For a short time a rocket travels up and to the left at a constant speed of v = 650 m/s along the parabolic path y=600−35x2m, where x isin m. The origin of polar coordinate system is the same as the origin of the rectangular coordinate system xy.

Part A

Determine the radial component of velocity of the rocket at the instant when its transverse coordinate θ = 60∘, where θ is measured counterclockwise from the x axis.

Express your answer to three significant figures and include the appropriate units.

Part B

Determine the transverse component of velocity of the rocket at the instant when its transverse coordinate θ = 60∘, where θ is measured counterclockwise from the x axis.

Express your answer to three significant figures and include the appropriate units.

Answer:

d) II and IV . See explanation below.

Explanation:

Assuming the following list of inputs:

I. The discount percentage

II. The total value of the purchase

III. The loyalty-discount amount

IV. The customer ID card number

V. The amount payable after discount  

Possible options for the answer:

a) I, II, and III

b) I and III

c) II, IV, and V

d) II and IV  

For this case we want to calculate the amount payable by the customer after the discounts.

And for this case is always necessary the value of the purchase so option II is true. The percent of discount is given so then option I is not true since we know this value.

The option III is not required since the discount is based on the info and if the customer have ID card so then this value is not necessary.

For option IV is necessary know the ID card in order to identify if the person have a permanent or non permanent card in order to apply discounts, this information is useful

And for the last option V that's not an input, since represent the output desired.

So then the correct options are II and IV

d) II and IV  

Answer:

11548KJ/kg

10641KJ/kg

Explanation:

Stagnation enthalpy:

[tex]h_{T} = c_{p}*T + \frac{V^2}{2}[/tex]

given:

cp = 1.0 KJ/kg-K

T1 = 25 C +273 = 298 K

V1 = 150 m/s

[tex]h_{1} = (1.0 KJ/kg-K) * (298K) + \frac{150^2}{2} \\\\h_{1} = 11548 KJ / kg[/tex]

Answer: 11548 KJ/kg

Using Heat balance for steady-state system:

[tex]Flow(m) *(h_{1} - h_{2} + \frac{V^2_{1} - V^2_{2} }{2} ) = Q_{in} + W_{out}\\[/tex]

Qin = 42 MW

W = -100 KW

V2 = 400 m/s

Using the above equation

[tex]50 *( 11548- h_{2} + \frac{150^2 - 400^2 }{2} ) = 42,000 - 100\\\\h_{2} = 10641KJ/kg[/tex]

Answer: 10641 KJ/kg

c) We use cp because the work is done per constant pressure on the system.

Answer:

The power is reduced by 19 percent.

Explanation:

The formula of power is given by:

[tex]P = \frac{V^{2}}{R}[/tex]

In which V is the voltage, and R is the resistance.

I am going to use R = 1 in both cases.

With the original voltage, V = 1, we have

[tex]P = \frac{V^{2}}{R} = \frac{1}{1} = 1[/tex]

With the modified voltage, V = 0.9, we have:

[tex]P = \frac{V^{2}}{R} = \frac{0.9^{2}}{1} = 0.81[/tex]

So the power is reduced by 1-0.81 = 0.19 = 19 percent.

Answer:

     int CENTS_PER_POUND = 25;

     shipWeightPounds = scnr.nextInt();

     shipCostCents = (shipWeightPounds * CENTS_PER_POUND) + FLAT_FEE_CENTS;

Explanation:

We declare a constant named CENTS_PER_POUND in the first line of ode as the answer.

scnr.nextInt(); is how we get our imput, then we declare it to shipWeightPounds.

and lastly the math, we get the weight and multiply it by how much the money costs per weight, and then lastly add the flat fee bc its mandatory fee.

Full Code:

import java.util.Scanner;

public class ShippingCalculator {

  public static void main(String[] args) {

     Scanner scnr = new Scanner(System.in);

     int shipWeightPounds;

     int shipCostCents = 0;

     final int FLAT_FEE_CENTS = 75;

     int CENTS_PER_POUND = 25;

     shipWeightPounds = scnr.nextInt();

     shipCostCents = (shipWeightPounds * CENTS_PER_POUND) + FLAT_FEE_CENTS;

     System.out.println("Weight(lb): " + shipWeightPounds);

     System.out.println("Flat fee(cents): " + FLAT_FEE_CENTS);

     System.out.println("Cents per pound: " + CENTS_PER_POUND);

     System.out.println("Shipping cost(cents): " + shipCostCents);

  }

}

Answer:

#Python

import re

password = input("Enter password: ")

p = re.compile('^[ABCDabcd]+.*[^e-zE-Z5-9_]{2,}[1-4][1-4]+$')

match = p.search(password)

if match == None:

    print('L(r) != L -> Incorrect password')

else:

    print('L(r) = L -> Correct password')

Explanation:

The regular expression needed is:

^[ABCDabcd]+.*[^e-zE-Z5-9_]{2,}[1-4][1-4]+$

To understand why see the step by step of the regex:

Note: if you don't have python you can use an online regex checker like myregextester, note that the string must be at least five characters long because you need one letter at the beginning, at least two characters in the middle and two numbers at the end.

Answer:

The moist unit weight of compaction = 109.05 lb/ft3

Explanation:

In order to determine the moist unit weight, the dry unit weight has to be evaluated first. If Y is the moist unit weight, then:

Y = Yd (1 + m)

Where:

Yd = dry unit weight

m = moisture content of soil = 8% = 0.08

But the dry unit weight is unknown. In order to calculate the dry unit weight, we will make use of the formula for relative density R;

R = [(Yd — Ydmin) ÷ (Ydmax — Ydmin)] × [Ydmax ÷ Yd]

Where:

R = relative density = 60% = 0.6

Yd = dry unit weight

Ydmin = minimum dry weight = 92 lb/ft3

Ydmax = maximum dry weight = 108 lb/ft3

Therefore R = 0.6 = [(Yd — 92) ÷ (108 — 92)] × [108/Yd]

0.6 = [(Yd — 92)/16] × [108/Yd], or

0.6 = (0.0625Yd — 5.75) × [108/Yd]

0.6Yd = 6.75Yd — 621

6.75Yd — 0.6 Yd = 621

6.15Yd = 621

And Yd = 100.98 lb/ft3 = dry unit weight

But we are asked to find the moist unit weight = Y = Yd (1 + m)

where Yd = dry unit weight and m = moisture content of soil = 8% = 0.08

Therefore, Y = 100.98 (1 + 0.08) = 109.05 lb/ft3.

Answer:

(A) Maximum voltage will be equal to 333.194 volt

(B) Current will be leading by an angle 54.70

Explanation:

We have given maximum current in the circuit [tex]i_m=385mA=385\times 10^{-3}A=0.385A[/tex]

Inductance of the inductor [tex]L=400mH=400\times 10^{-3}h=0.4H[/tex]

Capacitance [tex]C=4.43\mu F=4.43\times 10^{-3}F[/tex]

Frequency is given f = 44 Hz

Resistance R = 500 ohm

Inductive reactance will be [tex]x_l=\omega L=2\times 3.14\times 44\times 0.4=110.528ohm[/tex]

Capacitive reactance will be equal to [tex]X_C=\frac{1}{\omega C}=\frac{1}{2\times 3.14\times 44\times 4.43\times 10^{-6}}=816.82ohm[/tex]

Impedance of the circuit will be [tex]Z=\sqrt{R^2+(X_C-X_L)^2}=\sqrt{500^2+(816.92-110.52)^2}=865.44ohm[/tex]

So maximum voltage will be [tex]\Delta V_{max}=0.385\times 865.44=333.194volt[/tex]

(B) Phase difference will be given as [tex]\Phi =tan^{-1}\frac{X_C-X_L}{R}=\frac{816.92-110.52}{500}=54.70[/tex]

So current will be leading by an angle 54.70

To estimate the drag force on the prototype submarine, use the principle of dynamic similarity and scale up the measured drag force by a factor of 5.

To estimate the drag force on the prototype submarine, we can use the principle of dynamic similarity. The drag force is directly proportional to the density of the fluid, the velocity of the fluid flow, and the reference area of the object. Since the model submarine is one-fifth the size of the prototype, we need to scale up the measured drag force by a factor of 5. Additionally, we need to account for the difference in fluid density between air and water, as well as the viscosity of the fluid.

