a square is split into four triangles, and then three of the four triangles are shaded as shown. If the areas of the shaded triangles are 3,4, and 6, as shown, what is the area of the unshaded triangle?

11

Step-by-step explanation

We first let the side of the square be defined as x.

Therefore, we have ax/2 = 4, and bx/2= 3. Where a and b are the legs of the triangles with areas 4 and 3 respectively.

For the Triangle with area 6, we then have ((x-a)(x-b))/2 = 6. Expanding gives us x^2-bx-ax+ab=12. Using the equation above and plugging in values where bx = 6, ax=8, a = 8/x, and b = 6/x. We get

x^2-6-8+48/x^2 = 12.

Simplified gives us,

x^4-26x^2+48.

Factored gives us,

((x^2-2)(x^2-24).

Since the area cannot be any negative values and bigger than 6 (since there is already a triangle with area 6), we then have x^2 = 24.

Therefore a of unshaded region = 24-6-4-3= 11

step-by-step explanation:

we can use this expression to calculate the energy gain as a particle moves with a field or the energy loss as it moves against it. (note that it is also used to define the electron-volt, a unit of energy equal to that gained by an electron as it falls through a pd of 1 v, i.e. w = 1 ev = 1.6 10-19 c 1 v = 1.6 10-19j).in fact this expression is really nothing more than the statement that potential is the potential energy per unit charge. in this case, v= w/qis simply stating that the change in potential energy(or work done) per unit charge is equal to the change in potential (or potential difference), v.student questions: uniform electric fields2electron beamcathode+5 kvanode0 v