Given:
square based pyramid = 3.5 cm base
side length = 7 cm
Base Area = (3.5cm)² = 12.25cm²
Surface Area = Base Area + 2sl = 12.25cm² + (2 * 3.5cm* 7cm)
S.A = 12.25 cm² + 49 cm²
S.A = 61.25 cm²
Rewrite
log
(
2
x
)
=
4
log2x=4 in exponential form using the definition of a logarithm. If
x
x and
b
b are positive real numbers and
b
b
≠
≠
1
1, then
log
b
(
x
)
=
y
logbx=y is equivalent to
b
y
=
x
by=x.
10
4
=
2
x
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
Whatever the frequency is, that's how many tally marks you put.
