ANSWER:
r =
Explaination:
Convert the given curve into the the polar form.
x = rcosθ
y = rsinθ
in f(x,y) = (x²-y²) - √(x²+y²) = 0
put the values of x & y in given curve equation.
We get at,
g(r,θ) = (r²cos²θ - r²sin²θ) - √(r²cos²θ + r²sin²θ) = 0
g(r,θ) = r²(cos²θ - sin²θ) - √r² = 0
We know that,
cos²θ - sin²θ = cos2θ
g(r,θ) = r²(cos2θ) - r = 0
Solve for r
Finally we get:
r =
I'm going to rewrite the equation assuming this is the correct form:
Answer:
equation: 41+4x=45.80
answer: x=1.20
Step-by-step explanation:
Answer:
s = height above ground
s = 60 + 20 t - 4.9 t^2 (standard physics equation on earth)
at t = 0
s = 60 (clearly :)
now when does it hit the bleak earth?
That is when s = 0
4.9 t^2 - 20 t -60 = 0
solve quadratic and use the positive t (the negative t was back before you threw it if you had thrown it from the ground)
t = 6.09 or - 2.01
use t = 6.09
now to do the last part there are two obvious ways to get t at the peak
1. look for vertex of parabola
2. look for halfway between t = -2.01 and t = 6.09
I will do it the hard (11) waay by completing the square
4.9 t^2 - 20 t = -(s-60)
t^2 - 4.08 t = -.204 s + 12.2
t^2 - 4.08 t +2.04^2 = -.204 s +12.2 + 4.16
(t-2.04)^2 = -.204(s-80.2)
so
top at 80.2 meters at t = 2.04 s
===============
quick check on time
should be average of 6.09 and -2.01
=4.08 /2 = 2.04 check
Answer:
Step-by-step explanation:
Given
Required
Solve for w
In absolution functions;
So, the given expression can be rewritten as
Removing the absolute sign, will gibe
or
When the second inequality os rewritten, it gives
or
Reorder both inequalities
or
Lastly, both inequalities are combined