The table represents the number of cheese crackers in the lunchboxes of 9 boys and 9 girls. By looking at the table, does it app
2 answers:
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Consider the function 
, which has derivative 
.
The linear approximation of
for some value 
within a neighborhood of 
is given by
Let
. Then 
can be estimated to be
![\sqrt[3]{63.97}\approx4-\dfrac{0.03}{48}=3.999375](https://tex.z-dn.net/?f=%5Csqrt%5B3%5D%7B63.97%7D%5Capprox4-%5Cdfrac%7B0.03%7D%7B48%7D%3D3.999375)
Since
for 
, it follows that must be strictly increasing over that part of its domain, which means the linear approximation lies strictly above the function . This means the estimated value is an overestimation.
Indeed, the actual value is closer to the number 3.999374902...
The linear approximation of
Let
Since
Indeed, the actual value is closer to the number 3.999374902...
Marcario should use 4 pounds of macadamia nuts and 8 pounds of almonds.
Explanation
given
cost of macadamia nuts per pound=$9
cost of almond nuts per pound=$5.25
cost of the mixture per pound=$6.5
total pounds of the mixture to be made=12
let the pounds of macadamia nuts=x
pounds of almond nuts=y
total pounds of nuts=x+y=12
solving (1) and (2)
x=4
y=8