Answer:
C
Step-by-step explanation:
x^2 + (x+3)^2 = 117
x^2 + x^2+6x+9 =117
2x^2 + 6x - 108 = 0
(2x-12)(x+9)=0
x=-9,6
x cannot be negative therefore, x = 6
Answer:
the container is 1/4 full at 9:58 AM
Step-by-step explanation:
since the volume doubles every minute , the formula for calculating the volume V at any time t is
V(t)=V₀*2^-t , where t is in minutes back from 10 AM and V₀= container volume
thus for t=1 min (9:59 AM) the volume is V₁=V₀/2 (half of the initial one) , for t=2 (9:58 AM) is V₂=V₁/2=V₀/4 ...
therefore when the container is 1/4 full the volume is V=V₀/4 , thus replacing in the equation we obtain
V=V₀*2^-t
V₀/4 = V₀*2^-t
1/4 = 2^-t
appling logarithms
ln (1/4) = -t* ln 2
t = - ln (1/4)/ln 2 = ln 4 /ln 2 = 2*ln 2 / ln 2 = 2
thus t=2 min before 10 AM → 9:58 AM
therefore the container is 1/4 full at 9:58 AM
Answer:
the 30th term is 239
Step-by-step explanation:
The computation of the 30th term is as follows:
As we know that
a_n = a_1 + (n-1)d
where
a_1 is the first number is the sequence
n = the term
And, d = common difference
Now based on this, the 30th term is
= 152 + (30 - 1) × 3
= 152 + 29 × 3
= 152 + 87
= 239
Hence, the 30th term is 239
