I am horrible at the current chapter I'm doing in pre-cal and now I have to do this assignment filled with word problems. I really need to ace this thing but no matter how many times I re-do these questions, I'm still getting answers wrong.
1) A sheet metal worker must cut a rectangular sheet with a diagonal of 15 cm long and a perimeter of 42 cm. What length and width should be used?
these are the equations I came up with:
2L + 2W = 42
L^2 + W^2 = 15^2
2) The sum of the reciprocals of two numbers is 4. Four times the product of their reciprocals is 15. What are the two numbers?
I was able to get a hint from my math teacher and was able to come up with the equations (which he said was right):
1 1
---- + ---- = 4
X Y
1 1
4 x ( ---- x ---- ) = 15
X Y
Please show steps if you can! I really appreciate anyone taking the time to help me out. :)
Pre-Cal: Solving Systems of Equations Using Substitution/Elimination PLEASE HELP?
2017-01-10 11:52 am
回答 (2)
2017-01-10 12:09 pm
✔ 最佳答案
Both sets of equations are correct.
So I assume your problem is with solving.
1)
2L + 2W = 42
Solve for L:
2L = 42 − 2W
L = 21 − W
Now replace L with 21−W in 2nd equation, then solve for W
L² + W² = 15²
(21−W)² + W² = 225
441 − 42W + W² + W² = 225
2W² − 42W + 216 = 0
2 (W² − 21W + 108) = 0
2 (W − 9) (W − 12) = 0
W = 9 or 12
L = 21−W
L = 12 or 9
Length and width should be 9 cm and 12 cm in some order
——————————————————————————————
2.
1/x + 1/y = 4
1/y = 4 − 1/x
Replace 1/y with 4 − 1/x in 2nd equation
4 (1/x * 1/y) = 15
4 (1/x * (4−1/x)) = 15
4 (4/x − 1/x²) = 15
16/x − 4/x² = 15
Multiply both sides by x²
16x − 4 = 15x²
15x² − 16x + 4 = 0
15x² − 10x − 6x + 4 = 0
5x (3x − 2) − 2 (3x − 2) = 0
(3x − 2) (5x − 2) = 0
x = 2/3 or 2/5
x = 2/3
1/y = 4 − 1/x = 4 − 3/2 = 5/2
y = 2/5
x = 2/5
1/y = 4 − 1/x = 4 − 5/2 = 3/2
y = 2/3
The two numbers are 2/3 and 2/5
2017-01-10 11:54 am
WHOOPS, I tried putting some fractions in their and they turned out funny. It's supposed to be:
1/X and 1/Y
1/X and 1/Y
收錄日期: 2021-05-01 21:23:57
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