we did! but from there we can solve for side (and thus, solve for base and get area) with the following formula:

height = [(side)*√3]/2

we know that height = 6, so we can solve for side from there, and then multiply height by side. let me know if you have questions about the rest of the process for that problem, though. 🙂

in 10th question did not we get the height of triangle instead of it side,which is 6 units

hi kaitlin,

this is certainly a difficult question! the key to understanding this is to use the difference of squares formula. this is a difficult one to type out so i wrote the problem out and you can access it here. i numbered the steps which i will explain:
step 1: recognize that the left side of the equation can be simplified using the difference of squares and factor it.
step 2: once the left side of the equation is factored, we can see that we have the same term on both sides (9x^4+4t^2). divide both side by this term.
step 3: the right side of the equation now simplifies to 1 because we have the same term in the numerator and denominator.
step 4: recognize that the term on the left side of the equation can be factored again using the difference of squares.
step 5: factor the left side of the equation again and we get our answer.

does that make sense? please let me know if you have any more questions 🙂

hi james,

you raised some very important points! i spoke with our experts and we have adjusted the wording of the problem to take care of the correct issue you brought up. 🙂

hi dennis,

happy to help! if 90 is the largest number, no other number can be 90 or higher. we want to find the smallest possible number one of the four can be. keep in mind, we need the average (mean) to still be 75 as well. so let’s get the biggest possible numbers and our mystery number x:

90 + 89 + 88 + x

we need to divide this by 4 to get our mean:

(90 + 89 + 88 + x)/4 = 75

now we do some algebra, first by multiplying both sides by 4:

90 + 89 + 88 + x = 300

267 + x = 300

now subtract 267 to get x on its own:

x = 33

and that’s our answer. 🙂

the arithmetic mean question

the

hi frank,

good question! 🙂

it is true that it used to be assertively taught that a superlative cannot be used in a comparison between just two objects. if we put aside the fact that this is not commonly taught or enforced in style guides anymore, i want to point out some situations when it would be possible to say that there are grounds for ignoring it. imagine we want to refer to the “most young” individual in a group, but we do not know if there are 2 or 3 people in the group; in this case, we could comfortably use “youngest” despite the potential mismatch. also, for reasons of style, we might sometimes ignore this idea and say something like, “my father is the tallest of three children, and my mother is the tallest of two.”

now, all that said, if you want to stick to a rule, you can certainly say comparatives are for 2 objects and superlatives are for 3+ objects, but you might encounter debate with people saying that technically a limit (as expressed by a superlative) exists whether or not you have 3+ objects. (just because you are younger than your one sibling does not mean you are not also the youngest.) i hope this helps a bit, and thanks for reaching out! 🙂