1 yard = 3 feet = 36 in

so 1 in = 1/36 yard, 1 ft = 1/3 yard.

The volume of the layer of the topsoil, is:

5 in * 23 ft * 17 ft = 5 *(1/36)*23*(1/3)*17*(1/3) yard cubed =

(5*23*17)/(36*3*3)= 1955/324=6.034 yard cubed.

The store only sells increments of 1/4 = 0.25 cubic yards.

we need 6.034/0.25=24.136

So we need to buy 25 (24 will not be enough) increments of 1/4 cubic yards.

Answer: 25 increments of 1/4 cubic yard, that is 25*0.25=6.25 cubic yards.

5 0

3 years ago

Determine whether the sequence is arithmetic or geometric.

Zarrin [17]

S1.
32, 16, 0, -16, ...
It's an arithmetic sequence:
$a_1=32;\ d=16-32=-16\\\\a_n=a_1+(n-1)d\\\\a_n=32+(n-1)\cdot(-16)=32-16n+16=48-16n$

S2.
32, 16, 8, 4, ...
It's a geometric sequence:
$a_1=32;\ r=16:32=\dfrac{1}{2}\\\\a_n=a_1r^{n-1}\\\\a_n=32\cdot\left(\dfrac{1}{2}\right)^{n-1}$

Answer: sequence 1 is arithmetic and sequence 2 is geometric.

6 0

3 years ago