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.
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Step-by-step explanation:
The corcumference C of a circle is C= 2 x pie x radius
So radius= C/(2pie)
Volume of cylinder= pie x r(squared) x h
Answer:
SSS
Step-by-step explanation:
Given that the sides are equal and no angles are given
Answer:
The best estimate of the area of the larger figure is 
Step-by-step explanation:
step 1
<em>Find the scale factor</em>
we know that
If two figures are similar, then the ratio of its corresponding sides is equal to the scale factor
Let
z----> the scale factor
x-----> the corresponding side of the larger figure
y-----> the corresponding side of the smaller figure
so

we have


substitute
-----> the scale factor
step 2
<em>Find the area of the larger figure</em>
we know that
If two figures are similar, then the ratio of its areas is equal to the scale factor squared
Let
z----> the scale factor
x-----> the area of the larger figure
y-----> the area of the smaller figure
so

we have


substitute and solve for x
