In order to be differentiable everywhere, 
must first be continuous everywhere, which means the limits from either side as 
must be the same and equal to 
. By definition, 
, and
so we need to have 
.
For to be differentiable at 
, the derivative needs to be continuous at , i.e.
We then need to have
Then
The 5 is the number of years that the interest rate is fixed (at the initial amount set when you sign the mortgage contract)
The 1 represents the idea that the interest rate will change every year after the initial 5 years are up.
Eliminate A immediately, because "367,259 < 364,798" is false.
Elim. C because "367,313 < 367,259" is false.
Thus, B is the correct answer.
The surface area of a rectangular prism is given by
... S = 2(LW +H(L+W))
For your dimensions, the surface area is
... S = 2(3·1 + 2(3+1)) = 2(3 + 8) = 22 . . . ft²
Step-by-step explanation:
this creates a right-angled triangle.
the right angle (90°) being the angle between flag pole and ground.
the angle ground-wire is 50°.
because we know that the sum of all angles in a triangle is always 180°, we know then that the angle flagpole-wire is
180 - 90 - 50 = 40°
so, we have the situation to know 1 side and all angles.
to get the other sides we use best the law of sine :
a/sin(A) = b/sin(B) = c/sin(C)
where the sides and related angles are always opposite of each other.
in our case now we have
24/sin(50) = wire/sin(90) = wire/1 = wire = 31.32977494... ft
so, the rounded answer is that the wire must be
31.3 ft long
