Answer:

Step-by-step explanation:
we want to figure out the general term of the following recurrence relation

we are given a linear homogeneous recurrence relation which degree is 2. In order to find the general term ,we need to make it a characteristic equation i.e
the steps for solving a linear homogeneous recurrence relation are as follows:
- Create the characteristic equation by moving every term to the left-hand side, set equal to zero.
- Solve the polynomial by factoring or the quadratic formula.
- Determine the form for each solution: distinct roots, repeated roots, or complex roots.
- Use initial conditions to find coefficients using systems of equations or matrices.
Step-1:Create the characteristic equation

Step-2:Solve the polynomial by factoring
factor the quadratic:

solve for x:

Step-3:Determine the form for each solution
since we've two distinct roots,we'd utilize the following formula:

so substitute the roots we got:

Step-4:Use initial conditions to find coefficients using systems of equations
create the system of equation:

solve the system of equation which yields:

finally substitute:


and we're done!
<h3>
Answer: 138,240 cubic cm</h3>
Explanation:
If x is the side length of a cube, then x^3 is the volume. Think of it like length*width*height, but length = width = height.
It's no coincidence that the cubing operation or cubed exponent ties directly to the concept of things like volumes in cubic cm.
In this case, x = 12 cm is the side length of each small cube. The volume of each small cube is x^3 = 12^3 = 12*12*12 = 1728 cubic cm.
Eighty such small cubes get us a total volume of 80*1728 = 138,240 cubic cm.
Answer:
2 & 3
Step-by-step explanation:
they both equal -7
the temp dropped 7 degrees