9514 1404 393
Answer:
c = -3; d = 5
Step-by-step explanation:
The function is differentiable if it is continuous and the derivative is continuous.
This function will be continuous if the limit as x approaches 3 from either side is the same. From the left, the limit is ...
5(3^2) +c = 45 +c
From the right, the limit is ...
d(3^2) -3 = 9d -3
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The derivative will be continuous if the limit as x approaches 3 from either side is the same. From the left, the limit is ...
f'(x) = 10x
= 10(3) = 30
From the right, the limit is ...
f'(x) = 2dx
= 2d(3) = 6d
__
This gives us a pair of simultaneous equations in 'c' and 'd':
45 +c = 9d -3
6d = 30
The latter tells us d = 5. Then the former tells us ...
45 +c = 9(5) -3 ⇒ c = -3
The function is differentiable if c = -3 and d = 5.
_____
<em>Additional comment</em>
With these values, the function becomes ...

Answer:
<h2>20 cm.</h2>
Step-by-step explanation:
We know that the permiter is defined as

Where
is the longest side,
is the smallest and
is the middle side.
If
then,
, where we need to find an expression for
using the law of cosines.

Replacing all expression, the perimeter is

Using a calculator, the perimeter is 20 units centimeters.
Answer:
12y +16yi
Step-by-step explanation:
The thing about complex numbers is that you can treat them as binomials and use all of the things you know about multiplying and factoring polynomials.
Here, we assume you have ...
(5 +2yi)(4 -3i) -(5 -2yi)(4 -3i)
The factor (4 -3i) can be factored out, so you have ...
= ((5 +2yi) -(5 -2yi))(4 -3i)
= (4yi)(4 -3i)
= 16yi -12yi²
At this point, the definition of i comes into play, and you replace i² with -1.
= 12y +16yi