ANSWER
EXPLANATION
We use the method of completing the squares.
The equation is
We rewrite the above equation to obtain;
We divide through by 3 to obtain;
We add half the coefficient of
to both sides of the equation to get,
The right hand side is now a perfect square.
We now take square root of both sides to get;
We add -2 to both sides,
We simplify to obtain,
Answer:
Step-by-step explanation:
"When 200 gallons of oil were removed from a tank" algebraically looks like this:
V - 200.
"...the volume of oil left in the tank was 3/7 of the tank's capacity" algebraically looks like this:
3/7(V)
Therefore, the equation is
V - 200 = 3/7(V)
Begin by multiplying both sides by 7:
7(V - 200) = 3V and
7V - 1400 = 3V so
-1400 = -4V so
V = 350 gallons
That's if the volume of the oil in the tank was 3/7 of the tank's capacity.
For the other part of the problem, we set up the equation almost the same, except the 3/7 is a 1/2:
V - 200 = 1/2(V)
Multiplying both sides by 2 gives you
2(V - 200) = V and
2V - 400 = V so
-400 = -V so
V = 400
Answer:
The side length is 9 m
Step-by-step explanation:
The area of a square is given by
A = s^2
81 = s^2
Take the square root of each side
sqrt(81) = sqrt(s^2)
9 =s
The side length is 9 m
Answer:
5000 particles of size 10 nanometer should be stacked
Step-by-step explanation:
Average diameter of the of the human hair = 50 micron = 50 × 10⁻⁶ m
Now,
let the number of 10 nanometer i.e 10 × 10⁻⁹ m particle be 'n'
thus,
n × 10 × 10⁻⁹ m = 50 × 10⁻⁶ m
Therefore to find the number of 10 nanometer i.e 10 × 10⁻⁹ m particle,
n = 
or
n = 5000
Hence,
5000 particles of size 10 nanometer should be stacked
