Answer:
Step-by-step explanation:
A dependent variable in an expression is one whose value can be determined only when the value of other variable (i.e independent) is known.
A. The cost at the fitness center depends on the number of months (x).
The cost is the dependent variable, and number of months (x) is the independent variable.
f(x) = 100 + 40x
Example, the cost paid for 12 months can be determined as;
f(12) = 100 + 40(12)
= 100 + 480
= 580
Thus, $580 would be paid for 12 months at the fitness center.
B. The lettuce is sold at $1.69 per pound. The cost depends on the number of pounds of lettuce bought.
The cost is the dependent variable, while the number of pounds of lettuce (x) bought is the independent variable.
So that;
f(x) = 1.69x
The cost of 10 pounds of lettuce can be determined as;
f(x) = 1.69(10)
= 16.9
Thus, the cost of 10 lb of lettuce is $16.90.
Answer:
-y=5-x
Step-by-step explanation:
Starting amount: 982 pounds of grain
Since Mr. Parker fed 240 pounds of grain to his pigs, subtract 240 pounds from 982 pounds of grain.
982 - 240 = 742
After feeding pigs: 742 pounds of grain
Mr. Parker fed another 460 pounds of grain to his cows from his 742 pounds, so subtract 460 pounds from 742 pounds.
742 - 460 = 282
After feeding pigs and cows: 282 pounds of grain
Mr. Parker has 282 pounds of grain left.
are the critical points, and judging by the picture alone, you must have
and
. (You might want to verify with the derivative test in case that's expected.)
Then the shaded region has area
I'll leave the details to you.
Now, for part (iv), you're asked to find the minimum of
, which entails first finding the second derivative:
setting equal to 0 and finding the critical point:
This is to say the minimum value of
*occurs when
*, but this is not necessarily the same as saying that
is the actual minimum value.
The minimum value of
is obtained by evaluating the derivative at this critical point:
