What he has left in the bank is here :
(123.17 + 34.68) - 50 = 107.8
He still has $107.8 left in the bank and he has $50 in his pocket.
I hoped I helped!
A. 6
There will be 6 layers of cubes, since the height is 3 centimeters and the height of the cubes is 1/2
B. 24
The perimeter is the formula 2l+ 2w. With the length and width being 8 and 4, you get 16+8 which is 24 for the perimeter of the base
Answer: Choice D)
The angle between the two vectors is approximately 71.6 degrees
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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)
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|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)
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u dot v = <8,4> dot <9,-9>
u dot v = 8*9 + 4*(-9)
u dot v = 72-36
u dot v = 36
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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
Answer: <u>Irrational </u>
It's irrational because of how 37 comes out of the square root.
For example:
The square root of 64 comes out to 8, which is a whole number. But 37, comes out as an integer and a decimal.
