He solution to the initial value problem x′′+2x′+26x=5cos(4t),x(0)=0,x′(0)=0 x″+2x′+26x=5cos(4t),x(0)=0,x′(0)=0 is the sum of t
1 answer:
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Answer:
Step-by-step explanation:
We want to find the distance between two points, so the following formula is used.
Where (x₁, y₁) and (x₂, y₂) are the points we are finding the distance between.
We are given the points (-2, -1) and (3,2). If we match the corresponding value and variable we see that:
- x₁= -2
- y₁= -1
- x₂= 3
- y₂= 2
Substitute the values into the formula.
Solve the parentheses.
- -2 -3 = -5
- 2--1 = 2+ 1 = 3
Solve the exponents.
- (-5)²= -5*-5= 25
- (3)²= 3*3=9
Add.
This radical cannot be simplified, so the distance between the two points is <u>√34</u> and <u>choice 3 </u> is correct.
Answer: <u>110 feet per second</u>
Step-by-step explanation:
In this problem we will assume that the car at 45 miles per hour is moving into the x direction with a high of 100 feet, and the train is going in the y direction, so they trajectories will made an angle of 90º.
Now we can calculate the speed of the trains in feet per second so:
So we can make a right triangle with sides 66 and 88 and the hypotenuse will be the rate that the trains will separate per second so:
Is important to have in mind that the initial high is not going to change how fast the trains will separate, however, if we are going to calculate the distance we should have it in the calculations.