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Another question for me to ask again.

 

1.Given the product of 2x+3y and 3y+2x is z. Find the value of y when x=3.2 and z=457.96

2.3x+5y=-2

   -2x-3y=2

3.sqrt3(250/1024)

 

Pls help

twhtan  Sep 21, 2017
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2+0 Answers

 #1
avatar+77194 
+1

 

Note that we really have that

 

(2x + 3y)^2 = z   ...so....

 

 

(2(3.2)  + 3y)^2  = 457.96       simplify inside the parentheses

 

( 6.4 + 3y)^2  = 457.96          take the positive and negative square roots 

 

6.4 + 3y   = ±√457.96            subtract 6.4 from both sides

 

3y  = ±√457.96 - 6.4             divide both sides by 3

 

y  = [ ±√457.96 - 6.4 ] / 3 

 

So we have that   y  = [√457.96 - 6.4 ] / 3   = 5

 

And        y  = [ - √457.96 - 6.4 ] / 3   ≈  -9.2667

 

 

 

 

 

2.    3x+5y= -2   multiply through by 3     →  9x + 15y  =  - 6        (1)

      -2x-3y=  2    multiply through by 5    → -10x - 15y  =  10        (2)

 

Add (1) and (2)   and we get that

 

-1x  = 4      divide both sides by -1

x  = -4

 

Subbing this back into any of the equations for x to find y, we have

 

  3 (-4)  + 5y  = -2

-12  + 5y  = -2        add 12 to both sides

5y  = 10                divide both sides  by 5

y  = 2      

 

 

 

3. sqrt3(250/1024)

 

I'm guessing that this might actually be   ∛  [ 250 / 1024]  ....if so, we have....

 

 

∛ [ (2 * 125)  / ( 2 / 512) ] =

 

∛ [  (2 * 5^3)  / ( 2 * 8^3) ]   =

 

(5/8) ∛ (2/2)  =

 

(5/8)∛ 1  =

 

(5/8)

 

 

 

cool cool cool

CPhill  Sep 21, 2017
 #2
avatar+1224 
+1

1)

 

If \((2x+3y)(3y+2x)=z\), according to the given information, and \(x=3.2\) and \(z=457.96\), just plug those values in to solve for y:
 

\((2x+3y)(3y+2x)=z\) Plug in the appropriate values for the given variables of x and z.
\((2*3.2+3y)(2*3.2+3y)=457.96\) Simplify what is inside the parentheses first.
\((6.4+3y)(6.4+3y)=457.96\) You might notice that both the multiplicand and multiplier are the same, which means that we can make this equation a tad simpler.
\((6.4+3y)^2=457.96\) Take the square root of both sides. Of course, this breaks the equation up into its positive and negative answer.
\(6.4+3y=\pm\sqrt{457.96}\) Although it may not be obvious, the square root of happens to work out nicely.
\(6.4+3y=\pm21.4\) To solve for y, we must break up the equation.
\(6.4+3y=21.4\) \(6.4+3y=-21.4\)

 

Now, subtract by 6.4 in both equations.
\(3y=15\) \(3y=-27.8\)

 

Divide by 3 on both sides.
\(y_1=5\) \(y_2=-\frac{27.8}{3}*\frac{10}{10}=-\frac{278}{30}=-9.2\overline{6}\)

 

Both of these y-values satisfy the equation, and these are the solutions.
   

 

2)

 

This is a system of equations. I usually refrain from using the elimination method here because it is difficult to showcase. Therefore, I will use the substitution method. 

 

I will solve for y in equation 2:
 

\(-2x-3y=2\) Add 2x to both sides.
\(-3y=2x+2\) Divide by -3 to isolate y.
\(y=-\frac{2x+2}{3}\)  
   

 

Plug this value for y into equation 1 and then solve for x.

 

\(3x+5y=-2\) Plug in the value for y that was determined from the previous equation.
\(3x+5*\frac{2x+2}{-3}=-2\) Do the multiplication first to simplify this monstrosity.
\(5*\frac{2x+2}{-3}=\frac{5(2x+2)}{-3}=\frac{10x+10}{-3}\) Now, reinsert this back into the original equation.
\(3x+\frac{10x+10}{-3}=-2\) Multiply by -3 on all sides to get rid of the fraction.
\(-9x+10x+10=6\) Combine the like terms on the left hand side.
\(x+10=6\) Subtract 10 on both sides.
\(x=-4\)  
   

 

Now, plug x=-4 into either equation and solve for y. I'll choose equation 2 because it look easier to do:

 

\(-2x-3y=2\) Substitute all x's for -4.
\(-2*-4-3y=2\)  
\(8-3y=2\) Subtract by 8 on both sides.
\(-3y=-6\) Divide by -3 to isolate y.
\(y=2\)  
   

 

Therefore, the coordinate where both lines intersect is \((-4,2)\).

TheXSquaredFactor  Sep 21, 2017

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