Part A. You have the correct first and second derivative.
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Part B. You'll need to be more specific. What I would do is show how the quantity (-2x+1)^4 is always nonnegative. This is because x^4 = (x^2)^2 is always nonnegative. So (-2x+1)^4 >= 0. The coefficient -10a is either positive or negative depending on the value of 'a'. If a > 0, then -10a is negative. Making h ' (x) negative. So in this case, h(x) is monotonically decreasing always. On the flip side, if a < 0, then h ' (x) is monotonically increasing as h ' (x) is positive.
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Part C. What this is saying is basically "if we change 'a' and/or 'b', then the extrema will NOT change". So is that the case? Let's find out
To find the relative extrema, aka local extrema, we plug in h ' (x) = 0
h ' (x) = -10a(-2x+1)^4
0 = -10a(-2x+1)^4
so either
-10a = 0 or (-2x+1)^4 = 0
The first part is all we care about. Solving for 'a' gets us a = 0.
But there's a problem. It's clearly stated that 'a' is nonzero. So in any other case, the value of 'a' doesn't lead to altering the path in terms of finding the extrema. We'll focus on solving (-2x+1)^4 = 0 for x. Also, the parameter b is nowhere to be found in h ' (x) so that's out as well.
Answer: 9^-16
Step-by-step explanation:
a^b*a^c= a^b+c
I would say a triangle with two right angles because a triangle's angles add to 180 degrees. If a triangle has two right angles, it means that two angles will be 90 degrees, which add to 180 degrees. A triangle must have three angles and sides, and it is not possible for the last angle to be 0 degrees.
Hope this helps
Answer:
r=8
Step-by-step explanation:
Given formula:
r = C / 2π
It is given that C = 16π
hence
r = 16π / 2π = 8
Answer:
a = 14.19 feet
Step-by-step explanation:
Given that,
The area of a square shaped yard is 201.5 ft²
We need to find the side length of this yard in feet.
The area of a square shaped object is given by :
A = a², a is the side length of the object
Put A = 201.5 ft² in above formula,
So, the side of the square yard is 14.19 feet.
