This is just simple. For example you have a plane of the form x=a, then you just substitute x with a, and you'll get an equation with y and z only, hence you have a 2-d trace of the intersection. It is just similar for y=b and z=c.
(1) At z=1.5, 2x^2 + 5y^2 + 1.5^2 = 4
2x^2 + 5y^2 = 1.75
Now you have an ellipse in the z=1.5 plane as your trace.
(2) At x=1, 2(1)^2 + 5y^2 + z^2 = 4
5y^2 + z^2 = 2
Now you have an ellipse in the x=1 plane as your trace.
(3) At z=0, 2x^2 + 5y^2 + (0)^2 = 4
2x^2 + 5y^2 = 4
Now you have an ellipse in the z=0 plane as your trace.
(4) At y=0, 2x^2 + 5(0)^2 + z^2 = 4
2x^2 + z^2 = 4
Now you have an ellipse in the y=0 plane as your trace.
Answer:
627.65 times
2.51^(10 - m) times
Yes, it makes sense
Step-by-step explanation:
Given that,
A magnitude 9 star is 2.51 times as bright as a magnitude 10 star
To find
<h3>a) </h3>
How many times as bright is a magnitude 3 star as a magnitude 10 star
10 - 3 = 7
2.51^7
627.65 times
<h3>b)</h3>
Expression to compare a magnitude m star to a magnitude 10 star
2.51^(10 - m) times
<h3>c)</h3>
Yes, it makes sense as a full moon is magnitude -13
so,
2.51^(10 - (-13))
2.51^(23)
1557742231 times
49c^2 - 25d^6
(7c)^2 - (5d^3)^2
(7c + 5d^3)(7c - 5d^3)
The answer is: (7c + 5d^3)(7c - 5d^3).
