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vampirchik [111]
3 years ago
13

A robot can complete 7 tasks in 3 4 hour. Each task takes the same amount of time

Mathematics
1 answer:
kodGreya [7K]3 years ago
7 0

Answer:

a. 3/28 hours

b. 9 tasks

Step-by-step explanation:

a. The robot can complete 7 tasks in 3/4 hours.

The number of hours it will take to complete one task is:

= Time taken / Number of tasks

= 3/4 ÷ 7

= 3/4 * 1/7

= 3/28 of an hour

b. If the Robot can complete one task in 3/28 of an hour, in one full hour it will complete:

= 1 ÷ 3/28

= 9.33

= 9 tasks

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tensa zangetsu [6.8K]
Answer: Choice D) 
The angle between the two vectors is approximately 71.6 degrees

----------------------------------------------
----------------------------------------------

Work Shown: 

Each time I write the word "dot" I mean "dot product". 

|u| = length of vector u
|u| = sqrt(u dot u)
|u| = sqrt(<8,4> dot <8,4>)
|u| = sqrt(8*8 + 4*4)
|u| = sqrt(64 + 16)
|u| = sqrt(80)
|u| = sqrt(16*5)
|u| = sqrt(16)*sqrt(5)
|u| = 4*sqrt(5)

-----------------------

|v| = length of vector v
|v| = sqrt(v dot v)
|v| = sqrt(<9,-9> dot <9,-9>)
|v| = sqrt(9*9 + (-9)*(-9))
|v| = sqrt(81+81)
|v| = sqrt(2*81)
|v| = sqrt(2)*sqrt(81)
|v| = sqrt(2)*9
|v| = 9*sqrt(2)

-----------------------

u dot v = <8,4> dot <9,-9>
u dot v = 8*9 + 4*(-9)
u dot v = 72-36
u dot v = 36

-----------------------

cos(theta) = (u dot v)/(|u|*|v|)
cos(theta) = (36)/(4*sqrt(5)*9*sqrt(2))
cos(theta) = (36)/(36*sqrt(10))
cos(theta) = 1/(sqrt(10))
cos(theta) = sqrt(10)/10
theta = arccos(sqrt(10)/10)
theta = 71.56505
which rounds to 71.6 when rounding to one decimal place (nearest tenth)

That's why the approximate answer is roughly 71.6 degrees

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