Changes the tabname of invisible players (configurable). Posts: 0 Member Details; iniraz. View User Profile Send Message Posted Jun 4, 2021 #129. Assume the prices of labor and capital are $2 and $3 respectively. Refer to the above information. If the price of product A is $0.50, the firm will realize: A. An economic profit of $4. An economic profit of $2. An economic profit of $6.
The graph of y = f(x) is shown below.
[asy]
size(150);
real ticklen=3;
real tickspace=2;
real ticklength=0.1cm;
real axisarrowsize=0.14cm;
pen axispen=black+1.3bp;
real vectorarrowsize=0.2cm;
real tickdown=-0.5;
real tickdownlength=-0.15inch;
real tickdownbase=0.3;
real wholetickdown=tickdown;
void rr_cartesian_axes(real xleft, real xright, real ybottom, real ytop, real xstep=1, real ystep=1, bool useticks=false, bool complexplane=false, bool usegrid=true) {
import graph;
real i;
if(complexplane) {
label('$textnormal{Re}$',(xright,0),SE);
label('$textnormal{Im}$',(0,ytop),NW);
} else {
label('$x$',(xright+0.4,-0.5));
label('$y$',(-0.5,ytop+0.2));
}
ylimits(ybottom,ytop);
xlimits( xleft, xright);
real[] TicksArrx,TicksArry;
for(i=xleft+xstep; i if(abs(i) >0.1) {
TicksArrx.push(i);
}
}
for(i=ybottom+ystep; i if(abs(i) >0.1) {
TicksArry.push(i);
}
}
if(usegrid) {
xaxis(BottomTop(extend=false), Ticks('%', TicksArrx ,pTick=gray(0.22),extend=true),p=invisible);//,above=true);
yaxis(LeftRight(extend=false),Ticks('%', TicksArry ,pTick=gray(0.22),extend=true), p=invisible);//,Arrows);
}
if(useticks) {
xequals(0, ymin=ybottom, ymax=ytop, p=axispen, Ticks('%',TicksArry , pTick=black+0.8bp,Size=ticklength), above=true, Arrows(size=axisarrowsize));
yequals(0, xmin=xleft, xmax=xright, p=axispen, Ticks('%',TicksArrx , pTick=black+0.8bp,Size=ticklength), above=true, Arrows(size=axisarrowsize));
} else {
xequals(0, ymin=ybottom, ymax=ytop, p=axispen, above=true, Arrows(size=axisarrowsize));
yequals(0, xmin=xleft, xmax=xright, p=axispen, above=true, Arrows(size=axisarrowsize));
}
};
rr_cartesian_axes(-5,5,-5,6);
draw((-4,4)--(-1,0)--(0,2)--(4,-4),red);
label('$y = f(x)$', (3,3), UnFill);
[/asy]
size(150);
real ticklen=3;
real tickspace=2;
real ticklength=0.1cm;
real axisarrowsize=0.14cm;
pen axispen=black+1.3bp;
real vectorarrowsize=0.2cm;
real tickdown=-0.5;
real tickdownlength=-0.15inch;
real tickdownbase=0.3;
real wholetickdown=tickdown;
void rr_cartesian_axes(real xleft, real xright, real ybottom, real ytop, real xstep=1, real ystep=1, bool useticks=false, bool complexplane=false, bool usegrid=true) {
import graph;
real i;
if(complexplane) {
label('$textnormal{Re}$',(xright,0),SE);
label('$textnormal{Im}$',(0,ytop),NW);
} else {
label('$x$',(xright+0.4,-0.5));
label('$y$',(-0.5,ytop+0.2));
}
ylimits(ybottom,ytop);
xlimits( xleft, xright);
real[] TicksArrx,TicksArry;
for(i=xleft+xstep; i if(abs(i) >0.1) {
TicksArrx.push(i);
}
}
for(i=ybottom+ystep; i if(abs(i) >0.1) {
TicksArry.push(i);
}
}
if(usegrid) {
xaxis(BottomTop(extend=false), Ticks('%', TicksArrx ,pTick=gray(0.22),extend=true),p=invisible);//,above=true);
yaxis(LeftRight(extend=false),Ticks('%', TicksArry ,pTick=gray(0.22),extend=true), p=invisible);//,Arrows);
}
if(useticks) {
xequals(0, ymin=ybottom, ymax=ytop, p=axispen, Ticks('%',TicksArry , pTick=black+0.8bp,Size=ticklength), above=true, Arrows(size=axisarrowsize));
yequals(0, xmin=xleft, xmax=xright, p=axispen, Ticks('%',TicksArrx , pTick=black+0.8bp,Size=ticklength), above=true, Arrows(size=axisarrowsize));
} else {
xequals(0, ymin=ybottom, ymax=ytop, p=axispen, above=true, Arrows(size=axisarrowsize));
yequals(0, xmin=xleft, xmax=xright, p=axispen, above=true, Arrows(size=axisarrowsize));
}
};
rr_cartesian_axes(-5,5,-5,6);
draw((-4,4)--(-1,0)--(0,2)--(4,-4),red);
label('$y = f(x)$', (3,3), UnFill);
[/asy]
For each point (a,b) that is on the graph of y = f(x) the point $left( 3a - 1, frac{b}{2} right)$ is plotted, forming the graph of another function y=g(x). As an example, the point (0,2) lies on the graph of y=f(x) so the point $(3 cdot 0 - 1, 2/2) = (-1,1)$ lies on the graph of y=g(x)
(a) Plot the graph of y=g(x) Include the diagram as part of your solution.
(b) Express g(x) in terms of f(x)
(c) Describe the transformations that can be applied to the graph of y=f(x) to obtain the graph of y=g(x) For example, one transformation could be to stretch the graph vertically by a factor of 4
(a) Plot the graph of y=g(x) Include the diagram as part of your solution.
(b) Express g(x) in terms of f(x)
(c) Describe the transformations that can be applied to the graph of y=f(x) to obtain the graph of y=g(x) For example, one transformation could be to stretch the graph vertically by a factor of 4
How do you find parametric equations for the line through (2, 4, 6) that is perpendicular to the plane x − y + 3z = 7?
1 Answer
The parametric equation of our line is
#x=2+t#
#y=4-t#
#z=6+3t#
Explanation:
![Invisible 2 4 4 0 Invisible 2 4 4 0](https://m.media-amazon.com/images/I/61MNRW7nXMS._SL1000_.jpg)
![Tank Tank](https://www.perhokauppa.fi/image/cache/catalog/tuotteet/siimat/CHAMELEON3-1024x768.jpg)
A vector perpendicular to the plane #ax+by+cz+d=0#
is given by#〈a,b,c〉#
So a vector perpendiculat to the plane#x-y+3z-7=0#
is#〈1,-1,3〉#
The parametric equation of a line through#(x_0,y_0,z_0)#
and parallel to the vector#〈a,b,c〉# is
#x=x_0+ta#
#y=y_0+tb#
#z=z_0+tb#
is given by
So a vector perpendiculat to the plane
is
The parametric equation of a line through
and parallel to the vector
So the parametric equation of our line is
#x=2+t#
#y=4-t#
#z=6+3t#
The vector form of the line is #vecr=〈2,4,6〉+t〈1,-1,3〉#