A) The first step needs 100 bricks, the second needs 98, the third needs 96, and so on. Therefore the number of bricks for the nth step is: a_n = a_1 + d(n-1), where a_1 = 100 (the first term), d = -2 (difference).
a_n = 100 - 2(n-1) = 102 - 2n, and for the 30th step, a_30 = 102 - 2*30 = 42. So the top step will need 42 bricks.
b) The total staircase will need: 100 + 98 + 96 + ... + 44 + 42, and there are n = 30 terms. Using the formula for the sum of an arithmetic sequence:
S = (a_1 + a_n)*n/2 = (100 + 42)*30/2 = 2130
Therefore, 2130 bricks are required to build the entire staircase.
The point is not a solution to the equation of the line.
Hope this helps!
From the equation, you can see that (3,-2) is the center of the circle (the terms are 0 for those x,y values). The mentioned point has the same y value as the center. That's good news, because it tells us that the tangent line is exactly vertical. The x coordinate is given as x=8. Vertical lines have an equation of x=... so x=8 is the right answer.
If you mean 756.04, the answer is 756.0. 4 is closer to 0.
5 Or More, raise the score
4 Or Less, let it rest
