Perform the convolution of x[n] = [x[0]=3 5 7 9] with h[n]= [h[0]=1 2 3] using DFT. You can use MATLAB. 2) Perform the N=5 point circular convolution of x and h using DFT. 3) Perform the N=5 point circular convolution of x and h in time-domain. 4) Perform the convolution of x[n]= [3, x[0]=5 79] with h[n] = [h[0]=1 2 3] using DFT. What is the difference between Question 1 and this case?
Answers
Convolution is an essential operation in digital signal processing, which combines two signals to generate a third signal.
The convolution between the two discrete-time signals is calculated as a sum of the product of one signal with a time-reversed version of the other signal.To perform convolution of x[n] = [x[0]=3 5 7 9] with h[n]= [h[0]=1 2 3] using DFT, we will use the following procedure: 1. First, obtain the DFT of x[n] and h[n]2. Multiply X[k] with H[k]3.
Obtain the inverse DFT of the resulting productThe MATLAB code is shown below:% 1) Convolution using DFTx = [3 5 7 9];
h = [1 2 3];X = fft(x); % DFT of xH = fft(h); % DFT of hY = X.*H; % Product of X and HD = ifft(Y); % Inverse DFT of the product% Display the resultdisp('Convolution using DFT:');
disp(D);% 2) N=5 point circular convolution using DFTx = [3 5 7 9];
h = [1 2 3];N = 5;X = fft(x,N); % DFT of xH = fft(h,N); % DFT of hY = X.*H; %.
Product of X and HZ = ifft(Y); % Inverse DFT of the product% Display the resultdisp('N=5 point circular convolution using DFT:');disp(Z);% 3) N=5 point circular convolution in time-domainx = [3 5 7 9];h = [1 2 3];N = 5;Y = zeros(1,N);for n = 1:
Nfor k = 1:NY(n) = Y(n) + x(k)*h(mod(n-k,N)+1);
endend% Display the resultdisp('N=5 point circular convolution in time-domain:');
disp(Y);% 4) Convolution using DFTx = [3 5 79];h = [1 2 3];X = fft(x); % DFT of xH = fft(h);
% DFT of hY = X.*H; % Product of X and HD = ifft(Y);
% Inverse DFT of the product% Display the resultdisp('Convolution using DFT:');disp(D);
The difference between Question 1 and this case is the length of the signal. In Question 1, the length of the signal x[n] is 4, while the length of the signal x[n] is 3 in this case. Therefore, the N-point circular convolution will give different results in both cases.
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Related Questions
2. A wire, 1.5mm diameter, supports a mass of 60kg. calculate the stress.
Answers
Answer:
Therefore, the stress on the wire is 1.05 x 10^9 Pa.
Explanation:
To calculate stress, we need to know the force applied to the wire and its cross-sectional area.
The first step is to calculate the cross-sectional area of the wire:
A = πr² = π(0.75mm)² = π(0.00075m)² = 5.58 x 10^-7 m²
Next, we need to calculate the force applied to the wire due to the weight of the mass:
F = m*g = 60kg * 9.81 m/s² = 588.6 N
Now we can calculate the stress:
stress = F/A = 588.6 N / 5.58 x 10^-7 m² = 1.05 x 10^9 Pa
Therefore, the stress on the wire is 1.05 x 10^9 Pa.
Determine the design stress for bolts in a cylinder cover where the load is fluctuating due to gas pressure. The maximum load on the bolt is 50 kN and the minimum is 30 kN. The load is unpredictable and factor of safety is 3. The surface of the bolt is hot rolled and the surface finish factor is 0.9. During a simple tension test and rotating beam test on ductile materials (40 C 8 steel annealed), the following results were obtained : Diameter of specimen = 12.5 mm; Yield strength = 240 MPa; Ultimate strength = 450 MPa; Endurance limit = 180 MPa
Answers
Sorry I'm new and need points ty
A cylindrical bar of metal having a diameter of 20.5 mm and a length of 201 mm is deformed elastically in tension with a force of 46300 N. Given that the elastic modulus and Poisson's ratio of the metal are 60.5 GPa and 0.33, respectively, determine the following: (a) The amount by which this specimen will elongate in the direction of the applied stress. (b) The change in diameter of the specimen. Indicate an increase in diameter with a positive number and a decrease with a negative number.
