Consider the expression
Factorize the numerator and denominator a difference/sum of cubes:
Expand the denominator:
since <em>x</em> = 2020, and clearly 2020² + 2020 + 1 ≠ 0, so we can cancel the factor of <em>x</em> ² + <em>x</em> + 1. This leaves us with
so that <em>a</em> + <em>b</em> = 673 + 674 = 1347.
Answer:
(-2 , 2)
Step-by-step explanation:
A(-8 , 2) = (x1 , y1)
B(4 , -2) = (x2 , y2)
midpoint = (x1 + x2/2 , y1 + y2/2)
=(-8 + 4/2 , 2-(-2)/2)
=(-4/2 , 2+2/2)
(-2 , 2)
(3 , 7) = (x1 , y1)
(9 , 2) = (x2 , y2)
distance of PQ =
=
=
=
=
=7.8 unit
Given :
Distance covered by object , D = 63 cm .
Time taken to cover distance D , t = 2 days .
To Find :
The speed of object in m/s .
Solution :
First we will convert all units into m and hours .
D = 63 cm = 0.63 m .
.
Now , speed is :
Hence , this is the required solution .
Answer:
7.86 km
Step-by-step explanation:
Let x represent the distance point P lies east of the refinery. (We assume this direction is downriver from the refinery.)
The cost of laying pipe to P from the refinery (in millions of $) will be ...
0.5√(1² +x²)
The cost of laying pipe under the river from P to the storage facility will be ...
1.0√(2² +(9-x)²) = √(85 -18x +x²)
We want to minimize the total cost c. That total cost is ...
c = 0.5√(x² +1) +√(x² -18x +85)
The minimum value is best found using technology. (Differentiating c with respect to x results in a messy radical equation that has no algebraic solution.) A graphing calculator shows it to be at about x ≈ 7.86 km.
Point P should be located about 7.86 km downriver from the refinery.
