Answer:
Step-by-step explanation:
Given that there are two vectors U = (-8,0,1)
V = (1,3,-3)
To find projection of u on V and also projection of V on U
First let us find the dot product U and V
U.V = 
Projection of U on V =
Similarly projection of V on U
=
If two figures or lengths are similar, then the ratios of the corresponding lengths are equal.
Thus, 8/32 =5/x
8x = 160
x = 20 feet
Therefore, the length of the flag pole was 20 feet long
The question is missing the image given to go along with it, corresponding to the map being created. The image is attached to this answer.
The side angle side (SAS) similarity theorem states that two triangles with congruent angles and sides with identical ratios then the two triangles are similar. We have various points on the map, Home (H), Park (P), Friends house (F) and Grocery store (G).
In this example, we know the angle at the point Home on the map, is shared between the two triangles. If these two triangles are similar, then the ratio of the distances HF/HG = HP/HB. We know all of these values except for the HB which is the distance from home to the bus stop. But if these triangles are similar, we can solve for that distance.
15/9 = 10/HB
HB = 90/15
HB = 6 blocks.
To determine if the triangles are similar we need to know the distance from home to the bus stop, and if these are indeed similar, that distance must be 6 blocks.
"Formula of a circle" is too vague to be meaningful. Perhaps you meant, "Formula for the area of a circle in terms of its circumference."
The area of a circle in terms of its radius is A = πr^2. To put this formula to use, we have to know the radius of the circle. The circumference of a circle in terms of its radius is C = 2πr, so a formula for the radius is r = C / (2π).
Now let's find a formula for the area of a circle in terms of its circumference:
C C^2
A = πr^2 = π { ---------------- }^2 = ------------
2π 4π
or:
A = (C^2) / 4π
