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Determine if the graph is symmetric about the x-axis, the y-axis, or the origin. (5 points) r = 5 + 4 cos θ x-axis only y-axis only No symmetry Origin only
Find an explicit rule for the nth term of the sequence. (5 points) 7, -7, 7, -7, ... an = 7 (-1)n - 1 an = 7 (-1)n an = 7 1n - 1 an = 7 1n + 1
Given that the graph of cosine function is like the picture below: |dw:1435057103375:dw|. The 4 that multiplies the cos, means that every value of y is going to increase by a factor of 4. At the end, the shape remains and it is just that the graph is more stretched vertically. The 5 that adds the function, means that every coordinate has to increase by 5 at the y-coordinate. In this scenario, the graph will basically move upwards in the y-axis, but still maintaining the same shape. Ultimately, the graph still has a symmetry in the y-axis. Therefore, answer is A.
for the second question try plugging in values for n = 1,2 and 3 into the options to which one fits
for example when n = 1 a1 = 7 * (-1)^1-1 = 7* (-1)^0 = 7*1 = 7
so n =1 fits the first option now try n = 2
when n = 2 a2 = 7 * (-1)^(2-1) = ? can you work that out?
an = 7 1n - 1？？？
(-1)^(2-1) = (-1)^1 = ?
an = 7 1n - 1？？？
you replace the n by 2 an = 7 (-1)^(n-1) so a2 = 7 (-1)^(2-1)
a2 = 7 * (-1)^1 = 7* (-1) = -7 this is the same value as in the series so it looks like we have the correct option to confirm this work out the third term a3 which should come to 7 a3 = 7 * (-1)^(3-1) can you do that?
first work out the 3 -1
a3 = 7 * (-1)^2 can you continue?
you need to work out (-1)^2 next
(-1)^2 = -1 * -1 = ?
right so finally a3 = 7*1 = ?
yes so the first 3 terms are 7,-7,7 so we've found the correct option ( a4 = -7 ) correct option is A
Thank you so much... I love you
ok ok! yw
lol chappy you forgot to close the question /_^