For the first question which is y=x/3, here as we see that both are in top. So they represents direct variation and constant of variation is 1/3 .
For the second question , which is 6/y=x, y is denominator and x is in the denominator. So they represents inverse variation and the constant of proportionality is 6 here .
Answer:
a) y = 0, y = 4 and y = 5
b) y ⊂ (- ∞, 0) ∪ (0, 4) ∪ (5, ∞)
c) y ⊂ (4,5)
Step-by-step explanation:
Data provided in the question:
function y(t) satisfies the differential equation:
= y⁴ − 9y³ + 20y²
Now,
a) For constant solution
= 0
or
y⁴ − 9y³ + 20y² = 0
or
y² (y² - 9y + 20 ) = 0
or
y²(y² -4y - 5y + 20) = 0
or
y²( y(y - 4) -5(y - 4)) = 0
or
y²(y - 4)(y - 5) = 0
therefore, solutions are
y = 0, y = 4 and y = 5
b) for y increasing
> 0
or
y²(y - 4)(y - 5) > 0
or
y²
y ⊂ (- ∞, 0) ∪ (0, 4) ∪ (5, ∞)
c) for y decreasing
< 0
or
y²(y - 4)(y - 5) > 0
or
y²
y ⊂ (4,5)
Answer:
x = -2
y = 3
Step-by-step explanation:
-5x + 3y = 19
x = 3y - 11
-5x + 3y = 19
-5(3y - 11) + 3y = 19
-15y + 55 + 3y = 19
-15y + 3y + 55 = 19
-12y + 55 = 19
-12y = 19 - 55
-12y = -36
y = -36/-12
<u>y = 3</u>
x = 3y - 11
x = 3(3) - 11
x = 9 - 11
<u>x = -2</u>
Answer:
1) additive identity
2) associative property of multiplication
3) commutative property of addition
4) multiplicative identity
5) associative property of addition
6) commutative property of multiplication
Step-by-step explanation:
