Find the line that is normal to the parabola at the given point
remember that normal means perpendicular
perpendicular lines have slopes that multiply to -1
we can use point slope form to write the equation of the line since we are given the point (1,0)
we just need the slope
take derivitive
y'=1-2x
at x=1
y'=1-2(1)
y'=1-2
y'=-1
the slope is -1
the perpendicular of that slope is what number we can multiply to get -1
-1 times what=-1?
what=1
duh
so
point (1,0) and slope 1
y-0=1(x-1)
y=x-1 is da equation
solve for where y=x-1 and y=x-x² intersect
set equatl to each other since equal y
x-1=x-x²
x²-1=0
factor difference of 2 perfect squares
(x-1)(x+1)=0
set to zero
x-1=0
x=1
we got this point already
x+1=0
x=-1
sub back
y=-1-(-1)²
y=-1-(1)
y=-1-1
y=-2
it intersects at (-1,-2)
Answer: 103, 104, 105, and 106
Step-by-step explanation: This problem states that the sum of 4 consecutive integers is 418 and it asks us to find the integers.
First represent your 4 consecutive integers as follows.
X ⇒ first integer
X + 1 ⇒ second integer
X + 2 ⇒ third integer
X + 3 ⇒ fourth integer
Since their sum is 418, our equation reads
x + (x + 1) + (x + 2) + (x + 3) = 418.
Simplifying on the left side we get 4x + 6 = 418.
Now we can subtract 6 from both sides of the equation and we have
4x = 412.
Now just divide both sides by 4 and we find that <em>x = 103</em>.
Finally, make sure you list all your answers.
If <em>x</em> is 103, then <em>x </em>+ 1 is 104, <em>x</em> + 2 is 105, and <em>x</em> + 3 is 106
Therefore, our 3 consecutive integers are 103, 104, 105, and 106.
Answer:
He has 420 liters of paint.
Step-by-step explanation:
all you have to do is add 110 = 310
Answer:
I have this same question do you have the answer??
Step-by-step explanation:
