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Answer:
0.448 seconds
Step-by-step explanation:
d = -16t² -4t + 412
find t when d = 407
substituting d = 407 into the equation:
407 = -16t² -4t + 412 (subtract 407 from both sides)
-16t² -4t + 412 - 407 = 0
-16t² -4t + 5 = 0 (multiply both sides by -1)
16t² + 4t - 5 = 0
solving using your method of choice (i.e completing the square or using the quadratic equation), you will end up with
t = (-1/8) (1 + √21)= -0.70 seconds (not possible because time cannot be negative)
or
t = (-1/8) (1 -√21) = 0.448 seconds (answer)
Answer:
The inverse is 5x-6
Step-by-step explanation:
To find the inverse of a function
y = ( x+6) /5
Exchange x and y
x = ( y+6)/5
Solve for y
Multiply each side by 5
5x = (y+6)/5 *5
5x = y+6
Subtract 6 from each side
5x-6 = y+6-6
5x-6 =y
The inverse is 5x-6
Integration by parts will help here. Letting

and

, you end up with

and

. Now


For the remaining integral, setting

gives

, so

Putting everything together, you end up with