A telephone cable runs from A to B to C to D. How much cable is required to run from A to D directly, if

Mathematics

1 answer:

igor_vitrenko [27]3 years ago

3 0

You would have to know the angle measurements if you have a picture of the problem re-ask it and I'll be able to help

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Which of the following is a third root of the given complex number? 27(cos(pi/5)+isin(pi/5))

Digiron [165]

The third root of the given complex number 27(cos(pi/5)+isin(pi/5)) is 3(cos(pi/15)+i sin(pi/15))

The solution would be like this for this specific problem: 2^5 = 32 so you need a 2 out front the 5th root of cos(x) + i sin(x) is cos(x/5) + i sin(x/5). Additionally, 5 roots are located at even intervals around the circle. They are spaced every 2 pi/5 or 6 pi/15 radians. Roots are located at pi/15, pi/15+ 10pi/15 = 11 pi/15 and pi/15+ 20pi/15 = 21 pi/15 (or 7 pi /5 ).

5 0

3 years ago

Solve this equation pls

Aleksandr-060686 [28]

Answer:

${ \rm{y = \frac{3 \sqrt{x} + 2x}{ {4x}^{2} } }} \\$

• We are gonna use the quotient rule

${ \boxed{ \bf{ \frac{dy}{dx} = \frac{ {\huge{v} } \frac{du}{dx} - { \huge{u}} \frac{dv}{dx} }{ {v}^{2} } }}} \\$

u is (3√x + 2x)
v is 4x²
du/dx is 3/2√x
dv/dx is 8x

• Therefore:

${ \rm{ \frac{dy}{dx} = \frac{(4 {x}^{2})( \frac{3}{2 \sqrt{x} }) - (3 \sqrt{x} + 2x)(8x) }{16 {x}^{4} } }} \\ \\ { \rm{ \frac{dy}{dx} = \frac{(6 {x}^{2})( {x}^{ - \frac{1}{2} } ) - (24 {x}^{ \frac{3}{2} } + 16 {x}^{2} ) }{16 {x}^{4} } }} \\ \\ { \rm{ \frac{dy}{dx} = \frac{ 6 {x}^{ \frac{3}{2} } - {24x}^{ \frac{3}{2} } - {16x}^{2} }{16 {x}^{4} } }} \\ \\ { \rm{ \frac{dy}{dx} = \frac{ - 18 {x}^{ \frac{3}{2} } - 16 {x}^{2} }{16 {x}^{4} } }} \\ \\ { \rm{ \frac{dy}{dx} = - 2 {x}^{ \frac{3}{2} } (9 + 8 {x}^{ \frac{4}{3} } ) \div 16 {x}^{4} }} \\ \\ { \boxed{ \boxed{ \rm{ \: \: \frac{dy}{dx} = - \frac{8 \sqrt{ {x}^{ \frac{8}{3} }} + 9}{8x {}^{ \frac{8}{3} } } \: \: }}}}$