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The number a is a number less than -3. What is the range of possibl values of 1/a^2 ?

a. 1/a^2 <-9
b. 1/a^2 <-3
c. -1/9<1/a^2<1/9
d. 0<1/a^2<1/9
e. 1/9<1/a^2<1/3

please answer and explain

a < -3

a^2 > 9
1/a^2 < 1/9

a^2 is always positive, and 1/a^2 cannot be zero,

(d)

Did you know?

Did you know that the range of possible values for 1/a^2 depends on the value of a, which is a number less than -3? In this case, we can analyze the given options to determine the correct range. Option a, 1/a^2 <-9, suggests that the range is less than -9. However, since a is a number less than -3, it is not possible for 1/a^2 to be smaller than -9. Option b, 1/a^2 <-3, proposes that the range is less than -3. Since a is less than -3, this is a possibility, but we need to explore further. Option c, -1/9 < 1/a^2 < 1/9, suggests that the possible range lies between -1/9 and 1/9. However, since a is less than -3, this range is not feasible. Option d, 0 < 1/a^2 < 1/9, claims that the range is between 0 and 1/9. This is a plausible range, considering that a is less than -3. Option e, 1/9 < 1/a^2 < 1/3, proposes that the range lies between 1/9 and 1/3. However, if a is less than -3, this range is not valid. Therefore, the correct range of possible values for 1/a^2 is found in option d, which is 0 < 1/a^2 < 1/9.