Answer: cos²(θ) + sin(θ)sin(e)
<u>Step-by-step explanation:</u>
sin (90° - θ)cos(Ф) - sin(180° + θ) sin(e)
Note the following identities:
sin (90° - θ) = cos(x)
sin (180° + θ) = -sin(x)
Substitute those identities into the expression:
cos(x)cos(x) - -sin(x)sin(e)
= cos²(x) + sin(x)sin(e)
There are 2 cups in a pints
Answer:
P(F) = 143/280
Step-by-step explanation:
The total number of female students is 109+34 = 143.
The total number of non-female students is 38+99 = 137.
Then the total number of students is 143+137 = 280.
If a student is picked at random, the probability they are female is ...
P(F) = 143/280
Answer:
The answers to your three problem question are shown
1) the value of p is
p = -1
2) The coordinates of the focus are
Focus = (-1,0)
3) The equation of the directrix is
Directrix
x = 1
Step-by-step explanation:
The general equation for this parabola is
y^2 = 4px
Problem 1
Find the value of p.
We are told that the equation of the problem is
y^2 = -4x
And the general formula is
y^2 = 4px
From there, we can deduce that
p = -1, because
y^2 = 4(-1)x = -4x
This means that p = -1
Problem 2
Find the focus
To find the focus we can see the equations attached below for the focus, vertex and directrix.
In these case, the equations still apply, even though the variable is inverted, we just need to adjust it
y^2 = -4x =>
x = (-1/4)*y^2
x = a*y^2 + b*y +c
Focus
((4ac -b^2 + 1)/4a, -b/2a)
But, b = 0 and c = 0
=>
(1/4a,0) = (1/4(-1/4),0) = (-1,0)
Focus = (-1,0)
Problem 3
Find the directrix
The equation is
x = c - (b^2 + 1).4a
But, b = 0 and c = 0
x = -4*a
x = -4* (-1/4) = 1
x = 1
Directrix
x = 1