Answer: t = - 5 ∈ 
= ( -∞ , -4 )
Step-by-step explanation:
The standard form of O.D.E is written as :
+ 
Equation given :
+ 
= 
, 
The first thing to do is to write the O.D.E in standard form , that is we will divide through by 
, so we have
With this , we can see that 
and 
are both continuous in the same domain. Therefore , the intervals are :
= ( -∞ , -4 )
= ( - 4 , 4 )
= ( 4 , -∞ )
recall that y(−5) = 1 , then t = -5
This means that :
t = - 5 ∈ = ( -∞ , -4 )
Answer:
neither
parallel
neither
Step-by-step explanation:
y=-5/2x-5 ≅ 5x+2y=-10
Answer:
A is (10,0)
B is (3, 3).
Step-by-step explanation:
First we calculate the coordinates of the point A.
Here, y = 0 so we have:
7(0) - 3x + 30 = 0
-3x + 30 = 0
x = -30/-3 = 10.
So A has coordinates (10,0).
Next we find the coordinates of the points where the line passes through the y axis. Here x = 0:
7x - 3(0) = 30
x = 30/7.
So the point is (0, 30/7).
Let the point B have coordinates (x1, y1)
Now x1 = y1 (given).
If we draw a line from B perpendicular to the x axis ( its length will be = y1) then we have 2 similar triangles.
So as corresponding sides are in the same ratio:
y1/ (30/7) = (10-x1) / 10
But as x1 = y1:
x1/ (30/7) = (10-x1) / 10
7 x1 / 30 = (10-x1) / 10
70 x1 = 30(10 - x1)
70x1 = 300 - 30 x1
100 x1 = 300
x1 = 3
So the coordinates of B are (3,3)
Checking the solution to the equation:
LHS = 3 / 30/7 = 3*7 / 30 = 21/30 = 7/10.
RHS = (10 -3 ) / 10 = 7/10.
