explanation:

[tex]a+b=(3i+4j)+(-2i+5j)[/tex]

        [tex]=3i+4j-2i+5j[/tex]

        [tex]=1i+9j[/tex]

Answer:

net salary = 8047.5

Step-by-step explanation:

his basic salary is 8700

7.5% of that is (8700)(0.075) = 652.5

He gives this away, so his net salary will become

8700 - 652.5 = 8047.5 = net salary

Answer:

ds/dt ≈ 0.0324 cm/s

Step-by-step explanation:

V= lwh

As this is a cube, every side is the same length so:

V = [tex]s^{3}[/tex]

differentiate both sides:

[tex]\frac{dV}{dt} = (3s^{2})\frac{ds}{dt}[/tex]

We are given that dV/dt = 7/2 and that s = 6.

Plug these values in, and solve for ds/dt, which is the rate of change of the side.

[tex]\frac{7}{2} = (3(6^{2} ))\frac{ds}{dt} \\\\[/tex]

[tex]\frac{ds}{dt}[/tex] ≈ 0.0324 cm/s

The side length of the cube is increasing at a rate of 0.0324 cm/s when the side length is 6 cm and the volume of the cube is increasing at the rate of 7/2 cm³/s.

In Mathematics, particularly Calculus, the rate of change can be found using differentiation. Given that the volume of a cube (V) changes at the rate of 7/2cm³s⁻¹ and V=a³ (where a is the side length of a cube), we can find the rate at which the side length (a) changes, by using the derivative of the volume with respect to time (t).

Step 1: Take the derivative of the volume equation dv/dt = 3a²*da/dt, here dv/dt is the rate of change of the volume.

Step 2: In the problem, it is given that dv/dt = 3.5 cm³/s (or 7/2 cm³/s) and a=6 cm.

Substitute these values into the equation: 3.5 = 3*(6)²*da/dt.

Step 3: Simplify the equation to solve for da/dt. After simplification, da/dt = 3.5/(3*36), which gives da/dt = 0.0324 cm/s. Therefore, the side length of the cube is increasing at a rate of 0.0324 cm/s when a = 6 cm.

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The z-score of a time of 44 minutes is 1.2

From the question, we have the following parameters that can be used in our computation:

Normally distributed mean = 38 minutes

Normally distributed standard deviation = 5 minutes.​

Also, we have

Score = 44 miniues

The z-score of a time of 44 minutes is calculated as

z = (Score - Mean)/standard deviation

substitute the known values in the above equation, so, we have the following representation

z = (44 - 38)/5

Evaluate

z = 1.2

Hence, the z-score of a time of 44 minutes is 1.2

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Answer: 19:30 is the current time as per the 24-hour time format

Step-by-step explanation: We know that a day has 24 hours. The time can be shown in two different formats- the 12-hour format and the 24-hour format. 12 hour format ranges only from 1-12 on the hour while 24-hour format varies from 1-24 representing the hour.

      The 24 hour time format is quite simple- marks one number each for one hour. If the Reading says 19:30, it simply means hour 19 of that day. 12-hour time format is different since it makes use of A.M. (Ante Meridiem) and P.M. (Post Meridiem).

The perimeter of this parallelogram is equal to 32.4 units.

In Mathematics and Geometry, the perimeter of a parallelogram can be calculated by using this mathematical equation (formula);

P = 2(L + W)

Where:

For the length, we have:

Distance = √[(x₂ - x₁)² + (y₂ - y₁)²]

Distance = √[(-5 + 4)² + (-3 - 2)²]

Distance = √26

Distance = 5.1 units

For the width, we have:

Distance = √[(x₂ - x₁)² + (y₂ - y₁)²]

Distance = √[(7 + 4)² + (3 - 2)²]

Distance = √122

Distance = 11.1 units.

P = 2(5.1 + 11.1)

P = 2(16.2)

P = 32.4 units.

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Susan will pay $36.00 to the car park attendant for the period of parking.

Given information,

Charges of car parking for one hour = $6.00

Susan park the car at = 10:20 am

Susan returned the car at = 4:15 pm

Susan parked her car at 10:20 a.m. and returned for it at 4:15 p.m. The duration can be calculated by subtracting the start time from the end time:

4:15 p.m. - 10:20 a.m. = 5 hours and 55 minutes

Since the car park charges $6.00 per hour or part thereof, the duration is rounded up to the nearest hour. In this case, the duration is more than 5 hours, so 6 hours will be considered.

The parking cost: 6 hours x $6.00 per hour = $36.00

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If she decides to trade her in her car 8 years from now then the car will be worth of $8,782.52.

To estimate the future value of Tara's car 8 years from now, we can consider the average depreciation rate of vehicles and assume it applies to her car.

On average, cars tend to depreciate around 15-20% per year.

Let's assume a conservative depreciation rate of 15% per year for Tara's car. We can calculate the future value using the following formula:

Future Value = Current Value× (1 - Depreciation Rate)^Number of Years

Suppose the current value of Tara's car is $20,000.

Plugging in the values, we get:

Future Value = $20,000(1 - 0.15)⁸

Future Value = $20,000(0.85)⁸

Calculating this, we find:

Future Value = $8,782.52

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Answer:

R2400

Step-by-step explanation:

a. There is a 0.7643 percent probability that the website will have fewer than 5 million visitors in a single day.

b. There is a 0.0375 percent chance that the website will have 3 million or more visitors in a single day.

c. There is a 0.3186 percent chance that the website will receive between 3 million and 4 million visitors in a single day. Therefore, about 5,276,320 visits per day's worth of website traffic will necessitate Smiley's People buying more server space.

d. The amount of web traffic that will require Smiley's People to purchase additional server capacity is approximately 5,276,320 visitors per day.

In order to calculate the likelihood, we must standardise the data using the equation z = (x - mu) / sigma, where x is the value we are interested in, mu is the mean, sigma is the standard deviation, and z is the standardised value.

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