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.
It would take the faucet 18 hours to fill the tank because 18/12=1.5. That means it will be 1.5 times slower to fill the tank up with the hose on. 1.5*12=18.
Answer:
A'B'= 3 cm and B'D' = 1.6 cm
Step-by-step explanation:
First of all, we are told that the scale factor = 1/5
Now,we know that If the scale factor is less than 1, then the dilation is a reduction.
Thus, in this question the dilation is a reduction.
For us to calculate the dimensions of the dilated rectangle, we'll multiply the original dimensions by the scale factor
Thus;
A'B' = AB(1/5)
A'B' = 15(1/5) = 3 cm
B'D' = BD(1/5) = 8(1/5) = 1.6 cm
Thus, The length of each side of the dilated rectangle are;
A'B'= 3 cm and B'D' = 1.6 cm
Answer:
12
Step-by-step explanation:
4 x 3 is 12
