Question 55204: I have this problem that I would like someone to check my work:
If a skydiver jumps from an airplane at a height of 8256 feet, then for the first five seconds, her height above the earth is approximated by the formula h = -16t^2 + 8256. How many seconds does it take her to reach 8000 feet?
WORK DONE :
What I have done is:
h = 16^t + 8256
h = -16t^2 + 8256 = 8000
h = -16t^2 + 8256 - 8000 = 0
-16t^2 + 256 = 0
-16t^2 + 256 - 256 = - 256
16t^2 = -256
-16t^2/16 = -256/-16
t^2 = 16
t = 4
I'm not confident about the way I have worked this out. Could someone check.
Answer by venugopalramana(3286)   (Show Source):
You can put this solution on YOUR website! SEE MY COMMENTS BELOW...
I have this problem that I would like someone to check my work:
If a skydiver jumps from an airplane at a height of 8256 feet, then for the first five seconds, her height above the earth is approximated by the formula h = -16t^2 + 8256. How many seconds does it take her to reach 8000 feet?
WORK DONE :
What I have done is:
h = 16^t + 8256....HOW?TYPING ERROR..IT SHOULD BE -16T^2+8256
h = -16t^2 + 8256 = 8000...OK
h = -16t^2 + 8256 - 8000 = 0...DONT WRITE H=...IT IS NOT CORRECT.
SIMPLY WRITE
-16T^2+8256-8000=0.....GOT IT?
-16t^2 + 256 = 0...OK
-16t^2 + 256 - 256 = - 256...OK
16t^2 = -256 ......NO AGAIN TYPING ERROR? IT IS -16T^2=-256
-16t^2/16 = -256/-16 .....OK
t^2 = 16 ......OK
t = 4 .....OK....
I'm not confident about the way I have worked this out. Could someone check.
THE ANSWER IS OK.THE WORKING IS FAULTY AT SOME PLACES AS MENTIONED.
CORRECT THOSE ERRORS AND YOU WILL DO WELL.SEE THE FOLLOWING EXAMPLE ON SOLUTION OF EQNS.FOR PROPER STEPS OF WORKING.
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I really don't understand this problem. Can you please help me?
3(1-3x)+2=4x+14........OK
3-9x+2=4x+14................GOOD
so then add or subtract from both sides?
3-9x+9x+2=13+14......HERE YOU GOT CONFUSED..
THE STEPS INVOLVED ARE
1.REMOVE BRACKETS ......THIS YOU HAVE DONE.
2.TRANSFER ALL UNKNOWN TERMS TO ONE SIDE.... USUALLY L.H.S. AND KNOWN TERMS TO ONE SIDE ...USUALLY R.H.S.
3.THIS TRANSFER YOU CAN THINK OF AND DO AS FOLLOWS....
EVERY TERM HAS A + OR - SIGN INFRONT OF IT.WHEN YOU TRANSFER THAT TERM FROM ONE SIDE TO ANOTHER ,+ BECOMES - AND - BECOMES PLUS.
THIS IS BECAUSE...AS YOU WERE TRYING TO SAY 'ADD OR SUBTRACT FROM BOTH SIDES'
AN EQUATION IS UNALTERED IF WE ADD OR SUBTRACT SAME QUANTITY FROM BOTH SIDES OF THE EQN.SO IF WE WANT TO REMOVE +4X ABOVE FROM R.H.S.WE HAVE TO ADD -4X TO IT.SO TO BALANCE IT AND KEEP THE VALIDITY OF THE EQN.UNALTERED,WE ADD -4X TO L.H.S.ALSO.THEN ON R.H.S ,WE GET +4X-4X=0...THAT IS +4X DIAPPEARS AS WE WANTED.BUT -4X REMAINS ON L.H.S.....THIS IS THE FINAL EFFECT OF ADD AND SUBTRACT WHICH IS SUMMARISED FIRST ABOVE.
HENCE WE GET HERE
-9X-4X = 14-2-3
4.NOW SIMPLIFY BOTH SIDES COMBINING ALL UNKNOWNS ON L.H.S AND ALL KNOWNS ON R.H.S
WE GET HERE
-13X=9
5.NOW TRANSFER THE COEFFICIENT OF UNKNOWN ON L.H.S.TO R.H.S.
APPLYING THE SAME RULE & LOGIC MENTIONED ABOVE,HERE * WILL BECOME / AND / BECOMES *
HERE WE GET
X = -9/13....
THIS IS THE ANSWER.
6.IF YOU HAVE TIME AND WOULD LIKE TO DO....CHECK BACK THE ANSWER FOR CONFIRMATION BY SUBSTITUTION..
3{1-3*(-9/13)}+2=4*(-9/13)+ 14
3{1+27/13)+2=-36/13 +14
3*40/13 +2=(-36+14*13)/13
120/13 +2= 146/13
146/13 = 146/13.......OK
You may edit the question. Maybe convert formulae
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