help pls ! 15−24÷4⋅2

Answers

Answer 1

Answer:

9.28

Step-by-step explanation:

hope this help!!!


Related Questions

is -10 greather than -7​

Answers

Answer:

no

Step-by-step explanation:

-7 is bigger

Answer:

no, its less

Step-by-step explanation:

because in negatives the higher the number is (ex: -10) the less the value is, so its the opposite of positive numbers

solve the proportion r/72=1/3 r=?



please help meee

Answers

Answer:

R= 24

Step-by-step explanation:

Have a nice day/night :)

Also if you you can may you please mark me brainliest

The value of r is,

⇒ r = 24

What is Division method?

Division method is used to distributing a group of things into equal parts. Division is just opposite of multiplications.

For example, dividing 20 by 2 means splitting 20 into 2 equal groups of 10.

Given that;

The expression is,

⇒ r/72 = 1/3

Now, We can simplify for r as;

⇒ r/72 = 1/3

⇒ r = 72 / 3

⇒ r = 24

Thus, The value of r is,

⇒ r = 24

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Give the vector parameterization of the tangent line to r(t) = (t + 2)i + (t^2 + 1)j + (t^3 + 3)k| at the point P(2, 1, 3)| R(u) = (2i + j + 3k) + u(2i)| R(u) = (2i + j + 3k) + u(i)| R(u) = (2i + j + 3k) + u (i+ 2j + 3k)| R(u) = (2i + j + 3k) + u(3i + j + 3k)| R(u) = (2i+j + 3k) + u(i + 2j + k)|

Answers

The vector parameterization of the tangent line to r(t) at the point P(2, 1, 3) is R(u) = (2i + j + 3k) + u(3i + j + 3k).

To find the vector parameterization of the tangent line to the curve defined by the vector function r(t), we need to consider the point on the curve where the tangent line passes through. In this case, the point P(2, 1, 3) is given.

The vector form of the tangent line is given by R(u) = P + uT, where P is the position vector of the point P and T is the direction vector of the tangent line.

The position vector of the point P is P = 2i + j + 3k.

To find the direction vector of the tangent line, we differentiate the vector function r(t) with respect to t. The result gives us the derivative vector, which represents the direction of the tangent line at any given point on the curve.

Substituting t = 2 (since we want the tangent line at the point P), we get r'(2) = i + 4j + 12k.

Therefore, the direction vector of the tangent line is T = i + 4j + 12k.

Substituting the values of P and T into the vector form R(u) = P + uT, we get R(u) = (2i + j + 3k) + u(3i + j + 3k), which represents the vector parameterization of the tangent line to the curve at the point P(2, 1, 3).

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how much do i need to make to afford a $425,000 house

Answers

The income you need to afford a $425,000 house is largely dependent on your debt-to-income ratio, credit score, and down payment. However, a general rule of thumb is to have an annual income that is at least three times the purchase price of the home, which in this case would be $1,275,000.

To more accurately determine the income needed to afford a $425,000 house, consider factors such as the interest rate on the mortgage, property taxes, homeowners insurance, and any homeowner association fees.

These additional expenses can significantly impact your monthly mortgage payment and thus your income requirements.
It's important to keep in mind that lenders have varying criteria when determining mortgage eligibility and income requirements, so it's best to speak with a mortgage professional to get a more accurate estimate based on your individual circumstances.

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Can someone help me with this task please? !!

Can someone help me with this task please? !!

Answers

Answer:

we need to get your brain thinking in this way. that you begin to understand how to do these things.

airways to say that your brain is not working that way, is not a valid excuse. we need to change that. your brain needs to get used to this way of thinking.

so, please, please, PLEASE go through the explanations below and tell me, where exactly in these explanations you stopped understanding what I was saying. so that I can better explain to you what is happening.

1. (0, -2)

2. 4

3. a geometric sequence. the common ratio is -2.0

4. the third option

5. the fourth option

Step-by-step explanation:

1. as x increases, y decreases. until, suddenly after x=0, this tendency reverses, and with increasing x also y increases. so, this is a turning point.

2. look at the line. it only starts with x>0 (it looks like x is around 1).

"input" is all the values of x the function has a defined result for (y = result values).

so, as there is no line for negative x, we can eliminate the first 2 answers.

x=0 is no valid answer either (as mentioned above, the line only starts well after x=0).

in the answer options the only x value having an y value above or below this x value is x=4.

3. look at the difference between 2 numbers next to each other in the sequence.

2.4 to -4.8

-4.8 to 9.6

and so on.

what do we need to do to get from the left to the right ?

we need to multiply by -2.

so, the relationship between "sequence item n" (an) to "sequence item n-1" (an-1) is a ratio, a multiplication factor :

an/an-1 = -2

4. it is completely simple. a function can be many things. on an x/y coordinate grid it can have gaps, it can have sharp direction changes,...

but there us one thing a function can never have : multiple different y values for one x value.

in the first graph x=2 has two different y values (-1 and -3). so, it is not clear what the result for x=2 would be. and that means, it is not a function.

in the second graph x=4 has two different y values.

in the third graph all is OK.

in the fourth graph x=-2 has two different y values.

so, only the third option is a function.

5. this function calculates the height of the thrown rock after t seconds of flight.

therefore, only the fourth answer makes sense.

4 of 10
As an estimation we are told 5 miles is 8 km.
Convert 76 km to miles.
miles

Answers

Step-by-step explanation:

To help solve this question we will put it into a ratio:

MILES:KM

5        :8              This ratio shows that 5 miles equals 8km.

47.5         :76       We can put 76 on the km side because we are told that in                                    

                            in the question. Lets find out how many times 8 was

                            multiplied to equal 76. 76 divided by 8=9.5 Because 8 was

                            multiplied by 9.5 we shall multiply 5km by 9.5  5x9.5=47.5

Therefore 76km is equal to 47.5miles.

7 2/5 + 3 1/5=?
Explain show the work
Give me the answer

Answers

above is the solution to the question

7 2/5 + 3 1/5=?Explain show the workGive me the answer

Answer:

10 3/5 (10.6)

Step-by-step explanation:

 7 2/5 + 3 1/5

= (7+3) + ( 2/5 + 1/5)

= 10 + 3/5

= 10 3/5

(Which is also 10.6)

Brainlest pls. :)

how to solve and answer -(1/2) to the power of 4

Answers

The solution of (-1/2)⁴ is equal to 1/16.

We have to solve -(1/2) to the power of 4.

To solve this expression, you can simply raise -1/2 to the fourth power:

(-1/2)^4 = (-1/2) × (-1/2) × (-1/2) × (-1/2)

= 1/16

Therefore, (-1/2)⁴ is equal to 1/16.

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How many 5/16's are in 1 & 7/8? *

Answers

Answer:

oh so for one get them to look alike.. sooo keep 5/16 and change 1 7/8 to

1  14/16 and then  change it to 30/16 then simply compare 5 can go into 30 6 times soooooo    it can go into 1 & 7/8  6 times

Step-by-step explanation:

Danny is thinking of buying a gym membership. He has two gums available to choose from. Gym A has a $35 initial fee and costs $42 per month.Gym B has $65 initial fee and costs $36 per month. After how many months will the overall cost if both gym memberships be the same? How much will that be?

Answers

For this, all you have to do is create equations where all you have to do is change the x value. The equation for gym A would be 35 + 42x, where x is the number of months he has the membership, and the first number is the initial fee. The equation for gym B would be 65 + 36x, following the same rules. Now all you have to do is set both of these equations equal to each other:
65+36x=35+42x
Solving this equation results in x=5, which means that he has to have the memberships for 5 months for them to be equal. Now just plug that in to one side of the equation to get the amount he has to spend:
65+36(5) = $245

100bbl/ day of oil is flowing in a 2 inch inner diameter wellbore with pipe relative roughness of 0.001. The oil has density of 48lbm/ft 3 and viscosity of 1.8cp. The wellbore is deviated 15 degrees from horizontal flow and has length of 6,000ft. The bottom hole flowing wellbore pressure is 2,200psi.
a) Obtain the potential pressure drop in the wellbore (psi).
b) Determine the frictional pressure drop in the wellbore (psi).
c) If there is also gas flowing in the wellbore at 150ft 3 / day covering 20% of the total pipe volume, calculate the in-situ oil velocity (ft/s).
d) For case (c), determine the flow regime of the two-phase flow.

