Answer:
cos 2 x=1-sin^2 x
Step-by-step explanation:
x=-135°
cos 2x=cos (-270)=cos (-270+360)=cos 90=0
or cos 2x=1-2sin ²x=1-2(sin (-135))²
=1-2(-sin 135)²
=1-2(sin 135)²
=1-2(sin (180-45))²
=1-2(sin²45)
=1-2 (\frac{1}{\sqrt{2}})²
=1-1
=0
Answer:
At 2:00 there will be 38,400 bacteria.
Step-by-step explanation:
600/150 = 4
2400/600 = 4
So, the bacteria quadruples every half hour.
At 1:30, there will be 2400*4 = 9600.
At 2:00, there will be 9600*4= 38400
Answer:
The solution is (-2, 5, 3)
Step-by-step explanation:
2x + 3y - 4z = -1
2(-2) + 3(5) - 4(3) = -1
-4 + 15 - 12 = -1
-16 + 15 = -1
-1 = -1
x - 2y + 5z = 3
-2 - 2(5) + 5(3) = 3
-2 - 10 + 15 = 3
- 12 + 15 = 3
3 = 3
-4x + y + z = 16
-4(-2) + 5 + 3 = 16
8 + 5 + 3 = 16
16 = 16
Therefore, (-2, 5, 3) is a solution.
2x + 3y - 4z = -1
2(-3.6) + 3(0.2) - 4(1.4) = -1
-7.2 + 0.6 - 5.6 = -1
-12.8 + 0.6 = -1
-12.2 = -1
x - 2y + 5z = 3
-3.6 - 2(0.2) + 5(1.4) = 3
-3.6 -0.4 + 7 = 3
-4 + 7 = 3
3 = 3
-4x + y + z = 16
-4(-3.6) + 0.2 + 1.4 = 16
14.4 + 0.2 + 1.4 = 16
16 = 16
(-3.6, 0.2, 1.4) is not a solution.
2x + 3y - 4z = -1
2(2) + 3(5) - 4(-3) = -1
4 + 15 + 12 = -1
31 = -1
x - 2y + 5z = 3
2 - 2(5) + 5(-3) = 3
2 - 10 - 15 = 3
2 - 15 = 3
13 = 3
-4x + y + z = 16
-4(2) + 5 + -3 = 16
-8 + 5 - 3 = 16
-11 + 5 = 16
-6 = 16
(2, 5, -3) is not a solution.
2x + 3y - 4z = -1
2(4) + 3(-7) - 4(-3) = -1
8 - 21 + 12 = -1
-21 + 20 = -1
-1 = -1
x - 2y + 5z = 3
4 - 2(-7) + 5(-3) = 3
4 + 14 - 15 = 3
18 - 15 = 3
3 = 3
-4x + y + z = 16
-4(4) - 7 - 3 = 16
-16 - 7 - 3 = 16
-26 = 16
(4, -7, -3) is not a solution.
Answer:
ccccccccccc
Step-by-step explanation:
Answer:
All in all, Jonathan's piggy bank contains 100 coins. Among these coins, only 50 are one-dollar coins. Therefore, the theoretical probability of picking one-dollar coin from the piggy bank is equal to 50/100 or 1/2.
Similarly, from the experiment, 20 coins were picked and among these there are 12 one-dollar coins. The answer to the second question is therefore 12/20 or 3/5.
Step-by-step explanation:
