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Triangle(CDE)  is similar to  triangle(CAB).

Therefore:  CD / DE  =  CA / AB

Since  AD = x   --->   DE = x.

Since  CA = 8  and  AD = x   --->   CD = 8 - x.

Substituting:  CD / DE  =  CA / AB     --->     (8 - x) / x  =  8 / 15

Cross-multiplying:  8x  =  120 - 15x     --->   x  =  5.217

Thanks Alan,

That will give me something to chew on.   

Find \(\dfrac{1}{u^2} + \dfrac{1}{v^2}.\)

Hello Guest!

\(3x^2 + 5x + 7 = 0\\ x^2+\frac{5}{3}x+\frac{7}{3}=0\\ x=-\frac{5}{6}\pm \sqrt{\frac{25}{36}-\frac{7}{3}}\\ x=-\frac{5}{6}\pm \sqrt{\frac{25}{36}-\frac{84}{36}}\\\)

\(u=\dfrac{-5+i\sqrt{59}}{6}\\ v=\dfrac{-5-i\sqrt{59}}{6}\\\)

\(\dfrac{1}{u^2}+\dfrac{1}{v^2}=\dfrac{36}{ ( -5+i\sqrt{59})^2}+\dfrac{36}{ ( -5-i\sqrt{59})^2}=-\dfrac{17}{49}\)

  !

Find the value of y.

Hello Guest!

\( 9^y= 3^5\cdot 9^6\cdot \dfrac{81^4}{27^3}\\ 3^{2y}=3^5\cdot 3^{2\cdot 6}\cdot \dfrac{3^{4\cdot 4}}{3^{3\cdot 3}}\\ 3^{2y}=3^5\cdot 3^{2\cdot 6}\cdot 3^{4\cdot 4-3\cdot 3}\\ 2y=5+12+16-9\)

\(y=12\)

  !

Let a * b = a + sqrt(b + sqrt(b + sqrt(b + ...))). If 7 * g = 19, find the value of g.  

Never mind all that square root stuff.  

Just look at the last sentence:               If 7 * g = 19, find the value of g.  

Divide both sides by 7:                                  g = 19/7  =  2.714   

Is all that square root stuff a deliberate misdirection? 

Could it be that the problem was copied incorrectly?  

Something else that I'm not getting?  

_.

https://web2.0calc.com/questions/what-would-be-the-final-concentrations-of-ge-following

AD = a          AB = b           BD = c

b = sqrt(9 - a²)            

AM = sqrt(a² - 1)            (AM is the height of triangle ADM)

BD * AM = a * b

3[sqrt(a² - 1)] = a[sqrt(9 - a²)]

a = √3          b = √6

[ABCD] = 3√2

                 __

=    0.005681        4 digits then 81 repeating

             of the repeating   3996 digits       last one would be '1'

Vertex form of parabola with   vertex  ( 3,1)

y = a ( x-3)^2  + 1        when x = 0    y = 7      then 'a' = 7/10

y = 7/10 (x-3)^2 + 1      expand to find a , b  and c     

When x = 0, y = 7  so   7 = a*0^2 + b*0 + c

When x = 3, y = 1, so   1 = a*3^2 + b*3 + c

When x = 6, y = 7, so   7 = a*6^2 + b*6 + c

You now have three simultaneous equations for the three unknowns.  I'll leave you to solve them.

Here's my attempt at an analytical answer:

I should have written: This is the value of k at the minimum area.  The minimum area itself is \(k\pi\)

I've just noticed something went wrong with the display of equation (3)! It should be \(xp = \frac{a^2}{a^2-b^2}\)

7/1000

2 numbers out of 100 can be summed up in:

100 C 2 ==4,950 ways

Out of 4,950 ways, there are 1,225 ways of adding up 2 numbers whose sum is divisible by 4

So, the probability is: 1,225 / 4,950 ==25 / 99

Simplify by combining 'like' tems

 x  = 2y^2 -4y +13     a sideways parabola     the 'y' coordinate of the vertex will be found by   -b/2a = - -4/(2*2) = 1

                                      the 'x' coordinate will be found by substituting y = 1 into the equation = 11

1:9 ratio means that 1/(1+9) will be the salt solution     1/10 * .5M  = .05 M

.12 * .4 M = .048 M Sucrose soln

Like so:

Can you take it from here?

Calculate this on our homepage.

(0.28)² + (0.96)² = 1

Your answer is correct! 

n = 360/20 

Here is a much better graph.   Unfortunately, the answer still alludes me. 

The square is a rectangle too !!! 

If BD = 3 then [ABCD] = 4.5 square units 

a=13, b=-2, c=-3

x=(2+-sqrt(160))/26

x=0.5634 or 0.4096

sum of squares =0.4863