Answers

a) To obtain the potential pressure drop in the wellbore, we can use the hydrostatic pressure equation.

The potential pressure drop is equal to the pressure gradient multiplied by the length of the wellbore. The pressure gradient can be calculated using the equation: Pressure gradient = (density of oil × acceleration due to gravity) × sin(θ), where θ is the deviation angle of the wellbore from horizontal flow. In this case, the pressure gradient would be (48 lbm/ft^3 × 32.2 ft/s^2) × sin(15°). Multiplying the pressure gradient by the wellbore length of 6,000 ft gives the potential pressure drop.

b) To determine the frictional pressure drop in the wellbore, we can use the Darcy-Weisbach equation. The Darcy-Weisbach equation states that the pressure drop is equal to the friction factor multiplied by the pipe length, density, squared velocity, and divided by the pipe diameter. However, to calculate the friction factor, we need the Reynolds number. The Reynolds number can be calculated as (density × velocity × diameter) divided by the oil viscosity. Once the Reynolds number is known, the friction factor can be determined. Finally, using the friction factor, we can calculate the frictional pressure drop.

c) To calculate the in-situ oil velocity, we need to consider the total volume of the pipe, including both oil and gas. The total pipe volume is calculated as the pipe cross-sectional area multiplied by the wellbore length. Subtracting the gas volume from the total volume gives the oil volume. Dividing the oil volume by the total time taken by the oil to flow through the pipe (converted to seconds) gives the average oil velocity.

d) The flow regime of the two-phase flow can be determined based on the oil and gas mixture properties and flow conditions. Common flow regimes include bubble flow, slug flow, annular flow, and mist flow. These regimes are characterized by different distribution and interaction of the oil and gas phases. To determine the specific flow regime, various parameters such as gas and liquid velocities, mixture density, viscosity, and surface tension need to be considered. Additional information would be required to accurately determine the flow regime in this scenario.

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in their base 10 representations, the integer $a$ consists of a sequence of 1985 eights and the integer $b$ consists of a sequence of 1985 fives. what is the sum of the digits of the base 10 representation of $9ab$?

Answers

The integer $a$ consists of a sequence of 1985 eights in base 10 representation, while the integer $b$ consists of a sequence of 1985 fives. The sum of the digits of the base 10 representation of $9ab$ is 9925.

The integer $a$ consists of a sequence of 1985 eights in base 10 representation, while the integer $b$ consists of a sequence of 1985 fives. We need to find the sum of the digits of the base 10 representation of $9ab$.
To find the value of $9ab$, we first need to determine the value of $ab$. Since $a$ consists of 1985 eights and $b$ consists of 1985 fives, $ab$ will be a number with 3970 digits. Each digit in $ab$ will be either an eight or a five.
When we multiply $9$ by a digit $d$ that is either an eight or a five, the result will be a number that ends in a zero, except when $d$ is a five, in which case the result will end in a five.
Therefore, when we multiply $9$ by each digit in $ab$, we will obtain a number that ends in a zero for each eight and a number that ends in a five for each five. Since there are 1985 eights and 1985 fives in $ab$, the resulting number $9ab$ will have 3970 digits, all ending in either zero or five.
Now, let's find the sum of the digits in the base 10 representation of $9ab$. Since all the digits in $9ab$ end in either zero or five, the sum of the digits will depend on the number of zeros and fives.
In $ab$, there are 1985 zeros and 1985 fives. When we multiply these zeros and fives by 9, we obtain a number with 1985 zeros and 1985 fives as well.
Therefore, the sum of the digits in the base 10 representation of $9ab$ will be equal to $1985 \times 0 + 1985 \times 5$. Simplifying this expression, we have $0 + 9925 = 9925$.
Hence, the sum of the digits of the base 10 representation of $9ab$ is 9925.

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View Policies Current Attempt in Progress Using the information provided in the table, the network diagram and the project completion time = 25 weeks, reduce the completion time of the project by 5 we

Answers

Strategies such as fast-tracking, crashing, prioritization, and resource optimization can be employed to reduce the project completion time by 5 weeks.


To reduce the completion time of the project by 5 weeks, we need to analyze the provided information and make appropriate adjustments. The initial completion time of the project is 25 weeks.

To achieve a reduction of 5 weeks, we can consider several strategies:

1. Fast-tracking: This involves overlapping or parallelizing certain project activities that were initially planned to be executed sequentially. By identifying tasks that can be performed concurrently, we can potentially save time. However, it's important to evaluate the impact on resource allocation and potential risks associated with fast-tracking.

2. Crashing: This strategy focuses on expediting critical activities by adding more resources or adopting alternative approaches to complete them faster. By compressing the schedule of critical tasks, we can reduce the overall project duration. However, this may come at an additional cost.

3. Prioritization: By reevaluating the project tasks and their priorities, we can allocate resources more efficiently. This ensures that critical activities receive higher attention and are completed earlier, resulting in an accelerated project timeline.

4. Resource optimization: Analyzing the resource allocation and identifying potential areas for optimization can lead to time savings. By ensuring that resources are utilized effectively and efficiently, we can streamline the project execution process.

It's important to note that implementing any of these strategies requires careful evaluation, considering factors such as project constraints, risks, cost implications, and stakeholder agreements. A comprehensive analysis of the project plan, resource availability, and critical path can guide the decision-making process for reducing the project completion time.

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Consider the given pseudo code. Write the function T(n) in terms of the number of operations, and then give the asymptotic (big Oh) complexity of the algorithm, show all the work you do. [ write the summation formula and solve it, or use the "Look for pattern"method. a. Matrix Multiplication

Answers

The function T(n) in terms of the number of operations is:

T(n) = 2n^3 + 3n^2 + 2n + 1 and the asymptotic complexity of the matrix multiplication algorithm is O(n^3).

To analyze the provided pseudo code for matrix multiplication and determine the function T(n) in terms of the number of operations, we need to examine the code and count the number of operations performed.

The pseudo code for matrix multiplication may look something like this:

```

MatrixMultiplication(A, B):

   n = size of matrix A

   C = empty matrix of size n x n

   for i = 1 to n do:

       for j = 1 to n do:

           sum = 0

           for k = 1 to n do:

               sum = sum + A[i][k] * B[k][j]

           C[i][j] = sum

   return C

```

Let's break down the number of operations step by step:

1. Assigning the size of matrix A to variable n: 1 operation

2. Initializing an empty matrix C of size n x n: n^2 operations (for creating n x n elements)

3. Outer loop: for i = 1 to n

- Incrementing i: n operations  

- Inner loop: for j = 1 to n

- Incrementing j: n^2 operations (since it is nested inside the outer loop)

- Initializing sum to 0: n^2 operations

- Innermost loop: for k = 1 to n

- Incrementing k: n^3 operations (since it is nested inside both the outer and inner loops)

- Performing the multiplication and addition: n^3 operations

- Assigning the result to C[i][j]: n^2 operations

- Assigning the value of sum to C[i][j]: n^2 operations

Total operations:

1 + n^2 + n + n^2 + n^3 + n^3 + n^2 + n^2 = 2n^3 + 3n^2 + 2n + 1

Therefore, the function T(n) in terms of the number of operations is:

T(n) = 2n^3 + 3n^2 + 2n + 1

To determine the asymptotic (big O) complexity of the algorithm, we focus on the dominant term as n approaches infinity.

In this case, the dominant term is 2n^3. Hence, the asymptotic complexity of the matrix multiplication algorithm is O(n^3).

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Pls help I don’t have much time.

Pls help I dont have much time.

Answers

Answer:

Dude dont spend 100 points! This place is scamming people

Step-by-step explanation:

The length of a rectangular garden is 6 more than its width. If the perimeter is 32 feet, what is the width and the area of the garden.​

Answers

Answer:

\({\fbox{ \sf{Width \: of \: a \: rectangular \: garden \: = 5 \: feet}}}\)

\( \boxed{ \sf{ \: Area \: of \: a \: rectangular \: garden = 55 {ft}^{2}}}\)

Step-by-step explanation:

\( \star\) Let the width of a rectangular garden be 'w'

\( \star\) Length of a rectangular garden = 6 + w

\( \star\) Perimeter of a rectangular garden = 32 feet

\( \longrightarrow\) Finding the width of a rectangular garden :

