Answer:
Step-by-step explanation:
Before subtracting we require the fractions to have a common denominator.
The lowest common multiple of x + 4 and x + 6 is (x + 4)(x + 6)
Multiply the numerator/denominator of the first fraction by x + 6 and
multiply the numerator/denominator of the second fraction by x + 4
= -
Expand the numerators and simplify leaving the denominator
=
=
=
Answer:
The maximum distance traveled is 4.73 meters in 0.23 seconds.
Step-by-step explanation:
We have that the distance traveled with respect to time is given by the function,
.
Now, differentiating this function with respect to time 't', we get,
d'(t)=9.8t-2.3
Equating d'(t) by 0 gives,
9.8t - 2.3 = 0
i.e. 9.8t = 2.3
i.e. t = 0.23 seconds
Substitute this value in d'(t) gives,
d'(t) = 9.8 × 0.23 - 2.3
d'(t) = 2.254 - 2.3
d'(t) = -0.046.
As, d'(t) < 0, we get that the function has the maximum value at t = 0.23 seconds.
Thus, the maximum distance the skateboard can travel is given by,
.
i.e. .
i.e. .
i.e. .
i.e. d(t) = 4.73021
Hence, the maximum distance traveled is 4.73 meters in 0.23 seconds.
