Which expression is equivalent to 60 Σ n=1 (2n − 1)2 ? Check all that apply.
2 answers:
9514 1404 393
Answer:
B, D
Step-by-step explanation:
The quadratic expands to ...
(2n -1)² = (2n)² +2(2n)(-1) +(-1)² = 4n² -4n +1
The coefficients can be factored out of the sum, so ...
∑(4n²) = 4∑n² for example
The sum of 60 ones is 60:
So, the sum can be written as ...
_____
It appears that the key to choosing the correct answers is paying attention to signs.
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Given:
Dimensions of a tank are 50 cm by 32 cm by 20 cm
The tank is full of water and sand
Ratio of volume of water to the volume of sand is 5:1
To find:
Volume of water in the tank in liters
Solution:
Without loss of generality, let,
Length of tank = 50 cm
Breadth of tank = 32 cm
Height of tank = 20 cm
Then, we have,
Total Volume of the tank = Length * Breadth * Height
Total Volume = 50*32*20 cc
Total Volume = 32000 cc
It is given that,
Volume of water : Volume of sand = 5:1
(Volume of water)/(Volume of sand) = 5/1
Cross multiplying, we have,
Volume of sand = (Volume of water)/5
It is also given that the tank is full of water and sand. This implies that,
Volume of water + Volume of sand = Total Volume
Using the value, we obtained, we get,
Volume of water + (Volume of water)/5 = Total Volume
(6 * Volume of water)/5 = Total Volume
Plugging in the value of total volume, we get,
(6 * Volume of water)/5 = 32000 cc
Volume of water =
cc
Volume of water
26,666.6667 cc
We know that,
1 cc = 0.001 liters
26,666.6667 cc = (26666.6667 * 0.001) liters
26,666.6667 cc
26.667 liters
Thus, Volume of water in the tank is approximately 26.667 liters
Final Answer:
Volume of water in the tank (in liters) is approximately 26.667 liters