It's kinda like using variables, but shapes in their place. Let's set the circle to x, the triangle to y, and the square to z. Now the equations say x+(y+z)=13, (y+z)=8, and x+y=7. First thing we can do it plug 8 into the first equation for y+z, getting x+8=13. Subtract 8 to both sides and x (or circle) equals 5. Plug 5 into the last equation, x+y=7 to solve for y, getting 5+y=7. Subtract 5 to both sides and y (or triangle) equals 2. Finally, plug two in for y in y+z=8, getting 2+z=8. Subtract 2 from both sides and z (or square) equals 6. Hope I've explained it clearly!!
Answer:
the center is (3,1) and the radius is √6.
Step-by-step explanation:
The center of a circle can be found using the equation
and is (h,k) from it. Notice h and k are the opposite value as in the equation.
First write the equation in this form.
Complete the square with each variable to find what numbers should go in place of the question marks.
Add 1 and 9 to both sides of the equation.
So the center is (3,1) and the radius is √6.
True; always follow your instincts.
(.....is this even a question!?)
Answer:
We can find the solution using chain rule,
For instance, if u(x,y) = f(ax+by), then
which represents derivative of x with respect to x
and then derivative of
with respect to y is
,
Now, the derivative of
with respect to x, which is the second derivative, which is

and the derivative
and
are
,

Finally, the solution of PDE is


= 0,
As the PDE is equal to 0, it means the function u(x,y) = f(ax+by) is the solution of the given PDE.
Answer is A. Work is shown in picture. I tried my best to draw on my computer!