The drag force on the prototype submarine can be estimated using the equation:

Drag force (prototype) = Drag force (model) x (scale factor)^2 x (fluid density ratio) x (viscosity ratio)

By plugging in the given values and solving the equation, we can estimate the drag force on the prototype submarine.

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Answer:

B.gabbro

Explanation:

Gabbro is a coarse-grained, dark-colored igneous

rock . It is usually black or dark green in color and composed mainly of the minerals plagioclase and augite. It is the most abundant rock in the deep oceanic crust. Gabbro is used in construction.

Answer:

The java program to print all even numbers from 1 to 100 is given below.

import java.util.*;

public class Program

{

// integer array of size 100

static int[] num = new int[100];

public static void main(String[] args) {

// array initialized using for loop with values from 1 to 100

for(int j=0; j<100; j++)

{

num[j] = j+1;

}

System.out.println("Even numbers from 1 to 100 are ");

// enhanced for loop

for(int n : num)

{

// testing each element of the array

// only even numbers will be displayed

if( (n%2) == 0)

System.out.print(n + " ");

}

}

}

OUTPUT

Even numbers from 1 to 100 are  

2 4 6 8 10 12 14 16 18 20 22 24 26 28 30 32 34 36 38 40 42 44 46 48 50 52 54 56 58 60 62 64 66 68 70 72 74 76 78 80 82 84 86 88 90 92 94 96 98 100

Explanation:

The program works as described.

1. An integer array, num, of size 100 is declared.

2. Inside for loop which executes 100 times, array is initialized with numbers from 1 to 100.

3. An enchanced for loop differs from normal for loop such that it doesn't has initialization and increment or decrement conditions.

4. The syntax for an enchanced for loop is shown below.

for( datatype variable_name : array_name )

{ }

In the above syntax, the datatype of the variable_name should be the same as that of the array_name.

The array used in program is shown below.

for(int n : num)

5. Inside enhanced for loop, if statement is included to test each element of array, num, for even or odd number.

if( (n%2) == 0)

6. If the number is even, it is displayed followed by a space.

System.out.print(n + " ");

7. The method println() differs from print() such that new line is inserted after the message is displayed.

8. This program can also be used to display odd numbers by changing the condition inside if statement.

Answer:

"- Set the Orders object's sharing settings to Private in the Org-Wide Defaults

_Provide each partner with their own Salesforce login set to API Enabled on the profile

-Develop a custom Apex web service using the "With Sharing" keyword"

Explanation:

Universal Containers (UC) has a requirement to expose a web service to their business partners. The web service will be used to allow each business partner to query UC's Salesforce instance to retrieve the status of orders. The business partner should only be allowed access to orders for which the business partner is the fulfillment vendor. The Architect does not want the business partners to utilize the standard APIs and would prefer a custom API be developed. Which three design elements should the Architect consider in order to ensure the data security of the solution?

A. Query the Orders object with Dynamic SOQL based upon the fulfillment ID.

B. Set the Orders object's sharing settings to Private in the Org-Wide Defaults

C. Provide each partner with their own Salesforce login set to API Enabled on the profile.  

D. Develop a custom Apex web service with a fulfillment ID input attribute

E. Develop a custom Apex web service using the "With Sharing" keyword.

The above should be a follow up option to the question

The Architect should consider the following design

"- Set the Orders object's sharing settings to Private in the Org-Wide Defaults

_Provide each partner with their own Salesforce login set to API Enabled on the profile

-Develop a custom Apex web service using the "With Sharing" keyword"

 There is need for some sharing rule between the architect and the user

Answer:

p = 2*10^(-7) ohm m

Explanation:

The resistivity and Resistance relationship is:

[tex]p = \frac{R*A}{L}[/tex]

For lowest resistivity with R < 100 ohms.

We need to consider the possibility of current flowing across minimum Area and maximum Length.

So,

Amin = 2nm x 10 nm = 2 * 10^(-16) m^2

Lmax = 100nm

Using above relationship compute resistivity p:

 [tex]p = \frac{100*2*10^(-16)}{100*10^(-9)} \\\\p = 2 * 10^(-7)[/tex]

Answer: p = 2*10^(-7) ohm m

Answer: General purpose branch circuit

Explanation:

General purpose branch circuit are the type of circuits that are used mainly to supply light to two or more receptacle outlets for small appliances. This circuits are about 120v can be used either in residential, commercial and industrial buildings.

The stress in the brass cylinder can be calculated using a thermal stress formula that considers the modulus of elasticity, coefficient of linear expansion, and temperature change of the brass. Specific material properties for brass are needed to plug into the formula.

The stress in the cylinder can be found by considering that an increase in temperature will cause the brass cylinder BD to expand, while the steel rod AC remains the same length. This will cause an extra stress in the brass cylinder due to the constraints. The stress can be calculated using the formula σ = EαΔT where:

In order to use this thermal stress formula, you will need to look up the specific properties for brass in a materials textbook or reliable online resource. Substitute these values into the formula to get the stress in the brass cylinder caused by the temperature change.

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Answer:

Explanation:

Given that

initial velocity ,[tex]v= 3 m/s[/tex]

[tex]a=-1.1v^{\dfrac{1}{2}}[/tex]

We know that

[tex]a=v\dfrac{dv}{dx}[/tex]

Lets take x is the distance before coming to the rest.

The final speed of the particle = 0 m/s

[tex]v\dfrac{dv}{dx}=-1.1v^{\dfrac{1}{2}}[/tex]

[tex]\dfrac{dv}{dx}=-1.1v^{-\dfrac{1}{2}}[/tex]

[tex]v^{\dfrac{1}{2}}{dv}=-1.1dx[/tex]

[tex]\int_{3}^{0}v^{\dfrac{1}{2}}{dv}=-\int_{0}^{x}1.1dx[/tex]

[tex]\left [v^{\dfrac{3}{2}}\times \dfrac{2}{3}\right]_3^0=-1.1x[/tex]

[tex]3^{\dfrac{3}{2}}\times \dfrac{2}{3}=1.1x[/tex]

[tex]x=\dfrac{3.46}{1.1}\ m\\x=3.14\ m[/tex]

(b)time taken by it

[tex]a=\frac{\mathrm{d} v}{\mathrm{d} t}=-1.1\sqrt{v}[/tex]

[tex]\int_{3}^{0}\frac{dv}{\sqrt{v}}=-1.1\int_{0}^{t}dt[/tex]

[tex]\int_{0}^{3}\frac{dv}{\sqrt{v}}=1.1\int_{0}^{t}dt[/tex]

[tex]2\times 3\sqrt{3}=1.1t[/tex]

[tex]t=9.44\ s[/tex]

To determine the minimum hose diameter for lifting a 14 kg dog with a vacuum cleaner, physics principles related to pressure and force are applied. The calculation involves the dog's weight and the pressure difference a vacuum needs to create over the hose's cross-sectional area. However, without specific vacuum specifications, an exact diameter cannot be determined.

Calculating the Minimum Hose Diameter for a Vacuum Cleaner to Lift a Dog

To determine the minimum hose diameter of an ideal vacuum cleaner that could lift a 14 kg dog off the floor, we need to understand the principles of pressure and force in a vacuum system. This involves a bit of physics, specifically relating to the pressure difference created by the vacuum and the surface area over which this pressure acts.

The force required to lift the dog can be calculated using the formula F = m × g, where m is the mass of the dog (14 kg) and g is the acceleration due to gravity (approximately 9.8 m/s2). This gives us a force of approximately 137.2 N (newtons).

To lift the dog, the vacuum cleaner must create a pressure difference greater than the weight of the dog distributed over the area of the hose's opening. The pressure (Π) required can be found using Π = F/A, where A is the cross-sectional area of the hose. To find the minimum diameter, we rearrange the area formula A = πr2 (where r is the radius of the hose) to solve for diameter, taking into account that the area must be sufficient to create a pressure difference capable of lifting the dog.

Without specific pressure values from a vacuum cleaner, we cannot calculate an exact diameter but can assert the importance of a vacuum cleaner's pressure capability and the diameter's role in generating enough lift. In an ideal scenario, the vacuum would have to reduce the air pressure significantly inside the hose compared to the atmospheric pressure outside to create enough lift force.

Therefore, while this offers a theoretical framework, the practical application would depend on specific vacuum cleaner specifications, including its ability to create a low enough pressure and maintain a high flow rate, which were not provided in this question.

Answer:

c < 7

Explanation:

The cardinal indicates the number or quantity of the elements of a set, be this finite or infinite quantity.

Given, A = {1, 2, 42, 57, 99, 538, 677}  

B = {1, 5, 6, 7, {2, 3} }

C = {1, {7}, {8, 9} }

Let's say the cardinality of the subset is: c

Inequality that represents the cardinality of any proper subset of A is: c < 7

Hope this helps!

An inequality that represents the cardinality of any proper subset of A is c<7.

Given, A = {1, 2, 42, 57, 99, 538, 677}

B = {1, 5, 6, 7, {2, 3} }

C = {1, {7}, {8, 9} }

Inequalities are the mathematical expressions in which both sides are not equal. In inequality, unlike in equations, we compare two values. The equal sign in between is replaced by less than (or less than or equal to), greater than (or greater than or equal to), or not equal to sign.

Let's say the cardinality of the subset is: c

Inequality that represents the cardinality of any proper subset of A is: c < 7

Therefore, an inequality that represents the cardinality of any proper subset of A is c<7.

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Answer:

public static int average(int j, int k) {

return (int)(( (long)(i) + (long)(j) ) /2 );

}

Explanation:

The above code returns the average of two integer variables

Line 1 of the code declares a method along with 2 variables

Method declared: average of integer data type

Variables: j and k of type integer, respectively

Line 2 calculates the average of the two variables and returns the value of the average.

The first of two integers to average is j

The second of two integers to average is k

The last parameter ensures average using (j+k)/2

Answer:

C++ snippet is given below with appropriate comments and explanation

Explanation:

Code snippet:

double average=0;//declaring variable

      //using for loop

      for(int i=0;i<grades.length;i++)

      {

      average+=grades[i];//add each grade to average

      }

      average/=grades.length;//find average

Explanation :

Above code snippet need a for loop to add each grade from the array to the variable average,

average/=grades.length; this will compute average.

Answer:

58.44 g/mol The Molarity of this concentration is 0.154 molar

Explanation:

the molar mass of NaCl is 58.44 g/mol,

0.9 % is the same thing as 0.9g of NaCl , so this means that 100 ml's of physiological saline contains 0.9 g of NaCl.  One liter of physiological saline must contain 9 g of NaCl.  We can determine the molarity of a physiological saline solution by dividing 9 g by 58 g... since we have 9 g of NaCl in a liter of physiological saline, but we have 58 grams of NaCl in a mole of NaCl.  When we divide 9 g by 58 g, we find that physiological saline contains 0.154 moles of NaCl per liter.  That means that physiological saline (0.9% NaCl) has a molarity of 0.154 molar.  We can either express this as 0.154 M or 154 millimolar (154 mM).

Answer:

Aqueous solution of ionic compounds conduct electricity while solid ionic compounds don't.

Explanation:

Ionic compound conduct electricity when liquid or in aqueous solution that is resolved in water because the ionic bonds of the compound become weak and the ions are free to move from place to place.

Ionic compounds don't conduct electricity while in solid state because the ionic bonds are to strong and ions cannot move around with lack of space for movement which makes the electric conductivity zero.

Solid ionic compounds don't have any electrical conductivity as they are not free to move. Hence they lack the free space as compared to the molten or aqueous solution where there exist some gaps and pockets.

The solids ions that dissolve in the water are called electrolytes as compounds such as acids.

Learn more about the conductivity results observed for ionic compounds in the solid-state.

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Answer:

Issues addressed by Information Assurance (AI) that are often not addressed by Information Security:  

- Ensures the quality of information

- Ensures reliability of information

- Ensures retrievability of information

- Provides information restoration systems

- Provides an assorted response options for retrieving information  

Explanation:

Both, Information Assurance and Information Protection (or Information Security as defined by the NIST), provide preventive measures to uphold information systems´ integrity, confidentiality for protecting personal privacy and proprietary information with authorized restrictions on access and disclosure, and availability, ensuring protection of information systems from unauthorized access, use, disclosure, disruption, modification, or destruction.

