Even integer: 2 x a, where a is a natural number without 0;
Odd integer : 2 x b + 1 , where b is a natural number;
So, 2 x a + 2 x b+ 1 = 2 x ( a + b ) + 1, which is an odd integer.
Using sine law:
9/sinc = 15/sin22
sinc = 9sin22 / 15 = 0.225
so c = sin^-1(0.225) = 12.99 degrees ~~ 13 degrees
if B was required:
B = 180 - C - A ~~ 145
Answer:
shorter piece is 28.8 inches
Step-by-step explanation:
Answer:
9.6p + 0.4q + 2.2r meters (answer A)
Step-by-step explanation:
We sum up the three side lengths to obtain the perimeter of the triangle:
(6.2p + 4.5q) meters, , and (2.9r – 4.1q) meters
+ (3.4p – 0.7r) meters
+ (2.9r – 4.1q) meters
---------------------------------
9.6p + 0.4q + 2.2r meters (answer A)
Let t, f, and s be the amount of 25%, 40%, and 60% solutions used.
We are told s=3f. The general equation is:
100(0.25t+0.4f+0.6s)/(t+s+f)=45, and using s=3f we have:
(0.25t+0.4f+1.8f)/(t+4f)=0.45
(0.25t+2.2f)/(t+4f)=0.45
0.25t+2.2f=0.45t+1.8f
0.25t+0.4f=0.45t
0.4f=0.2t
t=2f, remembering that s=3f, will allow us to solve for f
t+s+f=60, using t and s from above
2f+3f+f=60
6f=60
f=10 L then
s=3f=30 L and t=2f=20L
So 20L of 25%, 10L of 40%, and 30L of 60% acid solutions need to be mixed to make 60L of 45% acid solution.
