Step-by-step explanation:
Use the quadratic formula to find the solutions.
−b±√b2−4(ac)2a-b±b2-4(ac)2a
Substitute the values a=9a=9, b=0b=0, and c=−81c=-81 into the quadratic formula and solve for xx.
x=±3x=±3
The final answer is the combination of both solutions.
x=3,−3x=3,-3
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
88.6 as a mixed number is 14 2/3
Answer:
Step-by-step explanation:
In order to solve this it is always a good idea to start by drawing a diagram of the situation (See attached picture).
From the diagram we can see that we are dealing with similar triangles. We can use similar triangles to build an equation that relates the length of the shadow with the height of the lamp, so we get:
the height of the lamp can be found by subtracting the 
distance the lamp falls in a given time t from the original 30ft the lamp was located at.
So the equation will now lok like this:
So now we can solve the equation for L, we can start by multiplying by the LCD SO WE GET:
next, we can distribute the right side of the equation so we get:
and subtract 6L from both sides so we get:
and factor L, so we get:
and solve for L:
now, we can differentiate this equation by using the chain rule, so we get:
which can be simplified to:
and now we can substitute t for 1s so we get:
Answer:
4/21 of a spool
Step-by-step explanation:
2/7 * 2/3 = 4/21
