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For ellipses ##a >= b## (when ##a = b## we have a circle) ##a## represents half the length of the major axis while ##b## represents half […]

If ##z^3-1=0## then we are looking for the cubic roots of unity i.e. the numbers such that ##z^3=1##. If you’re using complex numbers then every polynomial […]

Cartesian coordinates also known as Rectangular coordinates are defined in terms of ##x## and ##y##. So for this problem ##theta## has to be eliminated/converted using basic […]

##y^2=8x## The standard form of the parabola is ##y^2=4ax## giving a parabola with its axis parallel to the ##x##-axis vertex at the origin focus ##(a0)## and […]

##anti log 0.3010 = 10^(0.3010) ~~ 2## The function: ##f(x) = 10^x## is one to one and strictly monotonically increasing on its ##(-oo oo)## with ##(0 […]

I found: ##x=e^8=2980.95## We can use the property of the logs that allows you to take out the exponent of the argument and place it as […]

##0 = x^2+y^2-8x+6y+16 = (x-4)^2 + (y+3)^2 – 3^2## is a circle of radius ##3## with centre ##(4 -3)## The equation of a circle of radius […]

##y=0## ##y=-3/2## To find any horizontal we have to evaluate: ##lim_(x rarr+-oo)f(x)## if the limits are finite then they are horizontal asymptotes ##lim_(x rarr-oo)f(x)=lim_(x rarr-oo)3/2(e^x/(1-e^x))=## ##3/2lim_(x […]

##10^21## In general ##color(white)(XXX)b^pxxb^q =b^(p+q)## Therefore ##color(white)(XXX)10^18 xx 10^3 = 10^(18+3) = 10^21##