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BARSIC [14]
3 years ago
13

Let p: the book is interesting and q: the book has pictures.

Mathematics
1 answer:
777dan777 [17]3 years ago
4 0

Answer:

The notation p ∧ q represents the statement “The book is interesting  

✔ and  <-- Answer

the book has pictures.”

The notation p ↔ q represents the statement “The book is interesting  

✔ if and only if  <-- Answer

the book has pictures.”

The notation q ∨ p represents the statement “The book has pictures  

✔ or  <-- Answer

the book is interesting.”

The notation q → p represents the statement “The book is interesting  

✔ if <-- Answer

the book has pictures.”

Step-by-step explanation:

I took the test aswell.

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Arrange the systems of equations that have a single solution in Increasing order of the x-values in their solutions.
NemiM [27]

Complete question is;

Arrange the systems of equations that have a single solution in Increasing order of the x-values in their solutions.

1) 2x + y = 10

x - 3y = -2

2) x + 2y = 5

2x + y = 4

3) x + 3y = 5

6x - y = 11

4) 2x + y = 10

-6x - 3y = -2

Answer:

Arranging the systems in increasing value of x gives;

System 2, system 3, system 1

Step-by-step explanation:

1) 2x + y = 10 - - - (eq 1)

x - 3y = -2 - - - (eq 2)

Multiply eq 1 by 3 to get;

6x + 3y = 30

Add it to eq 2 to get;

7x = 28

x = 28/7

x = 4

2) x + 2y = 5 - - - (eq 1)

2x + y = 4 - - - (eq 2)

Multiply eq 2 by 2 to get;

4x + 2y = 8

Subtract eq 1 from it to get;

3x = 3

x = 3/3

x = 1

3) x + 3y = 5 - - - (eq 1)

6x - y = 11 - - - (eq 2)

Multiply eq 2 by 3 to get;

18x - 3y = 33

Add to eq(1) to get;

19x = 38

x = 38/19

x = 2

4) 2x + y = 10 - - - (eq 1)

-6x - 3y = -2 - - - (eq 2)

Make y the subject in eq 1 to get;

y = 10 - 2x

Put in eq (2);

-6x - 3(10 - 2x) = -2

-6x - 30 + 6x = -2

0 = 0

Thus,no solution exists.

Arranging the systems in increasing value of x gives;

System 2, system 3, system 1

3 0
3 years ago
List numbers that have 24 as a multiple
Vilka [71]
2,12, 1 ,24,3,8,4,3,6,
THese number has 24 as a multiple so they are actually factors
~JZ
Hope it helps
4 0
3 years ago
Read 2 more answers
If one quart is the same amount as 2 pints, how many are in 8 quearts?
Verizon [17]

Answer

16 pints

Step-by-step explanation:

its basically 8x2

6 0
3 years ago
Find a particular solution to the nonhomogeneous differential equation y′′+4y=cos(2x)+sin(2x).
I am Lyosha [343]
Take the homogeneous part and find the roots to the characteristic equation:

y''+4y=0\implies r^2+4=0\implies r=\pm2i

This means the characteristic solution is y_c=C_1\cos2x+C_2\sin2x.

Since the characteristic solution already contains both functions on the RHS of the ODE, you could try finding a solution via the method of undetermined coefficients of the form y_p=ax\cos2x+bx\sin2x. Finding the second derivative involves quite a few applications of the product rule, so I'll resort to a different method via variation of parameters.

With y_1=\cos2x and y_2=\sin2x, you're looking for a particular solution of the form y_p=u_1y_1+u_2y_2. The functions u_i satisfy

u_1=\displaystyle-\int\frac{y_2(\cos2x+\sin2x)}{W(y_1,y_2)}\,\mathrm dx
u_2=\displaystyle\int\frac{y_1(\cos2x+\sin2x)}{W(y_1,y_2)}\,\mathrm dx

where W(y_1,y_2) is the Wronskian determinant of the two characteristic solutions.

W(\cos2x,\sin2x)=\begin{bmatrix}\cos2x&\sin2x\\-2\cos2x&2\sin2x\end{vmatrix}=2

So you have

u_1=\displaystyle-\frac12\int(\sin2x(\cos2x+\sin2x))\,\mathrm dx
u_1=-\dfrac x4+\dfrac18\cos^22x+\dfrac1{16}\sin4x

u_2=\displaystyle\frac12\int(\cos2x(\cos2x+\sin2x))\,\mathrm dx
u_2=\dfrac x4-\dfrac18\cos^22x+\dfrac1{16}\sin4x

So you end up with a solution

u_1y_1+u_2y_2=\dfrac18\cos2x-\dfrac14x\cos2x+\dfrac14x\sin2x

but since \cos2x is already accounted for in the characteristic solution, the particular solution is then

y_p=-\dfrac14x\cos2x+\dfrac14x\sin2x

so that the general solution is

y=C_1\cos2x+C_2\sin2x-\dfrac14x\cos2x+\dfrac14x\sin2x
7 0
3 years ago
What is the sum of the first 10 terms of the sequence defined by an=3n-3?
netineya [11]
The answer is D. 135
3 0
3 years ago
Read 2 more answers
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