Answer: Hello there!
we have the function f(x) = IxI/x
Then this function can be piecewise writen as:
f(x) = 1 if x > 0
f(x) = -1 if x < 0
because:
suposse that n is a number greater than 0, then:
f(n) = InI/n = n/n = 1
and this is independent of the number n, so for all the positive values of x, we have f(x) = 1
and
f(-n) = I-nI/(-n) = n/(-n) = -1
and again, this does not depend on the value of n, so for all the negative values of x, we have f(x) = -1.
On the other hand, the Heaviside function is defined as:
H(x) = 1 if x>0
H(x) = 0 if x<0
Then the difference is that, when the Heaviside function takes the value of 0 for negative values of x, our function f(x) takes the value of -1 for negative values of x.
The area is what is given. Find the base and height and multiply that. Since, you done that, you simplify if any fraction is there. Then, you have an answer!
Answer:
1
Step-by-step explanation:
absolute values are always positive, so the absolute value of -1 is 1
always going to be positive
Answer:
(-3,4)
(-1,4)
(-3,7)
Step-by-step explanation:
(1,1) → (1-4, 1+3) → (-3,4)
(3,1) → (3-4, 1+3) → (-1,4)
(1,4) → (1-4, 4+3) → (-3,7)
Hello from MrBillDoesMath!
Answer: N = 143
Discussion:
This one took some trial and error! At first I listed all 2 digit primes, looked at the list, but didn't know how to proceed. So, I took the smallest 2 digit primes numbers: 11 and 13 and wondered if their product, 13*11 = 143, could be represented as the sum of 3 consecutive primes. I went back to my list of primes, added groups of three consecutive numbers that seemed to be in the right range to give the desired sum, and stumbled on 43, 47, and 53!
43 + 47 + 53 = 143 !
Therefore N = 143. It's the sum of 43, 47, and 53 as well as the product of 11 and 13.
Thank you,
MrB
