if the line〈3 + 2t,1 +t,2−t〉intersects the unit sphere inR3given byx2+y2+z2= 1,and if so, at what points.

Step-by-step explanation:

Solution:-

- We are given a parametric form for the vector equation of line defined by ( t ).

- The line vector equation is:

                        L: < 3 + 2t , t + 1 , 2 -t >

- The same 3-dimensional space is occupied by a unit sphere defined by the following equation:

- We are to determine the points of intersection of the line ( L ) and the unit sphere ( S ).

- We will substitute the parametric equation of line ( L ) into the equation defining the unit sphere ( S ) and solve for the values of the parameter ( t ):

- Solve the quadratic equation for the parameter ( t ):

- Plug in each of the parameter value in the given vector equation of line and determine a pair of intersecting coordinates:

93.8

step-by-step explanation:

lets say, first number = x

second number = 3x+7

total = 49

(x)+(3x+7)= 49

4x+7 = 49

4x = 42

x = 42/4

x= 10.5

x= 10.5

3x+7 = 3(10.5)+7 = 93.8

hope this