The cone equation gives
which means that the intersection of the cone and sphere occurs at
i.e. along the vertical cylinder of radius
when
.
We can parameterize the spherical cap in spherical coordinates by
where
and
, which follows from the fact that the radius of the sphere is 3 and the height at which the sphere and cone intersect is
. So the angle between the vertical line through the origin and any line through the origin normal to the sphere along the cone's surface is
Now the surface area of the cap is given by the surface integral,
1) Answer: 21
As y varies directly with x, this means that the ratio y/x is always a constant.
In other words, the equation can be written as y = kx, where k is a constant term.
Thus,
y = 21
2) Answer: C
Exactly the same process as above.
Here's another method:
25 = k(140)
k = 25/140 = 5/28
Thus, when y = 36, 36 = kx
36 = 5/28(x)
36 * 28/5 = x; x = 201.6
3) 9 = k(12)
9/12 = k and k = 3/4
4) On the graph, it hits y = 1 at x = 4.
Thus, we can rewrite the equation as:
y = (1/4)x, where the constant term is 1/4
5) y = kx
The distance represents the x-ordinates, and the time represents the y-ordinates.
9.5/475 = 0.02
4 = 0.02(x), in hours.
x = 200 miles.
Answer:
5 7/10
Step-by-step explanation:
First, we need to round the number.
5.7
Now that we've rounded the number we can convert it to a fraction based on where the decimal is located.
5.7
|
v
Tenths
So, the decimal is in the tenths that means we have to put 7 over 10.
5 7/10
Hope this helps! :)
Answer:
( 5x + 1 ) ( x - 4 )
Step-by-step explanation:
5x² - 19x - 4
= 5x² + x - 20x - 4
= x ( 5x + 1 ) - 4 ( 5x + 1 )
= ( 5x + 1 ) ( x - 4 )
Hence, factorized.