Information protection also uses security solutions, like encryption and other technologies. It can be considered as a sub-component of information assurance.

Differentiating both terms can be tricky, as the terms are inherently linked and both aim integrity of information preservation.

In addition to the benefits provided by information protection, information assurance also focuses on data integrity, authenticity, reliability, usability, non-repudiation, confidentiality, availability and timely access to information.  It means a broader strategic initiative comprised of a wide range of information protection and management processes.

Answer:

The solution code is written in Java.

Explanation:

To ask for the user input for two whole numbers and an operator, we can use Java Scanner class object. Since the input operator is a string, we can use nextLine() method to get the operator string (Line 3). We use nextInt() method to get whole number input (Line 5 & 7).

Next we use the switch keyword and pass the operator into the switch structure to determine which case statement should be executed. For example,  if the input operator is "*" the statement  "result = num1 * num2; " will run and multiply num1 with num2.

Answer:

The resistances of both coils are 131.7 Ω and 29.64 Ω.

Explanation:

Since, there are two coils, they can be used independently or in series or parallel. The power is given as:

Power = P = VI

but, from Ohm's Law:

V = IR

I = V/R

therefore,

P = V²/R

R = V²/P

Hence, the resistance (R) and (P) are inversely proportional. Therefore, the maximum value of resistance will give minimum power, that is, 300 W. And the maximum resistance will be in series arrangement, as in series the total resistance gets higher than, any individual resistance.

Therefore,

Rmax = V²/Pmin = R1 + R2

R1 + R2 = (220 V)²/300 W

R1 + R2 = 161.333 Ω    ______ en (1)

Similarly, the minimum resistance will give maximum power. And the minimum resistance will occur in parallel combination. Because equivalent resistance of parallel combination is less than any individual resistance.

Therefore,

(R1 R2)/(R1 + R2) = (220 V)²/2000 W

using eqn (1), we get:

(R1 R2) / 161.333 Ω = 24.2 Ω

R1 R2 = 3904.266 Ω²

R1 = 3904.266 Ω²/R2  _____ eqn (2)

Using this value of R1 in eqn (1), we get:

3904.266/R2 +R2 = 161.333

(R2)² - 161.333 R2 +3904.266 = 0

Solving this quadratic eqn we get two values of R2 as:

R2 = 131.7 Ω     OR     R2 = 29.64 Ω

when ,we substitute these values in eqn (1) to find R1, we get get the same two values as R2, alternatively. This means that the two coils have these resistance, and the order does not matter.

Therefore, the resistance of both coils are found to be 131.7 Ω and 29.64 Ω

Answer:

2.14 ft

Explanation:

We will use the following equation:

[tex]L = \frac{R_{T} * A}{p_{20C}*(1+\alpha _{20C}*dt ) }[/tex]

Data obtained:

[tex]R_{15.3 F , -9.27 C} = 15.3 ohms\\A_{28-gauge} = 8.2*10^(-8) m^2\\p_{20 C} = 1.723*10^(-6)\\\alpha _{20C} = 0.00393\\ dt = 20 - (-9.27) = 29.28[/tex]

Using the above equation:

[tex]L = \frac{15.3 * 8.2*10^(-8)}{1.723*10^(-6)*(1+0.00393*29.28 ) }\\\\L =0.6530 m = 2.14 ft[/tex]

Answer:

1. the bulb of the thermometer must be in the center of the lower calorimeter, about one inch from the bottom.

2.thermometer must face you to read

Explanation:

During an actual run with the calorimeter, there are two important criteria which must be satisfied by a correctly positioned thermometer. These two criteria include;

1. the bulb of the thermometer must be in the center of the lower calorimeter, about one inch from the bottom.

2. thermometer must face you to read

The thermometer must be fully immersed without touching the calorimeter’s sides or bottom and positioned to minimize heat exchange with the external environment to ensure accurate temperature readings.

When using a calorimeter, it is crucial to ensure that the thermometer is correctly positioned to obtain accurate measurements. The two important criteria for correctly positioning the thermometer in a calorimeter are:

1. Thermal Equilibrium:

  - The thermometer must be fully immersed in the substance being measured (typically a liquid) without touching the sides or the bottom of the calorimeter. This ensures that the thermometer accurately reflects the temperature of the substance rather than the container.

  - The immersion should be deep enough so that the thermometer's bulb is surrounded by the substance, allowing it to reach thermal equilibrium with the substance. This helps in obtaining a consistent and accurate temperature reading.

2. Minimize Heat Exchange with the Environment:

  - The thermometer should be positioned in a way that minimizes heat exchange with the external environment. The calorimeter is designed to be an insulated system, so the thermometer should not introduce significant thermal disturbance.

  - The top of the calorimeter should be closed or covered as much as possible to prevent heat loss or gain from the surroundings, which could affect the temperature reading. The thermometer should pass through a small hole or a sealed opening to maintain the insulation integrity of the calorimeter.

By adhering to these criteria, the thermometer can provide precise and reliable temperature measurements, which are essential for accurate calorimetric calculations.

Answer:

discharge = 0.310976 m³/s

Explanation:

given data

rectangular channel  wide = 2.9 m

length of weir L = 1.9 m

water level H = 0.2 m

solution

we get here discharge that is express as

discharge = [tex]\frac{2}{3} * C_d * L* \sqrt{2g} * H^{\frac{3}{2} }[/tex]    ............................1

we consider here Coefficient of discharge Cd = 0.62

put here value we get

discharge = [tex]\frac{2}{3} * 0.62 * 1.9* \sqrt{2*9.8} * 0.2^{\frac{3}{2} }[/tex]

discharge = 0.310976 m³/s

Answer:

Input power of the geothermal power will be 686000 J

Explanation:

We have given density of brine [tex]\rho =1050kg/m^3[/tex]

Rate at which brine is pumped [tex]V=0.3m^3/sec[/tex]

So mass of the pumped per second

Mass = volume × density = [tex]1050\times 0.3=315[/tex] kg/sec

Acceleration due to gravity [tex]g=9.8m/sec^2[/tex]

Depth h = 200 m

So work done [tex]W=mgh=315\times 9.8\times 200=617400J[/tex]

Efficiency is given [tex]\eta =0.9[/tex]

We have to fond the input power

So input power [tex]=\frac{617400}{0.9}=686000J[/tex]

So input power of the geothermal power will be 686000 J

Answer:

558.1918 kilocalories = 558191.8 calories

Explanation:

Data provided in the question:

Atmospheric pressure = 84.6 KPa

Mass of water, m = 900 g = 0.90 kg

Temperature = 15°C

Now,

Temperature at 84.6 KPa = 94.77°C

Therefore,

Heat energy required = m(CΔT + L)

here,

C is the specific heat of the water = 4.2 KJ/kg.°C

L = Latent heat of water = 2260 KJ/kg

Thus,

Heat energy required = 0.90[ 4.2 × (94.77 - 15) + 2260 ]

= 2335.53 KJ

also,

1 KJ = 0.239  Kilocalories

Therefore,

2335.53 KJ = 0.239 × 2335.53 Kilocalories

= 558.1918 kilocalories = 558191.8 calories

Answer:

The plot of the function production rate m(t) (in kg/min) against time t (in min) is attached to this answer.

The production rate function M(t) is:

[tex]m(t)=[H(t)\cdot10+H(t-20)\cdot5-H(t-80)\cdot14+H(t-81)\cdot9]kg/min[/tex] (1)

The Laplace transform of this function is:

[tex]\displaystyle m(s)=[\frac{10+5e^{-20s}-14e^{-80s}+9e^{-81s}}{s}]kg/min[/tex]    (2)

Explanation:

The function of the production rate can be considered as constant functions by parts in the domain of time. To make it a continuous function, we can use the function Heaviside (as seen in equation (1)). To join all the constant functions, we consider at which time the step for each one of them appears and sum each function multiply by the function Heaviside.

For the Laplace transform we use the following rules:

[tex]\mathcal{L}[f(x)+g(x)]=\mathcal{L}[f(x)]+\mathcal{L}[g(x)]=F(s)+G(s)[/tex]    (3)

[tex]\mathcal{L}[aH(x-b)]=\displaystyle\frac{ae^{-bs}}{s}[/tex]    (4)