Find y when x = 9 if y varies directly as the square of x, and y = 245 when x = 7.

Step-by-step explanation:

y is directly proportional to x^2.

This means that y = kx^2, where k is a real constant.

When x = 7, y = 245:

245 = k(7)^2 = 49k. By division, k = 5.

Now we know that y = 5x^2, when x = 9, y = 5(9)^2 = 5 * 81 = 405.

(a) common ratio in the given sequence is, 3

(b) push ups will do kendall do on the 20th week

step-by-step explanation:

geometric sequence is a sequence of numbers that follows a pattern were the next term is found by multiplying by a constant called the common ratio(r)

(a)

given the sequence: 6 , 18 , 54 , 162 ,

this sequence is geometric sequence where each term is 3 times the previous term.

therefore,

common ratio(r) = 3.

(b)

a formula for nth term of geometric sequence is given by;

,   where r is the common ratio between the successive terms and is the first term,

to find how many push ups will kendall do on the 20th week.

here. n = 20th term.

in the given sequence first term

then;

simplify:

therefore, push ups will do kendall do on the 20th week

if the angular bisector of an triangle bisects the opposite side, prove that the other two sides are equal.