\( \boxed{ \sf{ \: Perimeter \: of \: a \: rectangle \: = \: 2(length + width}}\)

\( \mapsto{ \text{32 = 2(6 + w + w)}}\)

\( \text{Step \: 1 \: : Collect \: like \: terms}\)

Like terms are those which have the same base

\( \mapsto{ \text{32 = 2(6 + 2w) }}\)

\( \text{Step \: 2 \: : Distribute \: 2 \: through \: the \: parentheses}\)

\( \mapsto{ \text{32 = 12 + 4w}}\)

\( \text{Step \: 3 \: : Swap \: the \: sides \: of \: the \: equation}\)

\( \mapsto{ \text{4w + 12 = 32}}\)

\( \text{Step \: 4 \: : Move \: 12 \: to \: right \: hand \: side \: and \: change \: its \: sign}\)

\( \mapsto{ \text{4w = 32 - 12}}\)

\( \text{Step \: 5 \: : Subtract \: 12 \: from \: 32}\)

\( \mapsto{ \sf{4w = 20}}\)

\( \text{Step \: 6 \: : Divide \: both \: sides \: by \: 4}\)

\( \mapsto{ \sf{ \frac{4w}{4} = \frac{20}{4}}}\)

\( \text{Step \: 7 \: : Calculate}\)

\( \mapsto{ \text{w = 5}}\)

Width of a rectangular garden = 5 feet

\( \longrightarrow\) Substituting / Replacing the value of w in 6 + w in order to find the length of a rectangular garden

\( \mapsto{ \sf{Length = 6 + w = 6 + 5 = \bold{11 \: feet} }}\)

\( \longrightarrow\) Finding the area of a rectangular garden having length of 11 feet and width of 5 feet :

\( \boxed{ \sf{Area \: of \: a \: rectangle = length \:∗ \: width}}\)

\( \mapsto{ \text{Area \: = \: 11 \: ∗ \: 5}}\)

\( \mapsto{ \sf{Area \: = 55 \: {ft}^{2} }}\)

Area of a rectangular garden = 55 ft²

Hope I helped!

Best regards! :D

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Answers

Answer:

256 miles

Step-by-step explanation:

The Pythagoras theorem is a² = b² + c² where a is the hypotenuse or longest side

To find the shorter side, the equation is rearranged so c² = a² - b² (whether it is b or c doesn't matter)

so √377² - 277² = 255.7342371

Answer to number 22

Answer: 256 miles

suppose a program uses two classes: airplane and jumbojet . which of these would most likely be the subclass?

Answers

A subclass refers to a class that can inherit properties of another class called a superclass. The subclass will have all the characteristics and behavior of the superclass, and it can be modified to meet the unique needs of a specific class. Therefore, if a program uses two classes, airplane, and jumbojet, then the most likely subclass is the jumbojet.

Suppose that the airplane is the superclass that will have all the characteristics and behavior of an airplane. On the other hand, the jumbojet will be the subclass that inherits the features of an airplane. As the subclass, the jumbojet can be modified to have additional features unique to it.

The inheritance concept in programming ensures that there is efficient use of code. It makes it easy to reuse code for creating new classes. When using inheritance, developers avoid copying and pasting code, which can lead to errors and repetition.

Suppose that the airplane and jumbojet are classes representing vehicles in a flight system.

Airplane is the superclass representing all the aircraft, while jumbojet is the subclass representing a specific type of airplane, which is a large passenger aircraft. Therefore, the jumbojet, being a specific type of airplane, is the most likely subclass.

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-20 divided by (-4) =

Answers

Answer: 5

Step-by-step explanation: -4×5=-20

What are tables in a research paper?

Answers

Tables and figures area way of presenting data in an organized form or more in a presentable way to attract more audience.

With tables and figures, it arranges your data to a simplified form and also it makes the content easy to understand for the front person.

Tables and figures in scientific papers are wonderful ways of presenting data. Effective data presentation in research papers requires understanding your reader and the elements that comprise a table.

It also several elements, including the legend, column titles, and body.

With all this tables in a research paper helps the reader understand the content for the data more effectively and efficiently.

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Alyssa invested $6,300 in an account paying an interest rate of 8¹% compounded continuously. Adriel invested $6,300 in an account paying an interest rate of 7% compounded quarterly. After 8 years, how much more money would Alyssa have in her account than Adriel, to the nearest dollar?​

Answers

Answer:

to the nearest dollar, Alyssa will have $1,107 more than Adriel after 8 years.

Step-by-step explanation:

We can use the formula for continuous compounding to find the amount of money Alyssa will have after 8 years:

A = Pe^(rt)

where A is the amount of money at the end of the investment period, P is the principal investment, e is the mathematical constant approximately equal to 2.71828, r is the annual interest rate as a decimal, and t is the time in years.

For Alyssa's investment, we have:

A = 6300e^(0.0818)

A ≈ 11,932.45

For Adriel's investment, we can use the formula for quarterly compounding:

A = P(1 + r/n)^(nt)

where n is the number of compounding periods per year, and t is the time in years.

For Adriel's investment, we have:

A = 6300(1 + 0.07/4)^(4*8)

A ≈ 10,825.45

The difference in the amount of money Alyssa will have compared to Adriel is:

11,932.45 - 10,825.45 = 1,107

Therefore, to the nearest dollar, Alyssa will have $1,107 more than Adriel after 8 years.

The simple interest for both 48months and 54 months option ,is 13,5%per annum .a deposit of 20% is also required for both option .calculate he balance owed

Answers

Answer:

The amount of deposit required is R37,999  for both

The percentage of purchase price for the required deposit is 20%

Therefore, deposit required=20%*R189,995

                                              =R37,999

The balance owed is the outstanding balance after payment of deposit plus the interest, bearing in mind that interest is computed using the simple interest approach

I=PRT

balance after payment of deposit=R189,995-R37,999

                                                       =R151,996

R=13.5% per year

T=48 months and 54 months

Interest on 48 month option=151,996*13.5%*48/12

                                              = R82,077.84

Interest on 54 month option=151,996*13.5%*54/12

                                              = R 92,337.57

The total payment without the initial deposit is the outstanding balance after payment of deposit plus the interest

Total payment for 48 month option=R151,996+R 92,337.57

                                                          =R  244,333.57

Total payment for 54 month option=R151,996+R82,077.84

                                                          =R 234,073.84

                                              Hope it helped!

hich of the following statements does not describe the structure of an atom?

An atom has a small, dense center called the nucleus.
Inside the nucleus of an atom are protons and electrons.
Protons are positively charged sub-atomic particles.
Electrons are negatively charged sub-atomic particles.

Answers

Answer:

it is the second one as a nucleus contains neutrons and protons

Answer:

the second one

Step-by-step explanation:

Inside the nucleus are protons and neutrons and electrons orbit the nucleus.

What is the greatest common factor of 48, 72 and 52? A.2 B.4 C.8 D.16

Answers

the answer is 4 since 4 is common in all the three digits

B).4

Jimmy rolls a number cube multiple times and records the data in the table above. At the end of the experiment, he counts that he has rolled 185 fours. Find the experimental probability of not rolling a four, based on Jimmy’s experiment. Round the answer to the nearest thousandth.

Answers

In this case, the experimental probability is D. 0.860

Why is this so?

First, note that Experimental probability, also known as Empirical probability, is founded on real experiments and adequate documentation of events.

In the table we can see that he rolled the cube 1000 times, and he recorded that 140 of those times he rolled a 5.

Then, the probability of rolling a 5 will be equal to:

P1 = 140/1000 = 0.14

Now, the probabilty of NOT rolling a 5, is equal to the rest of the probabilities, this is:

P2 = 1 - 0.14 = 0.86

then the correct option is D

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Full Question:

Although part of your question is missing, you might be referring to this full question:

Jimmy rolls a number cube multiple times and records the data in the table above. At the end of the experiment, he counts that he had rolled 140 fives. Find the experimental probability of not rolling a five, based in Jimmy’s experiment. Round the answer to the nearest thousandth.

A. 0.140

B. 0.167

C. 0.667

D. 0.860

Jimmy rolls a number cube multiple times and records the data in the table above. At the end of the experiment,

Tim bought a pair of Zeus running shoes on sale that were marked down 25% to $60 what was the original price of the shoe

Tim bought a pair of Zeus running shoes on sale that were marked down 25% to $60 what was the original

Answers

Tim bought a pair of running shoes marked 25% down at a price of $60

The formula to find the discount of an item on sale is

\(\text{ \% discount =}\frac{Discount\text{ price}}{\text{Original price}}\times100\text{\%}\)

Where

\(\begin{gathered} \text{Discount price = \$60} \\ \text{\% discount = 25\%} \end{gathered}\)

Let k represent the original price

Substitute the values into the formula above

\(\begin{gathered} 25=\frac{60}{k}\times100 \\ \text{Crossmultiply} \\ 25\times k=60\times100 \\ 25k=6000 \\ \text{Divide both sides by 25} \\ \frac{25k}{25}=\frac{6000}{25} \\ k=\text{\$240} \end{gathered}\)

Hence, the original price, k, of the pair of Zeus running shoes is $240

A square thin plane lamina of side length 4 cm is earthed along three sides and the potential varies sinusoidally along the fourth, being zero at the corners and increasing to a maximum of one volt at the centre of that side.

(i) Derive expressions for the potential and electric field strength at every point in the lamina.

(ii) Calculate values for both the potential (voltage) and the vectorr E field at the centre of the plate.

Answers

The given information provides a square thin plane lamina with side length 4 cm, which is earthed along three sides.

(i) Deriving expressions for the potential and electric field strength:

Electric Field Strength (E):

E = -∇V, where ∇ represents the gradient operator and V(x, y) = sin(πx/2a)sin(πy/2a).

Now, let's calculate the components of the electric field E using the partial derivatives:

E = -(∂V/∂x)î - (∂V/∂y)ĵ

= -[(πcos(πx/2a))/2a]î - [(πcos(πy/2a))/2a]ĵ

= -(π/2a)cos(πx/2a)î - (π/2a)cos(πy/2a)ĵ.

(ii) Calculating the values at the center of the plate:

Voltage at the center of the square:

V(x, y) = sin(πx/2a)sin(πy/2a)

V(0.02, 0.02) = sin(π/4)sin(π/4) = 0.5V.

Vector E field at the center of the square:

E = -(π/2a)cos(πx/2a)î - (π/2a)cos(πy/2a)ĵ

E(0.02, 0.02) = -(π/2(0.04))cos(π/4)î - (π/2(0.04))cos(π/4)ĵ

= -19.63î - 19.63ĵ V/m.

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If the line px -5y = 60 has a slope of -23 then p equals ....

Answers

Answer:

p = - 115

Step-by-step explanation:

The equation of a line in slope- intercept form is

y = mx + c ( m is the slope and c the y- intercept )

Given

px - 5y = 60 ( subtract px from both sides )

- 5y = - px + 60 ( divide all terms by - 5 )

y = \(\frac{1}{5}\) px - 12 ← in slope- intercept form

with slope m = \(\frac{1}{5}\) p , thus

\(\frac{1}{5}\) p = - 23 ( multiply both sides by 5 to clear the fraction )

p = - 115

Passing through (3, -3) and perpendicular to y=3x+5

Answers

Answer:

Find the negative reciprocal of the slope of the original line and use the point-slope formula y−y1=m(x−x1) to find the line perpendicular to y=3x−5. y=−13x−2

Step-by-step explanation:

Passing through (3, -3) and perpendicular to y=3x+5

if f(x) = f(7f(6f(x))), where f(0) = 0 and f '(0) = 1, find f '(0).

Answers

The value of F'(0) = 42

Consider:

y = f(g(x))

Then by the chain rule the derivative is:

f'(g(x)) . g'(x) .Thus the derivative of y = f(g(h(x)))  will be derived as being:

f'(g(h(x))) is derivative of g(h(x))

f'(g(h(x))) . g'(h(x)). h'(x)

If we return our attention to the problem at hand, we get:

F'(x) =  f'(7f(6f(x))) .7f'(6f(x)). 6f'(x)

F'(0) =   f'(7f(6f(0))) .7f'(6f(0)). 6f'(0)

Substituting our knowns:

F'(0) = f' (7f(0)). 7f'(0) . 6(1)

F'(0) = f'(0). 7(1) .6

F'(0) = 1 . 7 . 6

F'(0) = 42.

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