The required plane Π contains the line
L: (-1,1,2)+t(7,6,2)
means that Π is perpendicular to the direction vector of the line L, namely
vl=<7,6,2>
It is also required that Π be perpendicular to the plane
Π 1 : 5y-7z+8=0
means that Π is also perpendicular to the normal vector of the given plane, vp=<0,5,-7>.
Thus the normal vector of the required plane, Π can be obtained by the cross product of vl and vp, or vl x vp:
i j k
7 6 2
0 5 -7
=<-42-10, 0+49, 35-0>
=<-52, 49, 35>
which is the normal vector of Π
Since Π has to contain the line, it must pass through the point (-1,1,2), so the equation of the plane is
Π : -52(x-(-1))+49(y-1)+35(z-2)=0
=>
Π : -52x+49y+35z = 171
Check that normal vector of plane is orthogonal to line direction vector
<-52,49,35>.<7,6,2>
=-364+294+70
=0 ok
I'm not sure your question has enough information to be answered properly, but I'll try to help:
Assuming each of them are sweeping 1/2 of the garge, we're gonna cut each of their times in half.
Now the girl needs 10 minutes for half the garage and her brother needs 15 minutes.
So, if they work together, the first ten minutes will overlap each other while the girls brother gets left behind to finish up for an extra five minutes.
So, when working together, the boy and the girl need 15 minutes to sweep the garage.
0=4(x²+8x+16)-12
0=4x²+32x+64-12
0=4x²+32x+52
0=x²+8x+13
D=b²-4ac
D=64-52=12
x=(-b-√D)/2a
x=(-b+√D)/2a
x=(-8-2√3)/2= (-2(4+√3))/2= -(4+√3)
AND
x=(-8+2√3)/2=-2(4-√3)/2= -(4-√3)
The independent variable would be x, as it depends on nothing to determine its value. The dependent variable is f(x), as it depends on x to determine its value. This means we plug -4 into x and solve the equation to find f(x).
f(x) = -5(-4) + -4/-2
f(x) = 20 + 2
f(x) = 22
So the answer is C.
Answer:
Step-by-step explanation:
A polynomial of a third degree is a product of three binomials of the form 
. Let consider the following polynomial:
After some algebraic handling, the standard form of the polynomial is:
