Make a change of coordinates:


The Jacobian for this transformation is

and has a determinant of

Note that we need to use the Jacobian in the other direction; that is, we've computed

but we need the Jacobian determinant for the reverse transformation (from

to

. To do this, notice that

we need to take the reciprocal of the Jacobian above.
The integral then changes to

Answer:
The hawk reaches the rabbit at t=4.3 sec
Step-by-step explanation:
Let
h ----> is the height in feet
t ----> is the time in seconds
v ---> the initial velocity in feet pr second
s ----- is the starting height
we have

when the hawk reaches the rabbit the value of h is equal to zero
we have


substitute

Solve the quadratic equation by graphing
The solution is t=4.3 sec
see the attached figure
Answer:
Step-by-step explanation:
1 ) 2 + 7t [ there are no like terms , so no further simplifying ]
2) 6r + ( - 16 r )
= 6 r - 16 r [ both are like terms ]
= - 10 r
3) (3x + 2 ) + ( 2x - 4 )
= 3x + 2 + 2x - 4
= 3x + 2x - 4 + 2 [ arranging like terms together ]
= 5x - 2
4) (8 n² - 3 n + 6 ) + ( n - 2 )
= 8n² - 3n + 6 + n - 2
= 8n² - 3n + n + 6 - 2 [ bringing like terms together ]
= 8n² - 2n + 4