Answer:
The solution to the differential equation
y' = 1 + y²
is
y = tan x
Step-by-step explanation:
Given the differential equation
y' = 1 + y²
This can be written as
dy/dx = 1 + y²
Separate the variables
dy/(1 + y²) = dx
Integrate both sides
tan^(-1)y = x + c
y = tan(x+c)
Using the initial condition
y(0) = 0
0 = tan(0 + c)
tan c = 0
c = tan^(-1) 0 = 0
y = tan x
Hello!
Formula for the volume of a cylinder:
Plug in the values and solve
The answer is 12,127.5. Hope I helped!
(ab)² and ab² are not equal. When you have something in parentheses being squared, you have to square everything inside, so in the case of (ab)², you have to "distribute" the ² to both variables inside. That gives you a²b², not just ab².
If the abstract way is kind of confusing for you, just pick two random numbers for a and b and plug them in to test it. Say a = 3 and b = 4. Then
(3*4)² = 3*4²
(12)² = 3*16
144 ≠ 48
Answer: intersecting but not perpendicular
Step-by-step explanation: Let's start by eliminating a few options.
First off, parallel lines are coplanar lines that do not intersect.
In the diagram shown, lines <em>i </em>and <em>k</em> do intersect
so option A doesn't make any sense.
We can also eliminate option C because by definition,
parallel lines <em><u>do not intersect </u></em> so we can cross this off.
We also can't conclude that lines <em>i</em> and <em>k </em>are perpendicular,
because we don't have a box at the vertex and from the
diagram shown, it doesn't look like they form a perfect right angle.
That leaves us with option D.
Notice that these two lines cross at a point.
When two lines cross at a point, we say that they intersect.
So they are intersecting lines but not perpendicular.
A. 24.6/1.2 = 20.5
b. 1.95/0.25 = 7.8
