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.
Answer:
g(x) = x² - 3
Step-by-step explanation:
A quadratic function has been given as,
f(x) = x²
If the function f is translated by 'h' unit down over the y-axis, the new function obtained by the translation is,
g(x) = x² - h
From the graph attached, h = 3 units (shift of 3 units downwards)
Therefore, g(x) = x² - 3 will be the translated version of f(x).
Mult. these 3 dimensions together to obtain the volume of the prism:
(12 ft)(5/12 ft)(10 1/12 ft). Expressing all of these factors as improper fractions, we get:
12 5 121 5(121) ft^3
------ * ------ * -------- = ----------------- = 50.42 ft^3 = volume of the prism
1 12 12 12
Answer: the answer is 44R2
Step-by-step explanation:
0 4 4 R 2
7 )3 1 0
− 0
3 1
− 2 8
3 0
− 2 8
2