From the double-angle identity,
we can rewritte our given equation as:
By factoring 2cosx on the left hand side, we have
This equation has 2 solutions when
From equation (A), we obtain
and from equation (B), we have
On the other hand, we can find one more solution from the original equation by substituting x=0, that is,
then, x=0 is another solution. In summary, we have obtained the following solutions:
However, the intersection of the last set is empty. So the unique solution is x=0 as we can corroborate on the following picture:
Therefore, the solution set is: {0}
Gosh, when I saw that my mind went blank
Answer:
100$
Step-by-step explanation:
he profit from 1 popcorn=0.85$
from 200=170$
170$-70$=100
Dimensions of the room------------------- >16*13
1 in---------------- >0.0833333 foot
3 in----------------- >x
x=3*.0833333=0.25 ft
Let
<span>C-------------- > dimensions of the piece of carpet that Charlotte must purchase
C-------------- > (16+2*0.25)*(13+2*0.25)---------- > (16.50)*(13.50)=222.75 ft</span>²
<span>
The answer a the question 1) is 16.50 feet X 13.50 feet</span>
The answer a the question 2) is 222.75 ft²
<span>3. How many hours should it take for the four-person crew to lay the flooring in Charlotte's bedroom?
if </span><span>two-person carpet crew can lay 50 square feet of carpet---------- > 1 hour</span><span>
four person </span>carpet crew can lay 100 square feet of carpet---------- > 1 hour
therefore
if 100 ft² carpet----------------------- > 1 hour
222.75 ft² carpet--------------------- > x
x=222.75/100=2.2275 hours=2.23 hours
The answer is 2.23 hours
Answer:
The rate of the boat in still water is 73 km per hour, and the speed of the current is 24 km per hour.
Step-by-step explanation:
Given that a motorboat travels 441 kilometers in 9 hours going upstream and 388 kilometers in 4 hours going downstream, to determine what is the rate of the boat in still water and what is the rate of the current, the following calculation must be performed:
Upstream = 441/9 = 49 km per hour
Downstream = 388/4 = 97 km per hour
(97 + 49) / 2 = X
146/2 = X
73 = X
97-73 = 24
49-74 = -24
Therefore, the rate of the boat in still water is 73 km per hour, and the speed of the current is 24 km per hour.
