X + y = 15
x - y =3
First you have to work out what two numbers add together to make 15, for example 1 and 14 or 5 and 10.
Then you have to work out which set of numbers have a difference of 3.
The numbers would be 6 and 9.
Once you have the two numbers, multiply them together:
6 x 9 = 54
Since each odd (or even) is two greater than the previous number, two consecutive such numbers are n and n+2.
The we are told that the sum of two such number is 100, so we can say:
n+n+2=100 combining like terms on the left side you get:
2n+2=100
....
to solve, if you were interested...subtract 2 from both sides
2n=98 divide both sides by 2
n=49
So the two odd numbers are 49 and 51
We have that
(3y-8)/12=(y/5)---------> 5*(3y-8)=12*(y)
15y-40=12y-------------> 15y-12y=40
3y=40--------------> y=40/3
y=(40/3)----------> 13.33
the answer is y=40/3 (13.33)
Answer:
1.5 inches
Step-by-step explanation:
56.52/ 8 = 7.065
7.065 / pi =2.248859346
square root of 2.248859346 = 1.5
r = 1.5
Answer:
and ![2](https://tex.z-dn.net/?f=2)
Step-by-step explanation:
The given sphere is ![x^2 + y^2 + z^2 -6x + 2y =-6](https://tex.z-dn.net/?f=x%5E2%20%2B%20y%5E2%20%2B%20z%5E2%20-6x%20%2B%202y%20%3D-6)
This can be rearranged as ![(x-3)^2 -9+ (y+1)^2 -1 + (z-0)^2=-6](https://tex.z-dn.net/?f=%28x-3%29%5E2%20-9%2B%20%28y%2B1%29%5E2%20-1%20%2B%20%28z-0%29%5E2%3D-6)
![\Rightarrow (x-3)^2 + (y+1)^2 + (z-0)^2=4\\](https://tex.z-dn.net/?f=%5CRightarrow%20%28x-3%29%5E2%20%2B%20%28y%2B1%29%5E2%20%20%2B%20%28z-0%29%5E2%3D4%5C%5C)
On comparing with the standard equation of a circle
, with center
and radius
.
The center of the given circle is
.
Now, as the perpendicular distance,
, of a point
from a plane
is
.
[ as the given plane is y=2]
![\Rightarrow d=3 \; \cdots (i)](https://tex.z-dn.net/?f=%5CRightarrow%20d%3D3%20%5C%3B%20%5Ccdots%20%28i%29)
Similarly, the other equation of the circle,
can be rearranged as ![(x-0)^2 + (y+\frac {A}{2})^2 + (z+3)^2=11+\frac {A^2}{4}.](https://tex.z-dn.net/?f=%28x-0%29%5E2%20%2B%20%28y%2B%5Cfrac%20%7BA%7D%7B2%7D%29%5E2%20%20%2B%20%28z%2B3%29%5E2%3D11%2B%5Cfrac%20%7BA%5E2%7D%7B4%7D.)
Here, the center for this circle is ![\left( 0, -\frac {A}{2}, -3\rigfht).](https://tex.z-dn.net/?f=%5Cleft%28%200%2C%20-%5Cfrac%20%7BA%7D%7B2%7D%2C%20-3%5Crigfht%29.)
From the given condition, the distance of the center from the plane
is
.
[from equation (i) ]
![\Rightarrow \left | -\frac {A}{2}-2\right|=3](https://tex.z-dn.net/?f=%5CRightarrow%20%5Cleft%20%7C%20%20-%5Cfrac%20%7BA%7D%7B2%7D-2%5Cright%7C%3D3)
![\Rightarrow \frac {A}{2}+2=\pm 3](https://tex.z-dn.net/?f=%5CRightarrow%20%20%20%5Cfrac%20%7BA%7D%7B2%7D%2B2%3D%5Cpm%203)
![\Rightarrow \frac {A}{2}=-2\pm 3](https://tex.z-dn.net/?f=%5CRightarrow%20%20%20%5Cfrac%20%7BA%7D%7B2%7D%3D-2%5Cpm%203)
and ![2\times (-2+3)](https://tex.z-dn.net/?f=2%5Ctimes%20%28-2%2B3%29)
and
.