Answer:
Step-by-step explanation:
A. 2x+3y+z
X = -2
Y= -3
Z= 5
2(-2)+3(-3)+5
-4-9+5
=8
B. X-Y
-2–3
-2+3
=1
C. 2(x+y/z)
2(-2-3/5)
2(-1)
=-2
D. 3x^2-2x+1
3(-2)^2-2(-2)+1
3(4)+4+1
=17
E.3y(x+x^2-y)
3(-3)(-2+-2^2-(-3))
-9(1)
=-9
F.-z^2(1-2x)/y-x
5^2(1-2(-2)/-3–2
25(5/5)
25(1)
=25
Both equations are linear, so I'll use the integrating factor method.
The first ODE

has integrating factor

In the original equation, multiply both sides by eˣ :

Observe that
d/dx [xeˣ] = eˣ + xeˣ = (x + 1) eˣ
so that the left side is the derivative of a product, namely

Integrate both sides with respect to x :


Solve for y :

Use the given initial condition to solve for C. When x = 1, y = 2, so

Then the particular solution is

The second ODE

has integrating factor

Multiply both sides of the equation by 1/(1 + x²) :

and observe that
d/dx[1/(1 + x²)] = -2x/(1 + x²)²
Then



When x = 0, y = 3, so


Answer:
y= -2/5x-13/5
Step-by-step explanation:
The short answer is: when their fractions add up to full integers.
For examples, two halves make up a whole, or

so the mixed numbers with those will add up to full integers:

but if they don't add up to an interger, the whole sum won't be an integer:
Answer:
20160 ways
Probability = 0.0556
Step-by-step explanation:
We have 9 different letters, so the total number of words we can make is:

If we want just the words that begin with L and end with a vowel, we would have the first letter "locked", so we have 8 letters remaining, and it must end with a vowel, so the last "slot" has just 4 possible values (A, E, I or O). Then we would have 4 possible values for the last letter and 7 remaining letters in the middle of the word:

The probability is calculated by the division of the number of words we want over the total number of words:
