The LCD is 30.
Think of it this way. You and I are on an assembly line checking i-pads. Your job is to quality check every 6th one and my job is to check every 10th one.
Here are the ones you will check:
6, 12, 18, 24, 30 and so on
Here are the ones I will check
10, 20 30 and so on.
Notice the first one we both check? #30 - that is the LCD of 6 and 10
Answer:
a) d= 2x + (54/x)
b) x = √27 m ≈ 5.2 m
Step-by-step explanation:
a) Given
The average number of drops = n
Height in meters from the point where the whelk is dropped = x
If n(x) = 1 + (27/x²)
Then, the total vertical distance the crow travels upward to open a whelk is the height (x) times the average number of times the crow has to fly upwards to try again
d = 2xn = 2x*(1 + (27/x²)) = 2x + (54/x)
b) To minimize the distance consider the first derivative
d' = (2x + (54/x))' = 2 - (54/x²)
and d' = 0 give us (x must be positive)
2 - (54/x²) = 0 ⇒ x = √27 m ≈ 5.2 m
We can solve this question easiest by putting it as 2 equations.
First, well put the original equation, 2c+5b=55,000. B stands for the cost of backyard pool weddings and c stands for the cost of carribean weddings.
We got this equation because the question states that there were 2 carribean weddings and 5 pool weddings, and the amount of money obtained was $55,000 total as a result.
Now, we’ll put the extra information into an equation, c-10,000=b. We got this equation because it clearly states that backyard pool weddings cost 10,000 less than Caribbean, so c-10,000=b.
Now, we have to solve. Since the first equation has 2 variables, it is unsolvable. This is where the second equation comes in. We can rewrite c-10,000=b as b+10,000=c.
Now, since b+10,000=c, substitute b+10,000 for c in the first equation.
The result is 2(b+10,000)+5b=55,000.
Now that we only have one variable in the equation, it is solvable.
20,000+7b=55,000
7b=55,000
B=7,857
Now to solve for c, insert 7,857 for b in the second equation.
7,857+10,000=c
17,857=c
The cost of carribean weddings was $17,857.
The cost of a backyard pool wedding was $7,857.
Hope this helps!
