Triangular sequence = n(n + 1)/2
If 630 is a triangular number, then:
n(n + 1)/2 = 630
Then n should be a positive whole number if 630 is a triangular number.
n(n + 1)/2 = 630
n(n + 1) = 2*630
n(n + 1) = 1260
n² + n = 1260
n² + n - 1260 = 0
By trial an error note that 1260 = 35 * 36
n² + n - 1260 = 0
Replace n with 36n - 35n
n² + 36n - 35n - 1260 = 0
n(n + 36) - 35(n + 36) = 0
(n + 36)(n - 35) = 0
n + 36 = 0 or n - 35 = 0
n = 0 - 36, or n = 0 + 35
n = -36, or 35
n can not be negative.
n = 35 is valid.
Since n is a positive whole number, that means 630 is a triangular number.
So the answer is True.
D. 20/3 I think it’s the answe
Answer:
<h3><X = 63</h3>
Step-by-step explanation:
USing SOH CAH TOA
sin theta = opposite/hypotenuse
sin <X = WV/VX
sin <X = 8/9
<X = arcsin(8/9)
<X = arcsin(0.8889)
<X = 62.7 degrees
Hence the value of x is approximately 63degrees
Here is the expression:
(0.8a)^3. Hope it help!
