Answer:
(-∞, -7) ∪ (-3, ∞)
Step-by-step explanation:
The line y=0 is the x-axis. The graph is above the x-axis for x < -7 and for x > -3. The solution set is ...
(-∞, -7) ∪ (-3, ∞)
1 gal + 2 qt + 3 pts
1 gal + 3 qt + 7 pts
1 gal + 3 qt + 3 pts
----------------------------add
3 gal + 8 qt + 13 pts
1 gal = 4 qts
1 gal = 8 pts
1 pt = 1/2 qt
13 pts = 6.5 qts
now we have 3 gal + (8 + 6.5) = 3 gal + 14.5 qts
12 qts = 3 gal
now we have : 6 gal + 2.5 qts or 6 gal + 2 qts + 1 pt <=== answer
R = 2 / (1 + sin <span>θ)
Using the following relations:
R = sqrt (x^2 + y^2)
sin </span>θ = y/R
<span>
R = 2 / (1 + y/R)
R</span>(1 + y/R<span>) = 2
</span><span>R + y = 2
R = 2 - y
sqrt(x^2 + y^2) = 2 - y
Squaring both sides:
x^2 + y^2 = (2 - y)^2
x^2 + y^2 = 4 - 4y + y^2
x^2 + 4y - 4
</span>
See explanation below.
Explanation:
The 'difference between roots and factors of an equation' is not a straightforward question. Let's define both to establish the link between the two..
Assume we have some function of a single variable
x
;
we'll call this
f
(
x
)
Then we can form an equation:
f
(
x
)
=
0
Then the "roots" of this equation are all the values of
x
that satisfy that equation. Remember that these values may be real and/or imaginary.
Now, up to this point we have not assumed anything about
f
x
)
. To consider factors, we now need to assume that
f
(
x
)
=
g
(
x
)
⋅
h
(
x
)
.
That is that
f
(
x
)
factorises into some functions
g
(
x
)
×
h
(
x
)
If we recall our equation:
f
(
x
)
=
0
Then we can now say that either
g
(
x
)
=
0
or
h
(
x
)
=
0
.. and thus show the link between the roots and factors of an equation.
[NB: A simple example of these general principles would be where
f
(
x
)
is a quadratic function that factorises into two linear factors.
I think they should keep it around, even if it might not be the most efficient strategy. After all, what if you need to solve a problem using multiple strategies?
