Criticize the following proof by induction of the proposition, "happy families are all alike." consider a set consisting of one happy family. obvi- ously all its elements are the same. suppose it has been shown that for any set of n happy families, say {}, we have fi f2 ==fn. con- sider a set {f1. n+1} of n+1 happy families. then {f1.) is a set of n happy families, so f1 = f2 = = fn. similarly, {f2, f3, fn+1} is a set of n happy families, so fn+1 = = f2. thus fr+1 = fi also, and the set of n + 1 happy families are all alike. by the principle of induction, we see that for any finite set of happy families, they are all alike. since the set of all happy families is finite, we conclude: happy families are all alike.

something that characterises a right triangle is the fact that we may use pythagoras' theorem to find any one of its sides given that we have the length of the other two sides. here, we have the length of the hypotenuse, √(87) yd, and one other side, √(23) yd, thus we can easily find the length of the remaining side using pythagoras' theorem as defined below:

c^2 = a^2 + b^2, where c is the length of the hypotenuse, and a and b are the lengths of the other two sides.

thus, given that c = √(87) and a = √(23), we may substitute these into the formula we defined above to get:

c^2 = a^2 + b^2

(√87)^2 = (√23)^2 + b^2 (substitute c = √87 and a = √23 into the equation)

87 = 23 + b^2 (evaluate (√87)^2 = 87 and (√23)^2 = 23 - remember that the square root of a number, squared will equal that very same number)

64 = b^2 (subtract 23 from both sides)

√64 = b (take the square root of both sides)

8 = b (evaluate √64 = 8)

therefor, the length of the unknown leg in the right triangle is 8 yd (first answer).

what do you mean by fog

step-by-step explanation:

the answer will be the last one

0.84 dang lotta people are looking for this lol or if you round up its 1 but the overall answer to that is 0.84

step-by-step explanation: