Answer:
The actual cost incurred in manufacturing:
- the 111st oven is $114.07
- the 221st oven is 122.71
- the 311st oven is $140.59
The marginal cost when x = 110, 220, and 310 is
Step-by-step explanation:
We know that the daily cost function of producing microwave ovens is given by
(a) The actual cost incurred in manufacturing the 111st oven is the difference between the total cost incurred in manufacturing the first 111 ovens and the total cost of manufacturing the first 110 ovens:
![C(111)-C(110)=[0.0002(111)^3 - 0.06(111)^2 + 120(111) + 5000]-[0.0002(110)^3 - 0.06(110)^2 + 120(110) + 5000]\\\\C(111)-C(110)=17854.27-17740.2\\\\C(111)-C(110)=114.07](https://tex.z-dn.net/?f=C%28111%29-C%28110%29%3D%5B0.0002%28111%29%5E3%20-%200.06%28111%29%5E2%20%2B%20120%28111%29%20%2B%205000%5D-%5B0.0002%28110%29%5E3%20-%200.06%28110%29%5E2%20%2B%20120%28110%29%20%2B%205000%5D%5C%5C%5C%5CC%28111%29-C%28110%29%3D17854.27-17740.2%5C%5C%5C%5CC%28111%29-C%28110%29%3D114.07)
For the 221st
![C(221)-C(220)=[0.0002(221)^3 - 0.06(221)^2 + 120(221) + 5000]-[0.0002(220)^3 - 0.06(220)^2 + 120(220) + 5000]\\\\C(221)-C(220)=30748.31-30625.6\\\\C(221)-C(220)=122.71](https://tex.z-dn.net/?f=C%28221%29-C%28220%29%3D%5B0.0002%28221%29%5E3%20-%200.06%28221%29%5E2%20%2B%20120%28221%29%20%2B%205000%5D-%5B0.0002%28220%29%5E3%20-%200.06%28220%29%5E2%20%2B%20120%28220%29%20%2B%205000%5D%5C%5C%5C%5CC%28221%29-C%28220%29%3D30748.31-30625.6%5C%5C%5C%5CC%28221%29-C%28220%29%3D122.71)
For the 311st
![C(311)-C(310)=[0.0002(311)^3 - 0.06(311)^2 + 120(311) + 5000]-[0.0002(310)^3 - 0.06(310)^2 + 120(310) + 5000]\\\\C(311)-C(310)=42532.79-42392.2\\\\C(311)-C(310)=140.59](https://tex.z-dn.net/?f=C%28311%29-C%28310%29%3D%5B0.0002%28311%29%5E3%20-%200.06%28311%29%5E2%20%2B%20120%28311%29%20%2B%205000%5D-%5B0.0002%28310%29%5E3%20-%200.06%28310%29%5E2%20%2B%20120%28310%29%20%2B%205000%5D%5C%5C%5C%5CC%28311%29-C%28310%29%3D42532.79-42392.2%5C%5C%5C%5CC%28311%29-C%28310%29%3D140.59)
(b) If C(x) is a total cost function, then the marginal cost function is defined to be its derivative C'(x).
We need to find the derivative of the total cost function:
The marginal cost when x = 110, 220, and 310 is given by
Answer:
5
Step-by-step explanation:
Find the greatest common divisor:
gcd(20, 45, 15)
Find the divisors of each integer and select the largest element they have in common:
The divisors of 20 are:
1, 2, 4, 5, 10, 20
The divisors of 45 are:
1, 3, 5, 9, 15, 45
The divisors of 15 are:
1, 3, 5, 15
The largest number common to all divisor lists is 5:
divisors of 20: 1, 2, 4, 5, 10, 20
divisors of 45: 1, 3, 5, 9, 15, 45
divisors of 15: 1, 3, 5, 15
Answer: gcd(20, 45, 15) = 5
Problem 5
d = 29 = diameter
r = d/2 = 29/2 = 14.5 = radius
SA = surface area of sphere
SA = 4*pi*r^2
SA = 4*pi*(14.5)^2
SA = 841pi
SA = 841*3.14
SA = 2,640.74 square inches
To convert from square inches to square feet, we divide by 144. This is because 12^2 = 144.
2,640.74 square inches = (2,640.74)/144 = 18.3 sq ft
<h3>Answer:
18.3 square feet (approximate)</h3>
=====================================
Problem 6
d = 10.7 = diameter
r = d/2 = 10.7/2 = 5.35 = radius
L = 22.3 = slant height
SA = surface area of the cone
SA = pi*r^2 + pi*r*L
SA = pi*(5.35)^2 + pi*5.35*22.3
SA = 147.9275pi
SA = 147.9275*3.14
SA = 464.49235
<h3>Answer:
464.49235 square cm (approximate)</h3>
Ok to start this problem you must list two numbers that add to 14
7 and 7
9 and 5
10 and 4
6 and 8
those are the numbers that we will use for now..
Now multiply each pair of numbers and see which one equals 45
7 * 7 = 49, no
9 * 5 = 45, YES
10 * 4 = 40, No
6 * 8 = 48, No
The numbers discovered are 9 and 5
