Given u = (2, -8) and v = (8, -2), what is u times v?

Mathematics

1 answer:

jolli1 [7]3 years ago

3 0

Answer:

$u\cdot v=32$

Step-by-step explanation:

Assuming $u$ and $v$ are vectors, their dot product is $u\cdot v$ where $u_1v_1 + u_2v_2$ :

$u\cdot v=u_1v_1+u_2v_2=(2)(8)+(-8)(-2)=16+16=32$

Therefore, $u\cdot v=32$

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The Friendly Sausage Factory (FSF) can produce hot dogs at a rate of 5,500 per day. FSF supplies hot dogs to local restaurants a

Phantasy [73]

Answer:

a. 5218 hot dogs

b. 18 runs per year

c. 1 day per run

Step-by-step explanation:

(a) Let n represent the number of hotdogs in an optimal run. The number of runs needed in a year is ...

r = (260 hotdogs/day)·(365 days/year)/(n hotdogs/run) = 94900/n runs/year

The number of hotdogs in storage decreases from n at the end of a run to 0 just before a run. The decrease is linear, so the average number in storage is n/2.

We can go to the trouble to write the equation for total cost, then differentiate it to find the value of n at the minimum, or we can just jump to the solution. That solution is ...

holding cost = setup cost

(n/2)·0.46 = (94900/n)·66

n^2 = 94900·66·2/0.46 = 27,232,173.9

n ≈ 5218.446

The optimal number of hotdogs in a run is 5218.

___

(b) The number of runs needed per year is (from part (a)) ...

r = 94900/5218 ≈ 18.187

The number of runs per year is 18.

___

(c) The run lenght is 5218 hotdogs, and the run produces them at the rate of 5500 hotdogs/day, so the run length in days is ...

(5218 hotdogs)/(5500 hotdogs/day) = 0.9487 days