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\(\mbox{the surface area is } n. \sqrt{\frac{n}{4\pi}}= \mbox{the radius.}\)

Let's solve your equation step-by-step.

6(2y+6)=4(9+3)y

Step 1: Simplify both sides of the equation.

6(2y+6)=4(9+3)y

Simplify:

Let's simplify step-by-step.

6(2y+6)=4(9+3)y

(6)(2y)+(6)(6)=4(9+3)y(Distribute)

12y+36=48y

Step 2: Subtract 48y from both sides.

12y+36−48y=48y−48y

−36y+36=0

Step 3: Subtract 36 from both sides.

−36y+36−36=0−36

−36y=−36

Step 4: Divide both sides by -36.

−36y−36=−36−36

y=1

Answer:

y=1

e\(^x\)x = x\(^\pi\), what is x?

\(\small{ \begin{array}{rcll} e^x &=& x^{\pi} \qquad & | \qquad \ln{}\\ x\ln{(e)} &=& \pi \cdot \ln{(x)} \\ \frac{x}{\pi} \cdot \ln{(e)}&=& \ln{(x)} \\ \ln{( e^{\frac{x}{\pi}} )} &=& \ln{(x)} \qquad & | \qquad e^{}\\ e^{ \ln{( e^{\frac{x}{\pi}} )} } &=& e^{ \ln{(x)} }\\ e^{\frac{x}{\pi}} &=& x \\ x \cdot e^{-\frac{x}{\pi}} &=& 1 \qquad & | \qquad : -\pi\\ -\frac{x}{\pi} \cdot e^{-\frac{x}{\pi}} &=& -\frac{1}{\pi}\\ \\ \hline \end{array} }\\ \small{ \begin{array}{rcll} \text{Lambert W-Function(W) or ProductLog or Omega-Function } w\cdot e^w = z \qquad w = W(z) \end{array} }\\ \small{ \begin{array}{rcl} -\frac{x}{\pi} \cdot e^{-\frac{x}{\pi}} &=& -\frac{1}{\pi} \\ -\frac{x}{\pi} &=& W( -\frac{1}{\pi} ) \\ -x &=& \pi \cdot W( -\frac{1}{\pi} )\\ \mathbf{x} & \mathbf{=} & \mathbf{-\pi \cdot W( -\frac{1}{\pi} )}\\ \\ \hline \\ W( -\frac{1}{\pi} ) &=& -0.553827036644513 \\ x &=& -\pi \cdot (-0.553827036644513) \\ \mathbf{ x } & \mathbf{\approx} & \mathbf{1.73989894968181} \\ \end{array} }\\\)

\(2^{\frac{3}{2}}=2^{1\frac{1}{2}}=2^{1}\times2^{\frac{1}{2}}=2\times\sqrt{2}=\sqrt{2^{2}\times\sqrt{2}^{2}}=\sqrt{4\times2}=\sqrt{8} \mbox{ so } 2^{\frac{3}{2}}=\sqrt{8}\)

\(12\times 8 = 96\\\\ \mbox{so, divide both sides by 8} \\\\ 12=\frac{96}{8}\\\\ \)

Look at it like this:  \(\frac{23}{25}\rightarrow \frac{23*4}{25*4}\rightarrow \frac{92}{100}\rightarrow 0.92\)

The sum of 5x(squared)y, 4x(squared)y, 8x(squared)y is

You can add like terms and like terms are where all the letters are the same and each letter (pronumeral) is raised to the same power.

Each of these terms is  x squared y.  Which you could have written it as    x^2y    SO you can add them all together.

5 lots of x(squared)y  +    4  lots of   x(squared)y  +   8 lots of    x(squared)y 

= (5+4+8) lots of  x(squared)y 

= 17 lots of  x(squared)y 

= 17 x(squared)y 

= 17 x^2y

\(=17x^2y\)

This picture should help:

Note that the angle through which the ray turns is 180° - 60° - 60° = 60°

Electricity is charged per Kilowatt/hour. Since you have the lights of 600 watts on for 18 per day, that means you are using 18 X 600=10,800 watts per day, which is the same as 10,800/1000=10.8 Kilowatt/hour per day. Since they charge .135 cents per Kw/hour=10.8 X .135=$1.45 per day X 30 days=$43.50 per month is your electricity bill.

