Martin charges $10 for every 5 bags of leaves he rakes. Last weekend, he raked 2 bags of leaves. How much money did he earn?
2 answers:
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Answer:
minimum cost of construction box are x = x = 3.4199 in and y = 10.2598 in and z = 4.2750 in
Step-by-step explanation:
given data
volume = 150 in³
base material costing = 5 cents/in²
front cost = 10 cents/in²
remainder sides cost = 2 cents/in²
to find out
the dimensions that will minimize the cost
solution
we consider here length = x and breadth = y and height = z
and
area of base = xy
area of front = xz
and area of remaining side = xz + 2yz .....................1
so
cost of base will be = 5xy
cost of front = 10xz
cost of remaining side = 2 ( xz+ 2yz)
and
total cost will be
total cost TC = 5xy + 10xz + 2 ( xz+ 2yz)
total cost TC = 5xy + 10xz + 2xz+ 4yz
total cost TC = 5xy + 12xz + 4yz ....................2
and total volume will be = xyz
150 = xyz
z = .......................3
now put z value in equation 2
total cost TC = 5xy + 12xz + 4yz
total cost TC = 5xy + 12x + 4y
total cost TC = 5xy + +
...........4
now differentiate TC w.r.t x and y
TC (x) = 5y -
TC (x) = 5x -
now equating with 0 these
5y - = 0
x² =
and
5x - = 0
x =
solve we get
y = 10.2598
x = 3.4199
now put x and y value in equation 3
z =
z =
z = 4.2750
so minimum cost of construction box are x = x = 3.4199 in and y = 10.2598 in and z = 4.2750 in
If Ian uses 1/20 of the ketchup 4 times, this is equal to 4/20, or 
.
can be simplified to 
, which means we need to work out of 12.2
is equivalent to 20%, which as a decimal is 0.2
0.2 x 12.2 = 2.44 - however, this is how much he has used, and we need to figure out how much is left.
12.2 - 2.44 = 9.76
So, Ian has 9.76 oz remaining :)
0.2 x 12.2 = 2.44 - however, this is how much he has used, and we need to figure out how much is left.
12.2 - 2.44 = 9.76
So, Ian has 9.76 oz remaining :)