Points in space

There are n points, of which no three lie on one line and no four lies on one plane. How many planes can be guided by these points? How many planes are there if there are five times more than the given points?

Correct answer:

r =  10
r2 =  35

Step-by-step explanation:

C3(10)=(310)=3!(103)!10!=3211098=120 n=10  r=(3n)=120=10
C3(7)=(37)=3!(73)!7!=321765=35 5n=(3n) 5n=n /3 5n=n(n1)(n2)(n3) /3  5=(x1)(x2)/6  0.166667x2+0.5x+4.667=0 0.166667x20.5x4.667=0  a=0.166667;b=0.5;c=4.667 D=b24ac=0.5240.166667(4.667)=3.3611173333 D>0  x1,2=2ab±D=0.3333340.5±3.36 x1,2=1.499997±5.4999940909186 x1=6.9999910909246 x2=3.9999970909126   Factored form of the equation:  0.166667(x6.9999910909246)(x+3.9999970909126)=0  r2=(3x1)=35

Our quadratic equation calculator calculates it.

Did you find an error or inaccuracy? Feel free to write us. Thank you!

Tips for related online calculators
The line slope calculator is helpful for basic calculations in analytic geometry. The coordinates of two points in the plane calculate slope, normal and parametric line equation(s), slope, directional angle, direction vector, the length of the segment, intersections of the coordinate axes, etc.
Are you looking for help with calculating roots of a quadratic equation?
See also our combinations with repetition calculator.
Would you like to compute the count of combinations?

You need to know the following knowledge to solve this word math problem:

Related math problems and questions: