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3 years ago

9 < 11, so 9(5) < 11(5) true or false?

Mathematics

1 answer:

Zolol [24]3 years ago

7 0

It is true since you’re multiplying the same number on both the sides

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y=c1e^x+c2e^−x is a two-parameter family of solutions of the second order differential equation y′′−y=0. Find a solution of the

vagabundo [1.1K]

The general form of a solution of the differential equation is already provided for us:

$y(x) = c_1 \textrm{e}^x + c_2\textrm{e}^{-x},$

where $c_1, c_2 \in \mathbb{R}$ . We now want to find a solution $y$ such that $y(-1)=3$ and $y'(-1)=-3$ . Therefore, all we need to do is find the constants $c_1$ and $c_2$ that satisfy the initial conditions. For the first condition, we have: $y(-1)=3 \iff c_1 \textrm{e}^{-1} + c_2 \textrm{e}^{-(-1)} = 3 \iff c_1\textrm{e}^{-1} + c_2\textrm{e} = 3.$

For the second condition, we need to find the derivative $y'$ first. In this case, we have:

$y'(x) = \left(c_1\textrm{e}^x + c_2\textrm{e}^{-x}\right)' = c_1\textrm{e}^x - c_2\textrm{e}^{-x}.$

Therefore:

$y'(-1) = -3 \iff c_1\textrm{e}^{-1} - c_2\textrm{e}^{-(-1)} = -3 \iff c_1\textrm{e}^{-1} - c_2\textrm{e} = -3.$

This means that we must solve the following system of equations:

$\begin{cases}c_1\textrm{e}^{-1} + c_2\textrm{e} = 3 \\ c_1\textrm{e}^{-1} - c_2\textrm{e} = -3\end{cases}.$

If we add the equations above, we get:

$\left(c_1\textrm{e}^{-1} + c_2\textrm{e}\right) + \left(c_1\textrm{e}^{-1} - c_2\textrm{e} \right) = 3-3 \iff 2c_1\textrm{e}^{-1} = 0 \iff c_1 = 0.$

If we now substitute $c_1 = 0$ into either of the equations in the system, we get:

$c_2 \textrm{e} = 3 \iff c_2 = \dfrac{3}{\textrm{e}} = 3\textrm{e}^{-1.}$

This means that the solution obeying the initial conditions is:

$\boxed{y(x) = 3\textrm{e}^{-1} \times \textrm{e}^{-x} = 3\textrm{e}^{-x-1}}.$

Indeed, we can see that:

$y(-1) = 3\textrm{e}^{-(-1) -1} = 3\textrm{e}^{1-1} = 3\textrm{e}^0 = 3$

$y'(x) =-3\textrm{e}^{-x-1} \implies y'(-1) = -3\textrm{e}^{-(-1)-1} = -3\textrm{e}^{1-1} = -3\textrm{e}^0 = -3,$

which do correspond to the desired initial conditions.

3 0

3 years ago

Ms. Robinson has $75 in her bank account and is depositing $15

Leno4ka [110]

Answer:

It will take 6 weeks

Step-by-step explanation:

Ms. Robinson: 75+15(6)=$160

Ms. LaSpina: 225-60 =$160

Therefore both will take 6 weeks

6 0

3 years ago

What is the area of this irregular shape? .6 ft square feet 3 ft 8 ft 16 ft

Andrej [43]

Answer:

Step-by-step explanation:

area=16×8+1/2×3×6

=128+9

=137 sq. ft.

5 0

3 years ago

Given that exactly two of the six rolls resulted in a 1, find the probability that the first roll resulted in a 1. Note: Your an

Ganezh [65]

Answer:

1/3 or 0.333

Step-by-step explanation:

If we know that exactly 2 of the 6 rolls resulted in a 1. Then the number of ways to arrange the two 1s into 6 slots is

$C(6,2) = \frac{6!}{(6-2)!2!} = \frac{6*5}{2} = 15$ ways

Of these 15 ways, some of them have 1 at the 1 slot.

The number of ways to arrange the two 1s so that one 1 is in the 1st slot is 5. Because the 2nd 1 is in any of the other 5 slots.

Therefore, the probability that the first roll resulted in a 1,given that exactly two of the six rolls resulted in a 1 is

5 / 15 = 1/3 or 0.333

6 0

3 years ago

Please someone answer asap! given f(x)=6(8-x)+5. what is the value of f(-2)

ohaa [14]

Answer:

Step-by-step explanation:

8 0

4 years ago