Search up heating curve chemistry: it should look somewhat like that lol :). But, the last interval should have a small slope, the middle interval a big slope, and the first interval: a medium slope.
8*0=0 and 8+0=8
the answer is 8 and 0
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.
The chance of student 1's birthday being individual is 365/365 or 100%.
Then the chance of student 2's birthday being different is 364/365.
Then it's narrowed down to 363/365 for student 3 and so on until you get all 10 students.
If you multiply all these values together, the probability would come out at around 0.88305182223 or 0.88.
To get all the same birthday you'd have to the chance of one birthday, 1/365 and multiply this by itself 10 times. This will produce a very tiny number. In standard form this would be 2.3827x10'-26 or in normal terms: 0.23827109210000000000000000, so very small.
Answer:
The triangles are similar due to AAA
Step-by-step explanation:
'The triangles ABC and DBE are similar because they have a common angle < B, and also angle < E is marked as congruent to angle < A. Then the third angle <C is going to be congruent to angle D as well due to the property of addition of internal angles of a triangle must add to 180 degrees.
Then the triangles are similar due to AAA
