Since the population increases by 7 percent each year, we can multiply 850 by 1.07 seven times. In other words, we can do 850 • 1.07^7. This is equal to about 1365.
Answer:
Draw the line segment AB = 7 cm.
Draw ray BX making an acute ∠ABX.
Along BX. mark off five points B1, B2, B3, B4 and B5. Join B2 to A.
Through B5 draw B5P || B2A, intersecting BA produced at P.
The point P so obtained is the required point which divides AB externally in the ratio 3:5.
Answer:
Step-by-step explanation:
A) From the order of the exercise we already know that the intersection points lies on the Y-axis, so its coordinates are P(0;y;0). In order to find it, we only need to substitute the equation 4x+4z=0 into the equation 4x+3y+4z=1. Then,
1=4x+3y+4z = 3y + (4x+4z)= 3y+0.
From the expression above it is easy to obtain that y=1/3, and the intersection point is P(0;1/3;0).
B) To obtain the parallel vector to both planes we use the cross product of the normal vector of the planes.
![\left[\begin{array}{ccc}i&j&k\\4&3&4\\4&0&4\end{array}\right] = 12i-0j+12k](https://tex.z-dn.net/?f=%5Cleft%5B%5Cbegin%7Barray%7D%7Bccc%7Di%26j%26k%5C%5C4%263%264%5C%5C4%260%264%5Cend%7Barray%7D%5Cright%5D%20%3D%2012i-0j%2B12k)
As we want a unit vector, we must calculate the modulus of u:
.
Thus, the wanted vector is
. Therefore,
.
C) In order to obtain the vector equation of the intersection line of both planes, we just need to put together the above results.

where
is a real number.
For all points that lie on the y-axis, the x-coordinate is zero.
Answer:
About 425
Step-by-step explanation:
Tell me if you want the explanation.