2 to the power of 3 over 2

\( \small{ \begin{array}{rcl} 2^{ \frac 32 } \\ &=& 2^{ \frac{1+2}{2} } \\ &=& 2^{ \frac{1}{2}+\frac{2}{2} } \\ &=& 2^{ \frac{1}{2}+ 1 } \\ &=& 2^{ \frac{1}{2} }\cdot 2^1 \\ &=& 2^{ \frac{1}{2} }\cdot 2 \\ &=& \sqrt{2}\cdot 2 \\ &=& 2 \cdot \sqrt{2}\\ &=& 2.82842712475 \end{array} }\)

1-(x+3)\(\ge\)4-2x

\( \small{ \begin{array}{lrcll} & 1-(x+3) &\ge& 4-2x \\ \\ \hline \\ (1) & 1-(x+3) & = & 4-2x \\ & 1 - x - 3 &=& 4 - 2x \\ & -2 - x &=& 4 - 2x \qquad & | \qquad + 2x\\ & -2 + x &=& 4 \qquad & | \qquad +2\\ & \mathbf{x} & \mathbf{=} & \mathbf{6 }\\ \\ \hline \\ (2) & 1-(x+3) & > & 4-2x \\ & 1 - x - 3 & > & 4 - 2x \\ & -2 - x & > & 4 - 2x \qquad & | \qquad + 2x\\ & -2 + x &> & 4 \qquad & | \qquad +2\\ & \mathbf{x} & \mathbf{>} & \mathbf{6 }\\ \\ \hline \\ (1) + ( 2) & x = 6 ~ \text{ and } ~ x > 6 \\ & \mathbf{ x \ge 6 } \end{array} }\)

If the rate is 13.5 cents per kilowatt hour, we have ..... [600w =. 6kw ].......

13.5 x .6kw    = 8.1 cents per hour

We can only do this if we have a right triangle.....assuming that a and b are legs, we have

tanA = 16/26  .....  therefore.........

tan^-1 (16/26)  = A =  about 31.6°

If b is a hypotenuse, we have

sinA = (16 / 26)    therefore

sin^-1 (16/26)  = A  = about 37.98°

6(2y+6)=4(9+3y)  simplify both sides

12y + 36  = 36 + 13y     subtract 36 from both sides

12y = 13y      subtract 13t from both sides

12y - 13y = 0

-1y = 0      divide both sides by -1

y  = 0

Ummmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmm..................................................................

DN

Thx Lance :)

The result is :

x^5 - 2519424000000 x^6

y=-(x+6)^2-3

This is a parabola that turns downward whose vertex is (-6, -3)

The axis of symmetry is given by   x = the x coordinate of the vertex

So.......the axis of symmetry  is     ....     x = -6

Here's a graph  of the parabola and the axis  ........https://www.desmos.com/calculator/mwnmgvdtg8

.875 =  875 / 1000   = 7 / 8

(3/4) x (4/1)  =  12/4   = 3

(79 + -79) + |4| – 5   =

( 0 )  + 4  - 5  =

4 - 5  =

-1

2(X+3)^2 = -4X   simplify on the left side

2[x^2 + 6x + 9)  = -4x     divide both sides by 2

(x ^2 + 6x + 9)  = -2x       add 2x to both sides

x^2 + 8x + 9   =  0       this won't factor

Using the quadratic formula, the solutions are  x =   (plus/minus)sqrt(7)  - 4  

Or...in approximate form...... about -1.354   and -6.646

m/v = d

The units of d (density) will be dependent on what units m (mass) and v (volume) are measured in

The Surface Area =   4 * pi * r^2

So...in your case, we have

84.5 = 4 * pi * r^2       divide both sides by 4pi

84.5 / [4pi]   = r^2     take the square root of both sides

2.593 in ≈  r

The arc [perimeter] of a whole circle   = 2 * pi * r   where r = the radius of the circle

So......a semi-circle will be 1/2  of this =  pi * r