Solve the following equation:
Answers
Solution :
Let us assume that a = 3/7.
So, 7/3 = a^-1
According to the given question :
(7/3)^(-x+1/2) = (3/7)^(1/2-x)
> (a^-1)^(-x+1/2) = a^(1/2-x)
> a^( x - 1/2) = a(1/2-x) .
As the bases are equal, hence, the exponents should also be equal
> (x-1/2) = (1/2 - x)
> 2x = 1/2 + 1/2
> 2x = 1
> x =1/2.
Thus, the value of x = 1/2 is the required answer.
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Additional Information :
Always for solving questions on exponents, try to equate after making sure that the base is always equal for a shortcut.
The above problem can be done in various more methods; try to explore!
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Answer:
Calculate the first and second velocities of the car with two washers attached to the pulley, using the formulas
v1 = 0.25 m / t1, and
v2 = 0.25 m / (t2 – t1)
where t1 and t2 are the average times the car took to reach the 0.25 and the 0.50 meter marks. Record these velocities, to two decimal places, in Table E.
What is the first velocity of the car with two washers at the 0.25 meter mark?
m/s
What is the second velocity of the car with two washers at the 0.50 meter mark?
m/s