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(1 -1) ##2sqrt5 20pi62.83## The of a circle is ##color(red)(|bar(ul(color(white)(a/a)color(black)((x-a)^2+(y-b)^2=r^2)color(white)(a/a)|)))## where (a b) are the coords of centre and r the radius now ##(x-1)^2+(y+1)^2=20 is in […]

It is ##-1##. We apply the properties of the logarithm: ##ln(1/e)=ln(e^(-1))## the first property is that the exponent exit and multiply the log ##ln(e^-1)=-ln(e)## the second […]

##x = 5/8## You used Logarithm of a product (based on the symbol you used which is addition). ##log2 + log(4x-1) = 3## ##log 2(4x-1) = […]

Equation of circle is ##x^2+y^2+6x-6y+14=0## and ##y=1## is tangent at ##(-31)## The equation of a circle with center ##(-33)## with radius ##r## is ##(x+3)^2+(y-3)^2=r^2## or ##x^2+y^2+6x-6y+9+9-r^2=0## […]

The directrix is the line ##x=(a^2)/c##. For a hyperbola ##(x-h)^2/a^2-(y-k)^2/b^2=1## where ##a^2+b^2=c^2## the directrix is the line ##x=a^2/c##.

The notation ##H^-1## means the inverse function. The equation of the inverse function can be found by switching the ##x## and ##y## values inside the function. […]

Use the equation and plug in the center and the radius. ##(x+2)^2+y^2=25## Recall the equation for a circle: ##(x-h)^2+(y-k)^2=r^2## Where ##(hk)## is the center of a […]

##5.87849981 10^12 miles## ##9.4605284 10^15 metres= 5.87849981 10^12 miles##

##a_n = 25-10(n-1)## An is a sequence in which there is a constant difference between successive terms. Given an arithmetic sequence with initial term ##a_1## and […]