Answer:
Euler's method is a numerical method used in calculus to approximate a particular solution of a differential equation. As a numerical method, we have to apply the same procedure many times, until get the desired result.
In first place, we need to know all the values the problem is giving:
- The step size is 0.2; h = 0.2. This step size is a periodical increase of the x-variable, which will allow us to calculate each y-value to each x.
- The problem is asking the solution y(1), which means that we have to find the y-value assigned for x = 1, through the numerical method.
- The initial condition is y(0) = 9. In other words,
.
So, if the initial x-value is 0, and the step size is 0.2, the following x-value would be: 
; then 
; 
; and so on.
Now, we have to apply the formula to find each y-value until get the match of 
, because the problem asks the solution y(1).
According to the Euler's method:
Where 
, and 
; 
.
Replacing all values we calculate the y-value assigned to 
:
.
Now, 
, 
. We repeat the process with the new values:
Then, we repeat the same process until get the y-value for 
, which is 
, round to four decimal places.
Therefore, 
.
Answer:
C. 1:1
Step-by-step explanation:
In a 45 45 90 right triangle, the side lengths for the legs are both
x and the length of the hypotenuse is 
Answer:
A general line is written as:
y = a*x + b
where:
a is the slope
b is the y-intercept.
a) y-intercept = 2 and slope = 7.
This line is:
y = 7*x + 2
b) y-intercept = -1 and is parallel to y= 5x - 7.
Now, if two linear equations are parallel if they have the same slope and different y-intercept. Then if we want a line parallel to y= 5x - 7, this means that the slope of this line must also be equal to 5.
y = 5*x + (-1)
c) y-intercept 2 and is inclined at 45° to the x- axis.
When we have an inclination of A degrees from the x-axis, the slope of the equation is given by: a = Tan(A)
In this case, we have A = 45°
Then the slope is a = Tan(45°) = 1
Then the equation of this line is:
y = 1*x + 2
Answer:
y=-1/2x-5
Step-by-step explanation:
Well we know that the slope is -1/2 so we can write the equation like this:
y=-1/2x+b (This is because of y=mx+b) (m is slope) (b is y-intercept)
Now we can replace the y and x with -4 and -3 because of (x,y). (-4,-3) x is -4 and y is -3
-3=-1/2(-4)+b
-3=2+b
Subtract 2 on both side:
-2-3=2-2+b
-5=b
Answer:
y=-1/2x-5
Hope this helps!
The equation would be (3+√-16)(6-√-64)
A negative square root can not be a real number, meaning that we have to use the imaginary number.
(3+4i)(6-8i)
How to multiply imaginary numbers...
Treat this like an equation looking like (x-a)(y-b)
Use FOIL
(3+4i)(6-8i)
= 18-24i+24i-32i²
= 18-32i² (i²= -1 because i= √-1)
= 18- (-32)
= 18 + 32
= 50
