Here's the answer for either!
That is 12*11*10*9*8*7*6*5*4=79833600 ways
Answer:
36
Step-by-step explanation:
the first sequence starts
4 12 (3*4) 36 (3*12) 108 (3*36) ...
the second sequence starts
20 28 (8+20) 36 (8+28) 44 (8+36) ...
so, just by writing down a few elements you can see it already.
I knew it already before that just by thinking "the first sequence has only numbers that can be divided by 3. what is the first number of the second sequence that can be also divided by 3 ? oh, yeah, 36 !"
Answer:
32
Step-by-step explanation:
If you already have an angle of 148 on the arc TU, then 180-148=32
E) 2
Remember that the first derivative of a function is the slope of the function at any specified point. We've been told that f(0) = -5 and that f'(x) is always less than or equal to 3. So let's look at the available options and see what the average slope would have to be in order to get the specified value of f(2).
A) -10: (-10 - -5)/(2 - 0) = -5/2 = -2.5
B) -5: (-5 - -5)/(2 - 0) = 0/2 = 0
C) 0: (0 - -5)/(2 - 0) = 5/2 = 2.5
D) 1: (1 - -5)/(2 - 0) = 6/2 = 3
E) 2: (2 - -5)/(2 - 0) = 7/2 = 3.5
Now taking into consideration the mean value theorem, the value of the function f'(x) has to have the value equal to the average slope between the two points at at least one point between the two given values. For options A, B, C, and D it's possible for f'(x) to return values that make that slope possible. However, for option E, the mean value theorem indicates that f'(x) has to have the value of 3.5 for at least 1 point between x=0 and x=2. And since we've been told that f'(x) is less than or equal to 3 for all possible values of x, that is in conflict and f(2) can not have the value of 2.
