Consider the function
, which has derivative
.
The linear approximation of
for some value
within a neighborhood of
is given by
Let
. Then
can be estimated to be
![\sqrt[3]{63.97}\approx4-\dfrac{0.03}{48}=3.999375](https://tex.z-dn.net/?f=%5Csqrt%5B3%5D%7B63.97%7D%5Capprox4-%5Cdfrac%7B0.03%7D%7B48%7D%3D3.999375)
Since
for
, it follows that
must be strictly increasing over that part of its domain, which means the linear approximation lies strictly above the function
. This means the estimated value is an overestimation.
Indeed, the actual value is closer to the number 3.999374902...
so all those quadratics have their parent y = x², which has the graph of a "bowl".
and depending on the coefficient, the bowl is wider or not.
the larger the coefficient, the narrower the bowl, the smaller the coefficient, the wider the bowl.
well, 1/2 is smaller then 2, thus y = (1/2)x² is wider than y = 2x².
Angles 2 and 6 are corresponding angles, which would explain why they are congruent if lines a and b are parallel, but there is nothing in the problem to explain that any of the angles equals 60 degrees since no measurements were given in the diagram.
Answer:
x = 6
Step-by-step explanation:
Love proportions!
3x+2(x+6) = 35(21)
21(3x+2) = 35(x+6)
63x + 42 = 35x + 210
28x = 168
x = 6
Answer:
x > 2
Step-by-step explanation:
First simplify the bracket....to give you...x + 2...then
; 4x + x + 2 > 12....
; 5x + 2 > 12
; 5x > 12 - 2.....then gives you...5x > 10...then divide both sides by 5
then gives you....; x > 2
