3 sin ( 2 x ) = 3 cos x
3 · 2 sin x cos x - 3 cos x = 0
6 sin x cos x - 3 cos x = 0 /: 3
2 sin x cos x - cos x = 0
cos x ( 2 sin x - 1 )
cos x = 0,
x 1 = π/2, x 2 = 3π/2;
2 sin x - 1 = 0
2 sin x = 1
sin x = 1/2
x 3 = π/6, x 4 = 5π/6.

7 0

2 years ago

Math To Do Ready

emmasim [6.3K]

Answer:

At 1pm, the number of bacteria in the dish is 1,000,000

At 12pm, the number of bacteria in the dish is 500,000

Step-by-step explanation:

Given the information on the table

$\left|\begin{array}{c|c}$Hour&$Number of Bacteria (in millions)\\---&--------------\\12 p.m.&\\1 p.m.&\\12 p.m.&\\2 p.m.&\\3 p.m.&\\4 p.m.&\\5 p.m.&32\\6 p.m.&64\end{array}\right|$

We are to follow the pattern to determine how many million bacteria were in the dish at 1 p.m. and 12 p.m.

Now:

$32=2^5\\64=2^6$

It therefore means that the bacteria population doubles every hour. Following this pattern and reducing the exponents by 1 backwards, we have:

$\left|\begin{array}{c|c}$Hour&$Number of Bacteria (in millions)\\---&--------------\\12 p.m.&2^{-1}=0.5\\1 p.m.&2^0=1\\12 p.m.&2^1=2\\2 p.m.&2^2=4\\3 p.m.&2^3=8\\4 p.m.&2^4=16\\5 p.m.&2^5=32\\6 p.m.&2^6=64\end{array}\right|$

Therefore:

At 1pm, the number of bacteria in the dish is 1,000,000
At 12pm, the number of bacteria is 0.5 million=0.5 X 1,000,000=500,000

3 0

2 years ago

Carl is hanging pictures in his home. There is a space on a wall that has a width of 4 feet. Carl has pictures with different wi

scoundrel [369]

Answer:

A. 46 inches

Step-by-step explanation:

1 foot is 12 inches. Multiplying that by 4 tells you 4 feet is 48 inches.

The only dimension listed that is less than 48 inches is ...

A. 46 inches

5 0

3 years ago

Find the Lowest Common Multiple of 8 and 6.

olchik [2.2K]

Answer:

Step-by-step explanation:

4 0

3 years ago

Read 2 more answers