Plot the following trig functions using subplots, choosing an appropriate layout for the number of functions displayed. The subp
lots should include a title which is the equation displayed. The independent variable (angle) should vary from 0 to 360 degrees and the plots should use a solid red line.
1 answer:
The question is incomplete! The complete question along with Matlab code and explanation is provided below.
Question
Plot the following trig functions using subplots, choosing an appropriate layout for the number of functions displayed. The subplots should include a title which is the equation displayed. The independent variable (angle) should vary from 0 to 360 degrees and the plots should use a solid red line.
1. cos(u - 45)
2. 3cos(2u) - 2
3. sin(3u)
4. -2cos(u)
Matlab Code with Explanation:
u=[0:0.01:2*pi] % independent variable represents 0 to 360 degrees in steps of 0.01
y1=cos(2*pi*u-45); % function 1
y2=3*cos(2*pi*2*u)-2; % function 2
y3=sin(2*pi*3*u); % function 3
y4=-2*cos(2*pi*u); % function 4
subplot(4,1,1) % 4 rows, 1 column and at position 1
plot(u,y1,'r'); % this function plots y w.r.t u and 'r' is for red color
grid on % turns on grids
xlabel('u') % label of x-axis
ylabel('y1') % label of x-axis
title('y1=cos(2*pi*u-45)') % title of the plot
ylim([-3 3]) % limits of y-axis
xlim([0 2*pi]) % limits of x-axis
% repeat the same procedure for the remaining 3 functions
subplot(4,1,2)
plot(u,y2,'r');
grid on
xlabel('u')
ylabel('y2')
title('y2=3*cos(2*pi*2*u)-2')
ylim([-6 3])
xlim([0 2*pi])
subplot(4,1,3)
plot(u,y3,'r');
grid on
xlabel('u')
ylabel('y3')
title('y3=sin(2*pi*3*u)')
ylim([-3 3])
xlim([0 2*pi])
subplot(4,1,4)
plot(u,y4,'r');
grid on
xlabel('u')
ylabel('y4')
title('y4=-2*cos(2*pi*u)')
ylim([-3 3])
xlim([0 2*pi])
Output Results:
The first plot shows a cosine wave with a phase shift of 45°
The second plot shows that the amplitude of the cosine wave is increased and the wave is shifted below zero level into the negative y-axis because of -2 also there is a increase in frequency since it is multiplied by 2.
The third plot shows that the frequency of the sine wave is increased since it is multiplied by 3.
The fourth plot shows a cosine wave which is multiplied by -2 and starts from the negative y-axis.
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Answer:
The velocity at section is approximately 42.2 m/s
Explanation:
For the water flowing through the pipe, we have;
The pressure at section (1), P₁ = 300 kPa
The pressure at section (2), P₂ = 100 kPa
The diameter at section (1), D₁ = 0.1 m
The height of section (1) above section (2), D₂ = 50 m
The velocity at section (1), v₁ = 20 m/s
Let 'v₂' represent the velocity at section (2)
According to Bernoulli's equation, we have;
Where;
ρ = The density of water = 997 kg/m³
g = The acceleration due to gravity = 9.8 m/s²
z₁ = 50 m
z₂ = The reference = 0 m
By plugging in the values, we have;
50 m + 30.704358 m + 20.4081633 m = 10.234786 m +
50 m + 30.704358 m + 20.4081633 m - 10.234786 m =
90.8777353 m =
v₂² = 2 × 9.8 m/s² × 90.8777353 m
v₂² = 1,781.20361 m²/s²
v₂ = √(1,781.20361 m²/s²) ≈ 42.204308 m/s
The velocity at section (2), v₂ ≈ 42.2 m/s
Answer:
The given grammar is :
S = T V ;
V = C X
X = , V | ε
T = float | double
C = z | w
1.
Nullable variables are the variables which generate ε ( epsilon ) after one or more steps.
From the given grammar,
Nullable variable is X as it generates ε ( epsilon ) in the production rule : X -> ε.
No other variables generate variable X or ε.
So, only variable X is nullable.
2.
First of nullable variable X is First (X ) = , and ε (epsilon).
L.H.S.
The first of other varibles are :
First (S) = {float, double }
First (T) = {float, double }
First (V) = {z, w}
First (C) = {z, w}
R.H.S.
First (T V ; ) = {float, double }
First ( C X ) = {z, w}
First (, V) = ,
First ( ε ) = ε
First (float) = float
First (double) = double
First (z) = z
First (w) = w
3.
Follow of nullable variable X is Follow (V).
Follow (S) = $
Follow (T) = {z, w}
Follow (V) = ;
Follow (X) = Follow (V) = ;
Follow (C) = , and ;
Explanation:
Answer:
The attached figure shows the hydraulic circuit using one sequence valve to control two simultaneous operations performed in proper sequence in one direction only. In the other direction, both the operations are simultaneous.
When we keep the 4/2 DCV in crossed arrow position, oil under pressure is supplied to the inlet port of the sequence valve. It directly flows to Head end port-1. Hence Cylinder 'C1' extends first.
By the end of the extension of cylinder 'C1', pressure in the line increases and hence poppet of sequence valve is lifted off from its seat and allows oil to flow to port-2 and hence, Cylinder 'C2 extends completing the pressing operation.
In the straight-arrow position of 4/2 DCV the oil under pressure reaches the rod end of both the cylinders C1 and C2 simultaneously through port-3. This causes both the cylinders to retract simultaneously.
Also, a Flow control valve is provided tho control the velocity of clamping
Explanation:
find attached the figure
