SOLUTION: I need some help on these problems.
1. y varies directly as x and inversely as the square root of w; write the sentence as an equation.
2. write 3^x=y in log form.
3. w
Algebra.Com
Question 148022: I need some help on these problems.
1. y varies directly as x and inversely as the square root of w; write the sentence as an equation.
2. write 3^x=y in log form.
3. write log 2^x=y in exponential form.
4. solve for x; 5x/6-x/3=1/6
thanks for the help
Found 2 solutions by stanbon, jim_thompson5910:
Answer by stanbon(75887) (Show Source): You can put this solution on YOUR website!
1. y varies directly as x and inversely as the square root of w; write the sentence as an equation.
y = kx/(sqrt(x))
-----------------------
2. write 3^x=y in log form.
x = log(base3) y
-------------------------------------------------
3. write log 2^x=y in exponential form.
10^y = 2^x
----------------------------
4. solve for x; 5x/6-x/3=1/6
Multiply thru by 6 to get:
5x - 2x = 1
3x = 1
x = 1/3
=================
Cheers,
Stan h>
Answer by jim_thompson5910(35256) (Show Source): You can put this solution on YOUR website!
# 1
When "y varies directly as x", this means that as x increases y increases. Also as x decreases y decreases. So the first equation is . If let k be any number and you plug in values of x (say 1,2,3, etc), you'll notice that y will increase along with x.
Furthermore, when varies inversely as the square root of w, this means that as the square root of w increases y decreases. Also as square root of w decreases y increases. So the second equation is .
Now if you combine the two equations, you get
So the entire sentence "y varies directly as x and inversely as the square root of w" translates to
------------------------
# 2
Start with the given equation.
Rewrite the equation using the property: ===>
So the equation in logarithmic form is
-------------------------
# 3
Start with the given equation.
Rewrite the equation using the property: ====>
So the equation in exponential form is
----------------------------------
# 4
Start with the given equation.
Multiply both sides by the LCD to clear any fractions.
Distribute and multiply.
Combine like terms on the left side.
Divide both sides by to isolate .
----------------------------------------------------------------------
Answer:
So the answer is
Which approximates to
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