Answer:
7 horses and 8 chickens
Step-by-step explanation:
To solve this, first you would need to list out all of the available ratios. Then, find out how many legs are in each option.:
14 horses and 1 chicken = 58 legs
13 horses and 2 chickens = 56 legs
12 horses and 3 chickens = etc.
11 horses and 4 chickens
10 horses and 5 chickens
9 horses and 6 chickens
8 horses and 7 chickens
7 horses and 8 chickens = 44 legs!
6 horses and 9 chickens
5 horses and 10 chickens
4 horses and 11 chickens
3 horses and 12 chickens
2 horses and 13 chickens
1 horses and 14 chickens
Answer:(1) The correct option is b. (2) The correct option is c.
Explanation:
(1)
It is given that the △ABD≅△FEC.
So by (CPCTC) corresponding parts of congruent triangles are congruent.
It is given that the angle DAB is 63 degree.
Therefore, the correct option is b.
(2)
It is given that the △ABD≅△FEC.
So by (CPCTC) corresponding parts of congruent triangles are congruent.
Therefore, the correct option is c.
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.
The answer is 29,032,000,000
