Leslie's mistake lies in using a dilation, which either scales an object down or up. This transformation cannot be applied because congruent segments must maintain equal length; only rigid transformations like translations, reflections, and rotations are permissible. Thus, dilation is not considered a rigid transformation.
This can be expressed using the general formula for a² – b².
Response:
- Marti is declared the winner
Step-by-step explanation:
Continuation of question:
- After 10 seconds, the race concluded. The winner is the racer farthest from the starting point. Which car deserves the title of winner? Use mathematical reasoning to support your conclusion.
- Table is attached
Solution
Greg
- Travel speed = 13 ft/s
- Initial position = 30.7 ft from the starting point after 2 seconds
Distance from the starting point after 10 seconds:
30.7 + 13*(10 - 2) = 30.7 + 13*8 = 30.7 + 104 = 134.7 ft
Marti
Travel speed = 16.5 ft/s
- Starting position = 2 ft from the beginning line
Distance from starting point after 10 seconds:
2 + 10*16.5 = 2 + 165 = 167 ft
- In comparing the distances from the start line, 134.7 ft against 167 ft, Marti is further from the start line and is thus declared the winner.
The illustration is omitted. Please see the attachment below.
Answer:
The area of the shaded sector is 144π square units.
Step-by-step breakdown:
Given:
The central angle for the sector is, 
The circle's radius is, 
The area of a sector with radius 'R' and angle 
can be determined with:
Substituting 
gives
Thus, the area of the shaded sector calculates to 144π square units.
Answer:
The tangent plane equation for the hyperboloid
.
Step-by-step explanation:
We have
The ellipsoid's equation is
The equation for the tangent plane at the point 
(Given)
The hyperboloid's equation is
F(x,y,z)=
The tangent plane equation at point
The tangent plane equation for the hyperboloid is
The tangent plane equation
Hence, the required tangent plane equation for the hyperboloid is
