You can parameterize the curve
and compute the integral along each component curve, or you can use the fact that
is the continuous gradient of a function
and observe that the line integral is path independent.
In other words, there is a function
such that
, so the integral along any curve
from the points
to
is simply
You have
, and so
while
where
is an arbitrary constant. So we've found that
which means the line integral has a value of
Pretty sure you already had something posted about this... in case you've lost it, or have questions:
#25 is fairly simple. Plug in -4 and 3 into the equation, and the extraneous root will be the one that does not work.
Extraneous root in this case is positive four since +4≠-4
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</span>In this case it's negative 3, since -3≠3
#29 can be turned into a quadratic equation.
Square both sides to get
Then bring the 2x+3 to the other side, setting the quadratic equal to zero.
Factor to find that it's equivalent to
(x-3)(x+1)=0
Therefore x is equal to positive 3 and negative 1. Plug both back into the original equation. Whichever does not work is the extraneous root, and the answer is the one that does.
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</span><span>
</span><span>
</span>Extraneous root would be negative 3.
<span>
</span><span>
</span>Extraneous root would be positive 1.
Your answers are positive 3 and negative 1.
<span>Extraneous roots are negative 3 and positive 1.</span>
Step-by-step explanation:
100-15=85%
85% × 29.99
=$25.49
Answer:
And using the second point we have this:
If we divide both sides by 18 we got:
And taking the square roof of 16 we got:
But on this case the negative solution not makes sense since the function is increasing so then the correct exponential function that pass through the points (0,18) and (2,288) is:
Step-by-step explanation:
We want to construct an exponential function given by this general form:
And we know that the function needs to pass for two points (0,18) and (2,288). Using the first point we have this:
And using the second point we have this:
If we divide both sides by 18 we got:
And taking the square roof of 16 we got:
But on this case the negative solution not makes sense since the function is increasing so then the correct exponential function that pass through the points (0,18) and (2,288) is: