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Which expression is equivalent to ?
A) –63
B) 36
C)
D)
Answer:
The equivalent of is
Step-by-step explanation:
Given
Expression:
Required:
Find the Equivalent Expression
To find the equivalent of this expression, we make use of law of indices.
One of the laws of indices states that
If we apply this law to the expression above ()
By comparison a = 6 and b = 3.
So, becomes
=
Simplifying further;
=
This can also be written as
=
By splitting the above expression; we have that
=
Multiplication law of indices states that;
a * a * a = a³. (Because they have the same base of a)
So, can then be written as
Hence, =
So, the equivalent of is
Answer:
The general solution of the equation is y = + 5
Step-by-step explanation:
Since the differential equation is given as y'(t) = 3y -5
The differential equation is re-written as
dy/dt = 3y - 5
separating the variables, we have
dy/(3y - 5) = dt
dy/(3y - 5) = dt
integrating both sides, we have
∫dy/(3y - 5) = ∫dt
∫3dy/[3(3y - 5)] = ∫dt
(1/3)∫3dy/(3y - 5) = ∫dt
(1/3)㏑(3y - 5) = t + C
㏑(3y - 5) = 3t + 3C
taking exponents of both sides, we have
exp[㏑(3y - 5)] = exp(3t + 3C)
3y - 5 =
3y - 5 =
3y = + 5
dividing through by 3, we have
y = + 5
So, the general solution of the equation is y = + 5