Answers
Answer:
a) The amount by which this specimen will elongate in the direction of the applied stress is 0.466 mm
b) The change in diameter of the specimen is - 0.015 mm
Explanation:
Given the data in the question;
(a) The amount by which this specimen will elongate in the direction of the applied stress.
First we find the area of the cross section of the specimen
A = \(\frac{\pi }{4}\) d²
our given diameter is 20.5 mm so we substitute
A = \(\frac{\pi }{4}\) ( 20.5 mm )²
A = 330.06 mm²
Next, we find the change in length of the specimen using young's modulus formula
E = σ/∈
E = P/A × L/ΔL
ΔL = PL/AE
P is force ( 46300 N), L is length ( 201 mm ), A is area ( 330.06 mm² ) and E is elastic modulus (60.5 GPa) = 60.5 × 10⁹ N/m² = 60500 N/mm²
so we substitute
ΔL = (46300 N × 201 mm) / ( 330.06 mm² × 60500 N/mm² )
ΔL = 0.466 mm
Therefore, The amount by which this specimen will elongate in the direction of the applied stress is 0.466 mm
(b) The change in diameter of the specimen. Indicate an increase in diameter with a positive number and a decrease with a negative number.
Using the following relation for Poisson ratio
μ = - Δd/d / ΔL/L
given that Poisson's ratio of the metal is 0.33
so we substitute
0.33 = - Δd/20.5 / 0.466/201
0.33 = - Δd201 / 20.5 × 0.466
0.33 = - Δd201 / 9.143
0.33 × 9.143 = - Δd201
3.01719 = -Δd201
Δd = 3.01719 / - 201
Δd = - 0.015 mm
Therefore, The change in diameter of the specimen is - 0.015 mm
In a parallel circuit, as more resistances are added, what happens to the total circuit current?
Answers
Answer:
the equivalent resistance of the circuit decreases and the total current of the circuit increases.
Explanation:
hope this helps
5. It seems likely that young people will be at war with old people in another 15 or 20 years.
war
You can see it coming in the numbers. In 1900 only 1 percent of the population was older
than 75. Today 4 percent of all Americans are more than 75 years old, and in a few years it's
going to be 5 percent... 13 million people.
Answers
The following argument can best be interpreted as being inductive
What is an inductive sentence?An inductive sentence is one that arrives at conclusions by moving from the specifics to the general ideas. In the sentence above, there is a specific conclusion at the onset of the text.
This conclusion is that there will likely be a war between old and young people in some years to come. Now, the author gives general instances that led to the conclusion set forth in the sentence. Deductive sentences are the opposites of inductive sentences for they tend to move from general to specific.
Complete Sentence:
I. Determine whether the following arguments are best interpreted as being inductive or deductive. Also state the criteria you use in reaching your decision (i. e., the presence of indicator words, the nature of the inferential link between premises and conclusion, or the character or form of argumentation).
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Hey guys can anyone list chemical engineering advancement that has been discovered within the past 20 years
Answers
Nanopesticides. The world population keeps growing. ...
Enantio selective organocatalysis. ...
Solid-state batteries. ...
Flow Chemistry. ...
Porous material for Water Harvesting. ...
Directed evolution of selective enzymes. ...
From plastics to monomers. ...
Calculate the maximum value of shear flow, , in the web at a section 1m from the free end of the beam.
Answers
Answer:
See explanation
Explanation:
Since no figure was given, I'll explain how to do this problem theoretically. The formula for shear flow is \(q=\frac{VQ}{I}\) where V is the shear force, Q is the moment of area (more on this later), and I is the moment of inertia.
The first step to solve this problem is to find the resultant internal forces of the beam. This can be done in several ways, but the easiest is to solve the beam statically and draw a shear diagram to determine the maximum shear force V.
The second step to solving this problem is to determine the location of the neutral axis of the cross section if it is not given. The formula for the neutral axis is \(NA = \frac{\sum y*A}{\sum A}\). The y in this equation represents the middle of the small shapes that the web is divided into. An I-beam can be thought of as 3 rectangles, while a T-beam can be thought of as 2. The A in this formula represents the area of each of the rectangles (an I-beam will have 3 of these and a T-beam will have 2).
The third step for this problem is to find the moment of inertia. There are several formulas for moment of inertia depending on the shape of the cross section. I-beam's and T-beams both can be thought of as multiple rectangles, so they have the same base formula of \(I=\frac{1}{12}bh^3\) where b is the base of the rectangles and h is the height. For I-beams, the easiest way to calculate moment of inertia is to think of the entire cross section as a big rectangle that had two smaller rectangles cut out of it. The formula for this moment of inertia becomes \(I=\frac{1}{12} b_{big}h^{3} _{big}-\frac{1}{6}b_{small}h^{3}_{small}\). Note that this form of moment of inertia already takes into account subtracting 2 small rectangles. For T-beams, this approach will not work, so the parallel axis theorem must be used. The moment of inertia for the T-beam becomes \(I=\frac{1}{12}b_{1} h^{3}_{1} +b_{1}h_{1}dy_{1}^{2} +\frac{1}{12}b_{2} h^{3}_{2} +b_{2}h_{2}dy_{2}^{2}\) where the terms with the subscript 1 represent the first rectangle and the terms with the subscript 2 represent the second rectangle. The dy terms represent the distance from the center of that specific rectangle to the neutral axis.
The fourth step for this problem is to find Q. The formula to find Q is \(Q=\sum y'A'\) where y' represents the distance from the neutral axis to the center of the "wanted" point and A' is the area of the rectangle that has the wanted point at its center. (This would be the area above or below the thickness (t) if you were solving for maximum shear \(\tau=\frac{VQ}{It}\)).
The last step for this problem is to substitute the found values into the formula for shear flow \(q=\frac{VQ}{I}\). V came from step 1, Q came from step 4, and I came from step 3.
A vacuum-propelled capsule for a high-speed tube transportation system of the future is being designed for operation between two stations 10 km apart. If maximum accerlation and deceleration are to have a limiting magnitude of .6g and if velocities are to be limited to 400 km/h, determine the minimum time for the capsule to make the 10 km trip. answer t = 1.81 min
Answers
The minimum time for the vacuum-propelled capsule to make the 10 km trip is t = 1.81 minutes.
To determine the minimum time for the capsule to make the 10 km trip, we need to consider the limiting factors of maximum acceleration, maximum deceleration, and velocity limitation.
Maximum acceleration and deceleration:
Given that the maximum acceleration and deceleration have a limiting magnitude of 0.6g, we can convert this to meters per second squared (m/s^2) for calculations. One g is equivalent to 9.8 m/s^2.
Therefore, the maximum acceleration and deceleration are 0.6 * 9.8 = 5.88 m/s^2.
Velocity limitation:
The velocity is limited to 400 km/h. To convert this to meters per second (m/s), we divide by 3.6 (since 1 km/h = 1/3.6 m/s).
Therefore, the velocity limitation is 400 / 3.6 = 111.11 m/s.
Now, let's calculate the time using the equations of motion:
a. Calculate the time taken to accelerate from 0 m/s to the maximum velocity:
Using the formula v = u + at, where v is the final velocity, u is the initial velocity, a is the acceleration, and t is the time.
Initial velocity (u) = 0 m/s
Final velocity (v) = 111.11 m/s
Acceleration (a) = 5.88 m/s^2
Time taken to accelerate (t1) = (v - u) / a
b. Calculate the time taken to decelerate from the maximum velocity to 0 m/s:
Using the same formula v = u + at, where v is the final velocity, u is the initial velocity, a is the deceleration (the same as acceleration but with a negative sign), and t is the time.
Initial velocity (u) = 111.11 m/s
Final velocity (v) = 0 m/s
Deceleration (a) = -5.88 m/s^2 (negative sign because it is deceleration)
Time taken to decelerate (t2) = (v - u) / a
c. Calculate the time taken to travel at a constant velocity:
The distance traveled at a constant velocity is the remaining distance after acceleration and deceleration, which is 10 km - (2 * 10 km) = 0 km.
Time is taken at constant velocity (t3) = Distance / Velocity
d. Calculate the total time:
The total time taken is the sum of the time taken for acceleration (t1), deceleration (t2), and travel at a constant velocity (t3).
Total time = t1 + t2 + t3
By plugging in the values and performing the calculations, we arrive at the minimum time for the capsule to make the 10 km trip, which is t = 1.81 minutes.
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the steel used for light gauge steel framing differs from the steel discussed in steel frame construction chapter in that light gauge steel is:
Answers
The steel used for light guage steel framing differs from steel discussed in steel frame construction chapter in that light guage steel is cold-rolled.
In essence, cold rolled steel is hot rolled steel that has undergone annealing or temper rolling after being allowed to cool at room temperature. Compared to hot rolling, cold rolling creates steel with tighter dimensional tolerances and a larger range of surface treatments. Through the use of strength hardening, it is additionally up to 20% stronger than hot rolled.
Steel that has been cold rolled often has a better, more polished surface and tighter tolerances. Additionally, it produces shinier, oilier surfaces. Additional benefits include:
can be applied in specific situations.
stronger and harder compared to heat rolled steels.
a rise in hardness, resistance to tension breaking, and resistance to deformation brought on by work hardening.
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What does efficiency measure?
Answers
Answer:
Efficiency is defined as any performance that uses the fewest number of inputs to produce the greatest number of outputs. Simply put, you're efficient if you get more out of less.
Explanation:
Why do i pick the most exspensive hobbies
Airsoft and building pcs
Answers
Answer: You make more money
Explanation: A pc is like 2k+ to build so imagine all of the profits coming in from your business/work.
What is the transfer of energy from one object to another?
Answers
Answer:
Kinetic Energy
Explanation:
Energy is transferred from one object to another when a reaction occurs. Energy can be transferred from one object to another as heat, light, and motion.
DİGİTAL LOGİC DESİGN
Answers
Answer:
Uh- dude if you think I'm gonna download that, think twice...
An atom in a tetragonal unit cell has fractional coordinates of (0.1, 0.13, 0.2). Give the coordinates of the second atom in the unit cell that is related by the following (separately applied).
(a) Body centering.
(b) A center of symmetry at the origin.
(c) A mirror plane containing the x and z axes.
(d) A 42 axis parallel to z and passing through the origin.
(e) An a glide plane intersecting point (0.5, 0.5, 0.5).
Answers
The coordinates will be (a)0.6, 0.63,0.7 and (b)0.7,0.9, 0.87, 0.8 (c)0.6 and 0.7 (d)0.9, 0.87, 0.6 and (e)x+0.5, y+0.5, z+0.5.
(a) Body entering means we need to add 0.5, 0.5, 0.5 to the atomic position like 0.1 + 0.5, 0.13 + 0.5, 0.2 + 0.5 and we get new position that is
0.6, 0.63 and 0.7
(b) Center of symmetry will x, y, z into -x, -y, =z. Therefore the new position will be
-0.1, -0.13, -0.2 that is 0.9, 0.87, 0.8
(c) A mirror plane containing the x and z axes are 0.6 and 0.7 respectively
(d) The 42 will have the same effect as 4 fold axis plus the translation of the atom which c/4 and we get the new co-ordinates that is
-0.1, -0.13 and 0.4+0.2 which is
0.9, 0.87, 0.6
(e) it means that it will add 0.5, 0.5, 0.5 to each atomic position and thus for each x, y, z given position it will generate another one air x+0.5, y+0.5, z+0.5.
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Problem 07.015.a -
Determine the stress components after clockwise rotation of the element for the given state of stress. Determine the normal and the shearing stresses after the element shown has been rotated through 25 clockwise. (Round the final answers to two decimal places.) Normal stresses: σ_x= _____ksi (+ tensile; - compressive) σ_y=_____ k si (+ tensile: -compressive) Shearing stress: Tx'y'= ____ k si+ CCW on positive x-face)
Answers
To determine the stress components after a clockwise rotation of the element, we can use the transformation equations for plane stress.
Let's denote the initial stress components as σx, σy, and τxy, and the rotated stress components as σx', σy', and τx'y'. The angle of rotation is 25° clockwise.
