Answer:
The solution of the differential equation is .
Step-by-step explanation:
The first step is to take Laplace transform in both sides of the differential equation. As usual, we denote the Laplace transform of as . Then,
In the last step we use that and .
Notice that our differential equations becomes an algebraic equation for , which is more simple to solve.
In the expression we have obtained, we can write in terms of :
which is equivalent to
.
Now, we make a partial fraction decomposition for the term . Thus,
.
Substituting the above value into the expression for we get
) in both hands of the above expression. Recall that . So,
.
To obtain this we have used the following identities that can be found in any table of Laplace transforms
Answer:
170ft^2
Step-by-step explanation:
We need to find the areas of the partitioned areas and then add them to get the total area of the complex figure.
The area of the rectangle can be found by A = lw
The area of the triangle can be found by A = (1/2)*bh
We have already been given the length of the rectangle.
The base of the triangle is 22ft - 12ft = 10ft.
Since this is a 45-45-90 triangle, we can also say that the dashed line is also 10ft long, and this also represents the width of the rectangle.
This means that the height of the triangle and the width of the rectangle are both 10ft.
Area of rectangle = lw
A = 12ft * 10ft
A = 120ft^2
Area of triangle = (1/2)*bh
A = (1/2) * 10ft * 10ft
A = (1/2) * 100ft^2
A = 50ft^2
The total area of the figure is 120ft^2 + 50ft^2 = 170ft^2.
Answer:
H0: p = 0.078
Ha: p > 0.078
Step-by-step explanation:
The researchers want know if the proportion of low weight births for women exposed to secondhand smoke during their pregnancies is greater than 0.078.
Answer:
Which one you need me to answer
Step-by-step explanation:
Answer:
Option (C) n = 256
Therefore, there are 256 ways to select a car with 2 car models, 8 different colors and any combinations of 4 optional features.
Step-by-step explanation:
A new car is available in a sedan model and a hatchback model.
So that means customers can select the model of the car in,
n₁ = 2 ways
It is available in eight different colors.
After selecting the model, customers can select the color of the car in,
n₂ = 8 ways
Customers can choose to add any combination of four optional features.
After selecting the color, customers have the choice to add any combination of 4 optional features,
n₃ = 4² = 16 ways
Which means that there are 16 different ways to add 4 optional features e.g.
1. 0, 0, 0, 0
2. 0, 0, 0, 1
3. 0, 0, 1, 0
4. 0, 0, 1, 1
and the list goes on to 16 different ways.
Now the total ways to select a car is given by
n = n₁*n₂*n₃
n = 2*8*16
n = 256
Therefore, there are 256 ways to select a car with 2 car models, 8 different colors and any combinations of 4 optional features.