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604 not correct

Or if you really mean 1/2 * 4/3 * pi * 253 = 2/3 * pi * 253, that is an identity.

You mean\(\dfrac{1}{2}\times \dfrac{4}{3}\times \pi \times 253-\dfrac{2}{3}\times \pi \times 253\)?

\(\dfrac{1}{2}\times \dfrac{4}{3}\times \pi \times 253-\dfrac{2}{3}\times \pi \times 253\\ = \dfrac{2\times 253\times \pi}{3}-\dfrac{2\times 253\times \pi}{3}\\ = 0\)

\(\frac{12}{15}\div \frac{4}{45}\\ = \frac{\not4}{\not5}\times \frac{\not{45}^{\;9}}{\not4\;}\)

= 9.

Same as Omi67's answer.

That means if an angle in a right-angled triangle is 49 degrees, and hypotenuse of the triangle = 5, the side opposite to the 49-degree angle is 3.773547901115.And this diagram: 

Firstly, q is not an angle, it is the length of a side of a triangle.

\(\sin 49 = \dfrac{q}{5}\\ q=5\sin 49\)

No formula required.

5 sin 49 ≈ 3.773547901115

Just a guess.

604? :D

As follows:

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\(\frac{12}{15}:\frac{4}{45}=\frac{12}{15}*\frac{45}{4}=\frac{3}{1}*\frac{3}{1}=3*3=9\)

Ojemine which was a m****r errors!

Sorry!

Not quite asinus!   ln(y) is not equal to y*ln(x) + x*ln(y)

Do dy/dx = d(x^y)/dx  +  d(y^x)/dx  first, then treat the terms on the right seperately.

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Hello Max!

Find \(\frac{dy}{dx} \) when \(y= x^{y} +y^{x}\)  

\(lny=y\times lnx+ x\times lny \)

\(lny-x\times lny=y\times lnx\)

\(lny\times \left(1-x\right)= y\times lnx \)

\(\frac{y}{lny} = \frac{\left(1-x\right) }{lnx} \)

\(y=\frac{lny}{lnx} \times \left(1-x\right) \)

From here I have to capitulate.
To differentiate, I need
y isolated on one side of the equation.
I'm excited about the solution!

Greetings asinus :- )  !

-4/(1000000loge(1-(2/12)))

Let $x be the cost of each box of apples,

200x - 300 = 160x + 180

40 x = 480

x = 12

Each box of apples costs $12.

He used up $12 x 160 = $1920

He now have 50 x 160 = 8000 apples.

He sold 8000 - 95 apples which is 7905 apples.

He got $(7905 x .3) = 2371.5 Hope my mental calculation is correct.

Profit = 2371.5 - 1920 = $451.5

By the way I'd like to use array more though :P

I am going to provide the steps for the solving :D 

\(L+M = 1.74\\ L = M+0.16\\ (M+0.16)+M = 1.74\\ 2M + 0.16 = 1.74\\ M = \dfrac{1.74-0.16}{2}=0.79\\ L = 0.79 + 0.16 = 0.95\)

10000/8000

= 10/8

= 5/4

= 1 1/4

$ 1 1/4 for each question.

Give both of us $1.25? :D 

thank you both of u ;D