Answer: y=1/2x-3
Step-by-step explanation:
Slope-intercept form:y=mx+b
m=y2-y1/x2-x1
-1-(-2)/4-2=1/2
y=1/2x+b
-1=1/2(4)+b
-1=2+b
b=-3
Answer:
13 pieces
Step-by-step explanation:
First we convert 4m into cm :
1m = 100cm
4m = 400cm
Now we need to figure out how many 30s go into 400 :
400 ÷ 30 = 13 remainder 10
So 13 pieces can be cut from the ribbon
Hope this helped and have a good day
Answer:

Step-by-step explanation:
Multiply out
in order to find out which expression it is equivalent to.
1) Since the whole quantity is squared, write it out as
.

2) Multiply binomials by using the FOIL method. Multiply the terms that are listed first in each binomial, then the ones that are listed outermost when looking at both binomials, then innermost, and finally the last terms listed in each binomial. Simplify and combine like terms.


3)
, so
must be
. Thus,
is equivalent to -1. Knowing this, simplify and combine like terms.


Thus, it is equivalent to
.
Answer:
L=(4,-2)
Step-by-step explanation:Left = -2 units and down = -4 units, left is x direction and down is y direction. (x,y).
Answer:
Part A.
Let f(x) = 0;
suppose x= a+h
such that f(x) =f(a+h) = 0
By second order Taylor approximation, we get
f(a) + hf'±(a) +
f''(a) = 0
± ![\frac{\sqrt[]{(f'(a))^{2}-2f(a)f''(a) } }{f''(a)}](https://tex.z-dn.net/?f=%5Cfrac%7B%5Csqrt%5B%5D%7B%28f%27%28a%29%29%5E%7B2%7D-2f%28a%29f%27%27%28a%29%20%7D%20%7D%7Bf%27%27%28a%29%7D)
So, we get the succeeding equation for Newton's method as
± ![\sqrt{f(x_{i})^{2}-2fx_{i}f''x_{i} } ]](https://tex.z-dn.net/?f=%5Csqrt%7Bf%28x_%7Bi%7D%29%5E%7B2%7D-2fx_%7Bi%7Df%27%27x_%7Bi%7D%20%7D%20%5D)
Part B.
It is evident that Newton's method fails in two cases, as:
1. if f''(x) = 0
2. if f'(x)² is less than 2f(x)f''(x)
Part C.
In case
is close to
, the choice that shouldbe made instead of ± in part A is:
f'(x) =
⇔ 
Part D.
As given
=
= h
or h =
- 
We get,
f(a) + hf'(a) +(h²/2)f''(a) = 0
or h² = -hf(a)/f'(a)
Also, (
-
)² = -(
-
)(f(
)/f'(
))
So, f(a) + hf'(a) - (f''(a)/2)(hf(a)/f'(a)) = 0
It becomes h = -f(a)/f'(a) + (h/2)[f''(a)f(a)/(f(a))²]
Also,
=
-f(
)/f'(
) + [(
-
)f''(
)f(
)]/[2(f'(
))²]