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What rubbish, you do not try and do anything on your own.

You just want asinus to finish spoon-feeding you.

Do you see how we know that

b  =  90° - 2a   ?

(If you're confused on that part, let us know!!)

Then once we know that is true, there are a couple ways to think of the next step...

Given that:

b  =  90° - 2a

We can take the sin of both sides of that equation to get:

sin(b)  =  sin(90° - 2a)

Also......a kind of another way to think of this....

Looking at the expression:

sin(b)

Since  b = 90° - 2a,  we can substitute  90° - 2a  in for  b  to get the following equivalent expression:

sin(90° - 2a)

And so....

sin(b)  =  sin(90° - 2a)

Given that xy = 1/2  and both x and y are nonnegative real numbers, find the minimum value of 4x + 9y.

 \(xy=\frac{1}{2}\)       \(x=\frac{1}{2y}\)

\(f(y)=4x+9y\\ f(y)=\frac{2}{y}+9y=2y^{-1}+9y\)

\(\color{blue}\frac{df(y)}{dy}=-2y^{-2}+9=0\\ \frac{2}{y^2}=9\\ y^2=\frac{2}{9}\)

\(y=0.42140\\ x=1.06066\)

       ⇓

\(4x+9y=8.48528 \)

q.e.d.

  !

Given that xy = 1/2  and both x and y are nonnegative real numbers, find the minimum value of 4x + 9y.

Hello Guest!

\(xy=\frac{1}{2} \)       \(y=\frac{1}{2x}\)

\(f(x)=4x+9y\\ f(x)=4x+\frac{9}{2x}\\ f(x)=4x+4.5x^{-1}\)

\(\color{blue}\frac{df(x)}{dx}=4-4.5x^{-2}=0\\ \frac{4.5}{x^2}=4\\ x^2=\frac{4.5}{4}\)

\(x=1.06066\)

\(y=0.47140\)

\(4x+9y=8.48528\)

The minimum value of 4x + 9y is 8.48528.

  !

Yes you are right,

I will tweak my answer.

All the factors must be prime  THEN all the indices of these prme factors must by even.

So with your example. 

\(9^9=(3^2)^9=3^{18}\\ \text{18 is even so } 9^9 \text { is a square number}\)

Given:

3a + c = 38

3a+ 2c = 52       by selling ONE more child ticket they made 14 more dollars

                                 so c = 14

Plug this into one of the equations    3a + (14) = 38    to find a = $8

3.  Looks as though the entire rectangle is shaded...   I think we just want the 'ring' area

     area of big triangle   - area of smaller

      (  x+6)(2x+6)   - (2x)(x)  = ring area

     2x^2 +18x+36    - 2x^2 

            18x + 36    = ring area

   but   larger = 6 * smaller = 6 (2x)(x)

        6(2x)(x) - (2x)(x) = 10 x^2 = ring area too

Soooooo

18x + 36 = ring area = 10 x^2

or:

                0 =10x^2 - 18x-36    

                          quadratic formula shows  x = -1.2(throw out)   or      x = 3           so 'ring area = 10(3)^2 = 90 units^2

(x^2 + 8x) = 20

x^2 + 8x-20 = 0

(x-2)(x+10) = 0      x = 2 or -10 

English translation:

determine the equation and the graph of the straight line that has as slope m = - 1 and ordinate b = 6

Hi. So one thing we can do here is to use Desmos to graph it out. But that's not what you want to do first. 

The equation for the slope of a line is y=mx+b where x is the coordinate on the x axis, y is the coordinate on the y axis, m is the slope, and b is the y intercept. 

Good so far? (Reply to this answer if you need help here or on any other part in particular.)

So now we can plug in the m value. This gives us y=-1(x)+b. Also reprsented as y=-x+b by the way.

Now that we plugged in m, plug in b: y=-x+6.

This gives us the equation of the line. Use this to plot the graph as seen below. 

I hope you understand how I got to the equation. If not, comment below.

Hola. Entonces, una cosa que podemos hacer aquí es usar Desmos para graficarlo. Pero eso no es lo que quieres hacer primero.

La ecuación para la pendiente de una línea es y = mx + b donde x es la coordenada en el eje x, y es la coordenada en el eje y, m es la pendiente y b es la intersección en y.

¿Bien hasta ahora? (Responda a esta respuesta si necesita ayuda aquí o en cualquier otra parte en particular).

Así que ahora podemos introducir el valor m. Esto nos da y = -1 (x) + b. También representado como y = -x + b por cierto.

Ahora que conectamos m, inserte b: y = -x + 6.

Esto nos da la ecuación de la recta. Use esto para trazar el gráfico como se ve a continuación.

Espero que entiendas cómo llegué a la ecuación. Si no es así, comente a continuación.

Vaya aquí para ver el gráfico:

(b + 18) / 36 = b / 12

(c + 26) / 36 = c / 12

a = 27

b = 9

c = 13

d = 39

Except 9^9 = 3^18

Hint:    All the indices must be even numbers.

Hi Juriemagic,

\(y=(2x-1)^2+5\)

This is the parabola     \(y=(2x-1)^2\)      that has been lifted up 5 units.

\(y=(2x-1)^2\)    is the PARENT equation.

Since the PARENT equation has a double root, that means that the root is the vertex.

The turning point of the PARENT parabola is   

2x-1=0

2x=1

x=0.5

So the vertex of the parent equation  is  (0.5,0)

and the vertex of your equation is 5 units higher, that is   (0.5,5)

Answered.

That answer is not correct.

True..... I should not have put the (x-2) in the  'R'  ...

= Area of larger circle - area of smaller circle

area of circle = pi r^2

pi ( 10² )  - pi (6² )   =  pi (10^2 - 6^2 ) = ..........   units²

Hi Juriemagic,

It is really good to see you here.     

The largest number of cents that you CANNOT make = 29 cents. I will leave to you to justify it!

5 and 8 are equal

125-x   =    -10-28x      solve for x

then agle 5 =   125-x

and   angle 5 and angle 7 sum to 180^o

125-x     +    angle₇   = 180     

Area =   x * y  = xy

New    1.2 x   *   1.18 y = 1.416 xy      an increase of   41.6%

derivative function.