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.
Answer:
Step-by-step explanation:
Lines form 180 degrees on either side. The negative sign simply implies direction (clockwise instead of counter-clockwise), which is negligible as 180 is exactly half of 360 so you'd form the same line.
Answer:
Number of coupons sent to Existing members = 33
Step-by-step explanation:
Number of coupons sent out = 231
Let :
6 times as many to potential members = 6 * X = 6X
while existing members = X
therefore 6X + X = 231
7X = 231
therefore X = 231 / 7 = 33
so existing members = 33
while potential members = 6 * 33 = 198
Sin(63)=x/7
0.89100652418= x/7 > <span>0.89100652418 (7) = x/7(7)
</span><span>6.23704566932=x This is the height
</span>the area of a triangle is A=BH/2 or Base * Height /2
A= (<span>6.23704566932)(8)/2
</span>A=<span>24.9481826773 or 24.95 cm^2</span>