First, we can calculate the normal stresses σx' and σy' using the following equations:
σx' = (σx + σy)/2 + (σx - σy)/2 * cos(2θ) + τxy * sin(2θ)
σy' = (σx + σy)/2 - (σx - σy)/2 * cos(2θ) - τxy * sin(2θ)
Next, we can determine the shearing stress τx'y' using the equation:
τx'y' = -(σx - σy)/2 * sin(2θ) + τxy * cos(2θ)
Substitute the given values for σx, σy, τxy, and θ into the equations above and solve for σx', σy', and τx'y'. Round the final answers to two decimal places.
Normal stresses:
σx' = _____ ksi (+ tensile; - compressive)
σy' = _____ ksi (+ tensile; - compressive)
Shearing stress:
τx'y' = _____ ksi (+ CCW on positive x-face)
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3. Steam is distributed on a site via a high-pressure and lowpressure steam mains. The high-pressure mains is at 40
bar and 350◦
C. The low-pressure mains is at 4 bar. The
high-pressure steam is generated in boilers. The overall
efficiency of steam generation and distribution is 75%. The
low-pressure steam is generated by expanding the highpressure stream through steam turbines with an isentropic
efficiency of 80%. The cost of fuel in the boilers is 3.5
$·GJ−1, and the cost of electricity is $0.05 KW−1·h−1. The
boiler feedwater is available at 100◦
C with a heat capacity of
4.2 kJ·kg−1·K−1. Estimate the cost of the high-pressure and low-pressure steam
Answers
A detailed calculation considering various factors such as efficiency, fuel cost, electricity cost, and heat capacity is necessary to determine the cost the high-pressure and low-pressure steam.
To estimate the cost of high-pressure and low-pressure steam, we need to consider the efficiency of steam generation and distribution, fuel cost, electricity cost, and heat capacity. Here's a step-by-step explanation:
Determine the energy content of high-pressure steam: Calculate the enthalpy of high-pressure steam using the given pressure and temperature values. Convert it to energy units (GJ) based on the heat capacity of steam.steam.Calculate the energy content of low-pressure steam: Use the isentropic efficiency of the steam turbine to find the enthalpy of the low-pressure steam after expansion. Convert it to energy units (GJ).Calculate the total energy content of steam generated: Multiply the energy content of high-pressure steam by the efficiency of steam generation and distribution to get the total energy content.Convert energy content to fuel and electricity costs: Multiply the total energy content by the fuel cost per GJ to get the cost of fuel. Additionally, calculate the cost of electricity by multiplying the total energy content by the electricity cost per KWh.Sum up the costs: Add the cost of fuel and the cost of electricity to obtain the total cost of high-pressure and low-pressure steam.By following these steps, you can estimate the cost of the high-pressure and low-pressure steam considering the provided parameters.
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Back Savers is a company that produces backpacks primarily for students. They are considering offering some combination of two different models—the Collegiate and the Mini. Both are made out of the same rip-resistant nylon fabric. Back Savers has a long-term contract with a supplier of the nylon and receives a 5000 square-foot shipment of the material each week. Each Collegiate requires 3 square feet while each Mini requires 2 square feet. The sales forecasts indicate that at most 1000 Collegiates and 1200 Minis can be sold per week. Each Collegiate requires 45 minutes of labor to produce and generates a unit profit of $32. Each Mini requires 40 minutes of labor and generates a unit profit of $24. Back Savers has 35 laborers that each provides 40 hours of labor per week. Management wishes to know what quantity of each type of backpack to produce per week. (b) Use the graphical method by hand to solve this model (NOT THE CORNER POINT METHOD).
Answers
For the transistor... VCE,sat = 0 V VBE,on = 1 V B = 100 Given that VBB = Vcc = 4 V, R1 = 1 k2, R2 = 3 k2, and Rc 40 , find the value of Ic hint: Think about one or both of the equivalent circuits, C1 and C2, as seen from the perspective of the dashed line. Ic = mA
Answers
To find the value of Ic for the given transistor and circuit parameters:
1. The base current (Ib) using the voltage divider rule for R1 and R2:
\(Vb = VBB *\frac{R2}{R1+R2}\)
\(= 4V * \frac{3k}{1k+3k}\)
= 3V
2. The base-emitter voltage (VBE) and the base current (Ib):
VBE = 1V (given)
\(Ib = \frac{(Vb - VBE)}{R1}\)
\(=\frac{3V-1V}{1K}\)
= 2mA
3. Use the given transistor gain (B) to find the collector current (Ic):
B = 100 (given)
Ic = B * Ib
= 100 * 2mA
= 200mA
Therefore, the value of Ic for the given transistor and circuit parameters is 200mA.
