Simplify as much as possible 3x^2 - 27/x^2 +x-12 Find the domain of y = 5/square
ID: 3027509 • Letter: S
Question
Simplify as much as possible 3x^2 - 27/x^2 +x-12 Find the domain of y = 5/squareroot 1 - 2x Find k if lines 9x - ky = 9 and 6x + 2y + 3 = 0 are parallel. Find algebraically where the lines 2x + y = 8 and 3x + 2y = 13 intersect Solve the inequality: x + 3/3 - 2x > 0. Find the following, showing all working integral (4e^5t + 1)dt; integral[cos(5x) - sec^2(2x)]dx; integral (1/x + 1/x^3 + squareroot 2x)dx. sketch the area bounded by the curve y = x^2 - 9 and the x-axis from x = 0 to x = 6. Find the area.Explanation / Answer
Solutiona2 :
x<1/2
interval notation:(-infinity,1/2)
the domain of a function is the set of input or argument values for which the function is real and defined
sqrt(f(x)----=>f(x)>=0
solve (1-2x)>=0
-(2x-1)>=0
when u change sign inequality changes
(2x-1)<=0
2x<1
x<1/2
Solutionb:
findk:
when lines are parallel slopes are equal
m1=m2
slope of a line ax+by+c=0 is m=-a/b
-(9/-k)=-(6/2)
9/-k=3
-k=9/3
-k=3
k=-3
Solutionb2
find x,y where two lines meet
we solve the 2 equations to get intersection points x,y
2x+y=8---(1)
3x+2y=13-----(2)
solve (1) and (2)
(1)*2
4x+2y=16
3x+2y=13
subtract (3) from (4)
x=3
substitute x=3 in(1) to get y
y=8-2x
=8-2(3)
=8-6
y =2
(x,y)=(3,2) both lines intersect
Solutionc:
-3<x<3/2
interval notation(-3,3/2)