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DanielleElmas [232]
2 years ago
15

Question 2 (1 point)

Mathematics
1 answer:
Vedmedyk [2.9K]2 years ago
7 0

Answer:

Step-by-step explanation:

(-9+2)/2= -7/2= -3.5

(8 + (-1))/2 = 7/2= 3.5

(-3.5, 3.5) is the solution

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alexgriva [62]
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the answers are going across
6 0
3 years ago
Read 2 more answers
Y''+Y'+Y=1<br> solve ordinary differential equation
taurus [48]

Answer:

y(t) = c₁ e^(-1/2 t) cos(√3/2 t) + c₂ e^(-1/2 t) sin(√3/2 t) + 1

Step-by-step explanation:

y" + y' + y = 1

This is a second order nonhomogenous differential equation with constant coefficients.

First, find the roots of the complementary solution.

y" + y' + y = 0

r² + r + 1 = 0

r = [ -1 ± √(1² − 4(1)(1)) ] / 2(1)

r = [ -1 ± √(1 − 4) ] / 2

r = -1/2 ± i√3/2

These roots are complex, so the complementary solution is:

y = c₁ e^(-1/2 t) cos(√3/2 t) + c₂ e^(-1/2 t) sin(√3/2 t)

Next, assume the particular solution has the form of the right hand side of the differential equation.  In this case, a constant.

y = c

Plug this into the differential equation and use undetermined coefficients to solve:

y" + y' + y = 1

0 + 0 + c = 1

c = 1

So the total solution is:

y(t) = c₁ e^(-1/2 t) cos(√3/2 t) + c₂ e^(-1/2 t) sin(√3/2 t) + 1

To solve for c₁ and c₂, you need to be given initial conditions.

5 0
3 years ago
An airplane flying with the wind can cover a certain distance in 2 hours. The return trip against the wind takes 2.5 hours. Find
Anna [14]

Answer:

Wind speed = 30 mph

Plane speed = 270 mph

Step-by-step explanation:

Given that :

Distance = 600 miles

Let speed of airplane = a ; speed of wind = b

Net speed ; with wind = a + b

Net speed against wind = a - b

Time taken with wind = 2 hours

Time taken against wind = 2.5 hours

Recall :

Speed = distance / time ; distance = speed * time

(a + b) * 2 = (a - b) * 2.5

2a + 2b = 600

a + b = 300 - - - (1)

a = 300 - b

2.5a - 2.5b = 600

a - b = 240 - - - (2)

300 - b - b = 240

300 - 2b = 240

-2b = - 60

b = 30

a = 300 - 30

a = 270

Wind speed = 30 mph

Plane speed = 270 mph

4 0
2 years ago
What is the rate of change for the linear relationship modeled in the table? (4 points)
lozanna [386]

Answer:

-1/2

Step-by-step explanation:

In a linear relationship, the rate of change of one variable with respect to the other is <em>constant</em>. When we talk about <em>change</em>, we're looking for a <em>difference</em> of values.

If we look at the first and second rows, the change in x is 1 - (-1) = 2, while the change in y is 9 - 10 = -1. Usually we refer to these changes as Δx and Δy (read like "delta-x" and "delta-y"), and the <em>rate of change </em>is the number we get by dividing one of these by the other.

The rate of change we're used to seeing, sometimes called the <em>slope</em>, is Δy/Δx. So, using the values we've already found:

\Delta{x}=2\\\Delta{y}=-1\\\Delta{y}/\Delta{x}=-1/2

5 0
3 years ago
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For each pair, determine whether it is a solution to 6x+7y=19
Gre4nikov [31]

Answer:

Step-by-step explanation:

(0, -3) not a solution

(2,1) solution

(3,-4) not a solution

(-5,7) solution

5 0
2 years ago
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