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Which of the following is false about most machine learning models?
They require numbers or collections of numbers as input.
They are flexible enough to handle all issues you might see in your dataset (lack of data, incorrect data, etc)
They are trained by iteratively adjusting their parameters to minimize a loss function.
Once trained, their model parameters can be used to make new predictions in a process called a “model inference algorithm.”
Answers
The false statement about most machine learning models is that: B. they are flexible enough to handle all issues you might see in your dataset (lack of data, incorrect data, etc).
What is machine learning?Machine learning (ML) is also referred to as deep learning or artificial intelligence (AI) and it can be defined as a subfield in computer science which is typically focused on the use of data-driven techniques (methods), computer algorithms, and technologies to develop a smart computer-controlled robot with an ability to automatically perform and manage tasks that are exclusively meant for humans or solved by using human intelligence.
Generally speaking, machine learning models are designed and developed to accept numerical data (numbers) or collections of numerical data (numbers) as an input.
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A soil sample, taken from a borrow pit has a specific gravity of soil solids of 2.66. The sample was taken to a materials laboratory and tested. The results of a standard Proctor test are tabulated below.
Weight of Soil (lb) Moisture Content (%)
3.20 12.8
3.78 13.9
4.40 15.0
4.10 15.7
3.70 16.6
3.30 18.1
The maximum dry density in lb/ft3 is most nearly:_______
Answers
Answer:
115 Ib/ft^3
Explanation:
To determine the maximum dry density in Ib/ft3 we have to calculate :
Bulk unit weight ( yb ) ; W / v
Dry unit weight ( yd. ) : yb / ( 1 + w )
For every set of data given
assuming v = 1/30 ft^3
calculating for the 3 data set ( maximum dry density )
weight of soil (W) = 4.40
moisture content (%) (w) = 15.0 = 0.15
Bulk unit weight (yb) = 4.40 / (1/30) = 132 Ib/ft^3
Dry unit weight ( yd. ) = 132 / ( 1 + 0.15 ) = 114.702 Ib/ft^3
therefore after calculations the maximum dry density in Ib/ft^3 ≈ 115 Ib/ft^3
Which is the correct statement regarding the relative Rf values of the starting methyl benzoate vs the product, methyl m-nitrobenzoate on a silica gel TLC plate. The product has a lower Rf value on a silica gel TLC plate because it is more polar than the starting methyl benzoate. The product has a lower Rf value on a silica gel TLC plate because it is less polar than the starting methyl benzoate. The product has a higher Rf value on a silica gel TLC plate because it is less polar than the starting methyl benzoate. The product has a higher Rf value on a silica gel TLC plate because it is more polar than the starting methyl benzoate.
Answers
The product has a higher Rf value on a silica gel TLC plate because it is less polar than the starting methyl benzoate. In general, on a silica gel TLC plate, compounds with lower polarity will have higher Rf values than more polar compounds.
On a silica gel TLC plate, the product (methyl m-nitrobenzoate) will have a higher Rf value than the starting material (methyl benzoate) because it is less polar. This is because the silica gel has a non-polar surface, and less polar compounds will have a stronger affinity for the surface of the silica gel. As a result, less polar compounds will move more slowly up the plate, giving them a higher Rf value. On the other hand, more polar compounds will have a weaker affinity for the non-polar silica gel, and will move more quickly up the plate, giving them a lower Rf value.
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A good place to get hints about how to answer a response question could be
a.
Your teacher
c.
Both of these
b.
The rest of the test
d.
None of these
Please select the best answer from the choices provided
A
B
C
D
Answers
Answer:
I think its A
Explanation:
...............................
what do you need to craft netherite ingots come on man you should know this
Answers
4 netherite scrap and 4 gold
in a crafting table
How is the foundation for a skyscraper different from a house?
Answers
Answer:
Shallow foundations, often called footings, are usually embedded about a metre or so into soil. ... Another common type of shallow foundation is the slab-on-grade foundation where the weight of the structure is transferred to the soil through a concrete slab placed at the surface.
Explanation:
Because I said so.
The acceleration of a particle is defined by the relation a = 9 − 3t2, where a and t are expressed in ft/s2 and seconds, respectively. The particle starts at t = 0 with v = 0 and x = 5 ft. Determine (a) the time when the velocity is again zero, (b) the position and velocity when t = 4 s, (c) the total distance travelled by the particle from t = 0 to t = 4 s.
Answers
(a) To find the time when the velocity is again zero, we set the velocity equal to 0 and solve for t:
0 = v0 + at = 9t - 3t^3
Solving for t, we find that t = ±1.
(b) To find the position and velocity when t = 4 s, we first need to find the velocity equation by integrating the acceleration equation:
v = ∫a = ∫(9 - 3t^2)dt = 9t - t^3 + C
Using the initial condition v(0) = 0, we find C = 0 and
v(t) = 9t - t^3
Next, we integrate v(t) to find the position equation:
x = ∫v = ∫(9t - t^3)dt = 3t^2 - t^4 + C
Using the initial condition x(0) = 5, we find C = 5 and
x(t) = 3t^2 - t^4 + 5
Evaluating x(t) and v(t) at t = 4 s, we have:
x(4) = 3(4^2) - 4^4 + 5 = 51
v(4) = 9(4) - 4^3 = -36
(c) To find the total distance travelled by the particle from t = 0 to t = 4 s, we need to find the distance between the initial and final positions:
d = x(4) - x(0) = 51 - 5 = 46 ft
So the total distance travelled by the particle from t = 0 to t = 4 s is 46 ft.
One good way to improve your gas mileage is to _____.
Answers
Perform a delete operation on the following min heap, what does the corresponding tree look like?
Answers
The root key of a Min Binary Heap must rank lowest among all other keys in the Binary Heap. For every node in a binary tree, the same property has to be recursively true.
The root Max (or Min) Heap is always cleared of the highest (or lowest) value. Get rid of the root node first. Move the last element from the previous level to the root in step two. Comparing this child node's value to that of its parent is the third step. The smallest key in the tree is stored at the root node of a Min Heap Binary Tree. The aforementioned definition holds true for each and every sub-tree in the tree. Here, the issue is the Min Heap property. Nearly every node must have two offspring, with the exception of the top two tiers. The replacement for the root node should be the lowest, rightmost item in the heap. Decrease the quantity.
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Consider a vapor compression system used for cooling a home and rejecting energy to the outdoor ambient. What will happen to the cooling COP as the temperature difference between the indoor air and the ambient air decreases
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In a vapor compression system used for cooling a home and rejecting energy to the outdoor ambient, the cooling COP (Coefficient of Performance) will decrease as the temperature difference between the indoor air and the ambient air decreases.
The cooling COP is a measure of the cooling efficiency of the system, which is defined as the ratio of the amount of cooling provided to the amount of energy consumed by the compressor. When the temperature difference between the indoor air and the ambient air decreases, the compressor has to work harder to remove the same amount of heat from the indoor air. This results in a decrease in the cooling efficiency of the system and hence a decrease in the cooling COP.
For example, if the outdoor ambient temperature is very high and the indoor air temperature is much lower, the cooling COP will be high
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select three of the prerequisites for becoming a civil engineer
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What are the corresponding minimum and maximum velocities that the rocket experiences? Express your answer as two numbers separated by a comma
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The corresponding minimum and maximum velocities that the rocket experiences are 23.195m/s and 37.249m/s.
How to calculate the value?The minimum value will be:
V(t) = 3t³ + (-24)t² + 54t
V(3.721) = 3(3.721)³ - 24(3.721)² + 54(3.721)
= 23.195m/s.
The maximum value will be:
V(.1613) = 3(1.613)³ - 24(1.613)² + 54(1.613)
= 37.249m/s
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