You have the following expression:
To verify the identity, you have that the left side of the equation becomes:
(1 + cosx)(1 - cosx) = (1 - cos^2 x)
because of the product of an expression by its conjugate result in a difference of squares. Or simplfy by expanding the factors and simplying.
Next, you have:
1 - cos^2 x = sin^2 x
because the Pythagorean identity.
Then, the identity is verified.
Answer:
(B)
Step-by-step explanation:
Volume of fluid in the tank =1000 gallons
Initial Amount of Salt in the tank, A(0)= 30 pounds
Incoming brine solution of concentration 2 pounds of salt per gallon is pumped in at a rate of 4 gallons per minute.
Rate In=(concentration of salt in inflow)(input rate of brine)
The resulting mixture is pumped out at the same rate, therefore:
Rate Out =(concentration of salt in outflow)(output rate of brine)
Therefore:
The rate of change of amount of salt in the tank,
Answer:
rolling a number cube with sides labeled 1 through 6 and tossing a coin.
Step-by-step explanation:
We will resolve each statement to determine the events that has exactly 12 possible outcomes.
N = number of possible outcomes for a cube
Nc = number of possible outcomes for a coin
Nca = number of possible outcomes for the cards
i. rolling a number cube with sides labeled 1 through 6 and then rolling the number cube again
Nt = N × N
N = 6 ( cube has 6 possible outcomes and its rolled twice)
Nt = 6 × 6 = 36
ii. tossing a coin and randomly choosing one of 4 different cards.
Nt = Nc × Nca
Nc = 2 ( coin has two outcomes)
Nca = 4 ( 4 possible cards )
B = 2 × 4 = 8
iii. rolling a number cube with sides labeled 1 through 6 and tossing a coin.
N = N × Nc
N = 6 ( cube has 6 possible outcomes)
Nc = 2 (coin has two faces)
N = 6 × 2 = 12 (correct)
Iv. tossing a coin 6 times.
N = Nc^6
Nc = 2
N = 2^6 = 64
Therefore, the correct answer is iii.
rolling a number cube with sides labeled 1 through 6 and tossing a coin.
Answer:
at first we put the numbers in order from least to greatest
2 , 6 , 6 , 7 , 8 , 9
1st quartile = 6
median = (6+7)/2 = 6.5
3rd quartile = 8
Answer:
D
Step-by-step explanation:
