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A source of green laser light has a wavelength of 560nm, what is its frequency? Give your answer to an appropriate number of significant figures and using the correct units.

1.) using the wave speed formula for an electromagnetic wave, c=fλ, (c=3.00x10^8 m/s) f=c/λ where c=the speed of an electromagnetic wave. f=(3.00x10^8)/(560x10^-9)= 5.36x10^14 Hz
JE
Answered by Joel E. • Physics tutor
3388 Views

(1.) f(x)=x^3+3x^2-2x+15. (a.) find the differential of f(x) (b.) hence find the gradient of f(x) when x=6 (c.) is f(x) increasing or decreasing at this point?

(1.) (a.) f’(x)=3x^2+6x-2 (b.) x=6 gradient=142 (c.) since f’(x)>0 at x=6, the function is increasing.
JE
Answered by Joel E. • Maths tutor
4076 Views

The equation x^3 - 3*x + 1 = 0 has three real roots; Show that one of the roots lies between −2 and −1

In order to prove that one real root of an equation is situated in a certain interval, we calculate the value of the function at the ends of the given interval. In the given case, f(-2) = (-2)^3 - 3*(-2) + 1...
PT
Answered by Paul T. • Maths tutor
12584 Views

Complete the square and find the roots (where y=0) of: "x^2+4x-5"

completing the square: (x+2)^2-9 finding the roots: (x+2)^2=9 x+2=+/-3 at y= 0, x= -5 or 1
LQ
Answered by Liam Q. • Maths tutor
4527 Views

y=4x^3+6x+3 so find dy/dx and d^2y/dx^2

dy/dx=12x^2+6 d^2y/dx^2=24x
SP
Answered by Swapnil P. • Maths tutor
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