Answer:
p = - 14
Step-by-step explanation:
Using the rules of exponents
÷ 
= 
= 
Note 81 = 9² and 729 = 9³
Given
÷ 
= 
÷ 
= 
÷ 
= 
= 
= 
Thus
= 
Since bases on both sides are equal then equate the exponents
4p = 3p - 14 ( subtract 3p from both sides )
p = - 14
Answer:
Step-by-step explanation:
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:
6541.7 mm³ (nearest tenth)
Step-by-step explanation:
Given that the height is 40mm, h= 40mm.
Diameter= 2(radius)
Radius of cone
= 25 ÷2
= 12.5mm
Volume of cone
= 6541.7 mm³ (nearest tenth)
