Answer:
-8x+5
Step-by-step explanation:
txt if you need a explanation
Answer:
value of x = 8
Step-by-step explanation:
if the given lines are parallel, then the shown pair of angles are corresponding angles,
and we know that the the pair of corresponding angles are equal so,
=》16x - 8 = 120
=》16x = 128
=》x = 128 ÷ 16
=》x = 8
X can you please give me braknlistest yes yes thank yoy
Answer:
y(t) = c₁ e^(-1/2 t) cos(√3/2 t) + c₂ e^(-1/2 t) sin(√3/2 t) + 1
Step-by-step explanation:
y" + y' + y = 1
This is a second order nonhomogenous differential equation with constant coefficients.
First, find the roots of the complementary solution.
y" + y' + y = 0
r² + r + 1 = 0
r = [ -1 ± √(1² − 4(1)(1)) ] / 2(1)
r = [ -1 ± √(1 − 4) ] / 2
r = -1/2 ± i√3/2
These roots are complex, so the complementary solution is:
y = c₁ e^(-1/2 t) cos(√3/2 t) + c₂ e^(-1/2 t) sin(√3/2 t)
Next, assume the particular solution has the form of the right hand side of the differential equation. In this case, a constant.
y = c
Plug this into the differential equation and use undetermined coefficients to solve:
y" + y' + y = 1
0 + 0 + c = 1
c = 1
So the total solution is:
y(t) = c₁ e^(-1/2 t) cos(√3/2 t) + c₂ e^(-1/2 t) sin(√3/2 t) + 1
To solve for c₁ and c₂, you need to be given initial conditions.
Answer:
63 units
Step-by-step explanation:
The profit function P(x) is given by the revenue function minus the cost function:
The number of units sold 'x' for which the derivate of the profit function is zero, is the number of units that maximizes profit:
The number of units that should be manufactured so that profit is maximum is 63 units.
