Answer:
Part A:
The probability of hitting the black circle is the ratio between the area of the black circle and the white square (including the black circle)
Area of circle:
Ac = pi x r^2 = pi x (2/2)^2 = pi (diameter = 2)
Area of square:
As = side^2 = 11^2 = 121 (side = 11)
=> P = pi/121 = ~0.025 (P = 0.025 < 0.5 => P is closer to 0 than 1)
Part B:
The probability of hitting the white portion could be calculated in a similar way as shown in part A. However, the event of hitting the white portion is the complement event of the event of hitting the black circle.
Because P(event) + P(complement of event) = 1
=> P = 1 - 0.025 = 0. 975 (P = 0.975 > 0.5 => P is closer to 1 than 0)
<span>the missing exponent is
-3</span>
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
Answer:
7/9
Step-by-step explanation:
Answer:
9 inches
Step-by-step explanation:
The formula for the volume of a rectangular pyramid is 
- Here we have volume (V), base (L), and width (W)
- V = 360 in³, L = 12 in, W = 10 in
We need to manipulate the volume equation to solve for the height (H)
- First we need to multiply both sides by 3 to get rid of the fraction: 3V = L×W×H
- Then we need to divide both sides by (L×W) to get:
Now we can plug in the given values:
- The height is 9 inches
