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2 years ago

Consider the equation 2x+1=16

Mathematics

2 answers:

Aliun [14]2 years ago

6 0

Step-by-step explanation:

2x + 1 = 16

2x = 15 (subtract 1 on both sides)

x = 7.5 (divide 2 om both sides)

Since 7.5 is not an integer, (a) is No.

However 7.5 is rational, therefore (b) is Yes.

photoshop1234 [79]2 years ago

6 0

Answer:

$2x + 1 = 16 \\ 2x = 15 \\ x =\frac{15}{2} \\ \boxed{x = 7.5 }$

a. Does the equation have a solution in the set of integers? ____

→As 7.5 is not a integer, the right answer is No.

b. Does the equation have a solution in the set of rational numbers? ____

→7.5 is a rational number, the right answer is Yes.

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2 years ago

Solve these linear equations in the form y=yn+yp with yn=y(0)e^at.

WINSTONCH [101]

Answer:

a) $y(t) = y_{0}e^{4t} + 2$ . It does not have a steady state

b) $y(t) = y_{0}e^{-4t} + 2$ . It has a steady state.

Step-by-step explanation:

a) $y' -4y = -8$

The first step is finding $y_{n}(t)$ . So:

$y' - 4y = 0$

We have to find the eigenvalues of this differential equation, which are the roots of this equation:

$r - 4 = 0$

$r = 4$

So:

$y_{n}(t) = y_{0}e^{4t}$

Since this differential equation has a positive eigenvalue, it does not have a steady state.

Now as for the particular solution.

Since the differential equation is equaled to a constant, the particular solution is going to have the following format:

$y_{p}(t) = C$

$(y_{p})' -4(y_{p}) = -8$

$(C)' - 4C = -8$

C is a constant, so (C)' = 0.

$-4C = -8$

$4C = 8$

$C = 2$

The solution in the form is

$y(t) = y_{n}(t) + y_{p}(t)$

$y(t) = y_{0}e^{4t} + 2$

b) $y' +4y = 8$

The first step is finding $y_{n}(t)$ . So:

$y' + 4y = 0$

We have to find the eigenvalues of this differential equation, which are the roots of this equation:

$r + 4 =$

$r = -4$

So:

$y_{n}(t) = y_{0}e^{-4t}$

Since this differential equation does not have a positive eigenvalue, it has a steady state.

Now as for the particular solution.

Since the differential equation is equaled to a constant, the particular solution is going to have the following format:

$y_{p}(t) = C$

$(y_{p})' +4(y_{p}) = 8$

$(C)' + 4C = 8$

C is a constant, so (C)' = 0.

$4C = 8$

$C = 2$

The solution in the form is

$y(t) = y_{n}(t) + y_{p}(t)$

$y(t) = y_{0}e^{-4t} + 2$

6 0

3 years ago

4. ABCD below is a rectangle. BE=6x+2 and ED=4x+6. Find the length of AC.

Nikolay [14]

Answer:

28 units

Step-by-step explanation:

ABCD is a rectangle. AC and BD are diagonals intersecting at point E.

Diagonals of a rectangle bisect each other.

$\therefore BE = ED$

$\therefore 6x + 2 = 4x + 6$

$\therefore 6x - 4x= 6-2$

$\therefore 2x= 4$

$\therefore x= \frac{4}{2}$

$\therefore x= 2$

$\therefore 6x + 2= 6*2+2= 12+2= 14$

$\therefore BE= 14\: units$

$\because BD = 2BE$

$\therefore BD = 2(14)= 28\: units$

$\because AC = BD$ (diagonals of a are equal in measure)

$\therefore AC = 28\: units$

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3 years ago