(81^-0.25)^3 = ( 1 / (81^0.25) )^3
<span>81^.025 is the 4th root of 81 which is 3 </span>
<span>Therefor </span>
<span>( 1 / (81^0.25) )^3 = (1/3)^3 </span>
<span>(1/3)^3 = 1/27 <-----
Hope I Helped You!!! :-)
Have A Good Day!!!</span>
Answer:
Option "B" as per the list of possible answers
Step-by-step explanation:
Notice that the parabola has a minimum at the point (2, 1), therefore first look at which of the options gives you 
. You would be able then the discard the last two functions listed (they render "-1" (not 1) for x = 2.
Now to decide between the first and the second option, notice that the first option has a negative coefficient (-0.2) multiplying the perfect square 
which means that the branches of such parabolic function would be pointing down. So you discard the first option, and now the only one left is the second option:
which you can check briefly by evaluating a couple of easy points (like what values you get for x = 0, and at x = 4, and confirm it is the correct option.
Answer:
Step-by-step explanation:
Let x represent the distance travelled by the helicopter and the plane.
Let t represent the time it takes the the helicopter to travel x miles
Speed of the helicopter is 180 miles per hour.
Distance travelled = speed × time
x = 180t
Twenty minutes later, a plane leaves the airport and follows the helicopter at 330mi/hr. Converting 20 minutes to hours, it becomes 20/60 minutes
Time taken for the plane to travel x miles is t - 20/60
x = 330(t - 20/60)
Before the plane overtakes the helicopter, they would have travelled equal distance. Therefore
330(t - 20/60) = 180t
330t - 110 = 180t
330t - 180t = 110
150t = 110
t = 110/150 = 0.73 hours
Hmm, the 2nd derivitve is good for finding concavity
let's find the max and min points
that is where the first derivitive is equal to 0
remember the difference quotient
so
f'(x)=(x^2-2x)/(x^2-2x+1)
find where it equals 0
set numerator equal to 0
0=x^2-2x
0=x(x-2)
0=x
0=x-2
2=x
so at 0 and 2 are the min and max
find if the signs go from negative to positive (min) or from positive to negative (max) at those points
f'(-1)>0
f'(1.5)<0
f'(3)>0
so at x=0, the sign go from positive to negative (local maximum)
at x=2, the sign go from negative to positive (local minimum)
we can take the 2nd derivitive to see the inflection points
f''(x)=2/((x-1)^3)
where does it equal 0?
it doesn't
so no inflection point
but, we can test it at x=0 and x=2
at x=0, we get f''(0)<0 so it is concave down. that means that x=0 being a max makes sense
at x=2, we get f''(2)>0 so it is concave up. that means that x=2 being a max make sense
local max is at x=0 (the point (0,0))
local min is at x=2 (the point (2,4))
Answer: C.
Explanation: It's a topographic maps
