Top answers

Find all real solutions of (x^2 +4x +3)^(x^2 -6x+8) = 1

Rewrite as a^b = 1, where a = x^2+4x+3 and b = x^2-6x+8List the cases for which a^b = 1Case 1: a = 1:So x^2+4x+3=1 => x^2+4x+2=0 => x=-2 +/- sqrt(2)Case 2: b=0, a ≠ 0:b=(x-4)(x-2) => x = 2, x=4Check...
NM
Answered by Nicholas M. • PAT tutor
1499 Views

A function is defined piecewise f(x) = ( e^x for x<0, e^(-x) + 2x for x>= 0). Sketch f(x) and its first, second and third derivatives

f(x) = ( e^x for x&lt;0, e^(-x) + 2x for x&gt;= 0)f'(x) = ( e^x for x&lt;0, -e^(-x) + 2 for x&gt;= 0)f''(x) = ( e^x for x&lt;0, e^(-x) for x&gt;= 0)f'''(x) = ( e^x for x&lt;0, -e^(-x) for x&gt;= 0)(Will sket...
NM
Answered by Nicholas M. • PAT tutor
1633 Views

Estimate the radius of the moon based on a solar eclipse given the distances between the earth and the moon, the earth and the sun, and the radius of the sun.

A diagram showing the moon directly between the earth and the sun is key here. If we call the radii of the sun and the moon r s and r m and the distances from earth D s and D m. respectively, there are simil...
AM
Answered by Alastair M. • PAT tutor
2269 Views

Five point charges, each of positive charge q, are arranged to form the corners of a uniform pentagon. A point charge Q is placed at the pentagon's centre. One of the corner charges is removed. What force does the centre charge experience?

There are four keys to answering this problem - when taken together, they turn a seemingly difficult calculation into a trivial one-line answer. The first is knowing Coulomb's inverse square law for the forc...
TA
Answered by Theo A. • PAT tutor
2867 Views

Question below as would not fit in here

A parachutist jumps out of a plane at height h. She is subject to air resis- tance with a force of −αv2. The equation of her motion is given bymdv/dt =mg−αv^2 What are the units of α?Calculate the terminal v...
MS
Answered by Matthew S. • PAT tutor
4117 Views