Sean began jogging to live a healthier lifestyle. on his first run, he ran one-half mile. he increased his workouts by adding two miles a month to his run. he wrote the equation f(x) = 0.5 + 2x to model his progress. the variable x represents the number of .
a. miles he runs
b. months he runs
c. miles he ran the first day
d. calories he burns
options a and b
amplitude of the graph = 3 but shown correctly
hence option a is right
there is a vertical shift of 1/2 down. shown correctly
option b is right
horizontal shift is 1 unit to the left after adjusting x for x/4. shown incorrectly
option c is not right
period is 8 pi not shown correctly
option d is wrong.
horizontal expansion is not shown at all for x/4
hence option e is wrong.
an exponent is a way to represent repeated multiplication. that is
x² = x·x . . . . the exponent of 2 means x is a factor 2 times in the product
so, your expression means
(14√6)² = (14·√6)·(14·√6)
of course, the commutative and associative properties of multiplication allow us to regroup these factors to some convenient order, such as
(14·14)·(√6)(√6) = 196·(√6)(√6)
we know that multiplying a square root times itself gives the original number. (this is the whole point of a square root.) that is
(√6)(√6) = 6
so, the product above is
(14√6)² = 14·14·(√6)(√6) = 196·6 = 1,176
since there are no variables involved here, your calculator can give you this answer.