Answer:
Two equal sides = 14.4 inches each
Shortest side = 7.2 inches
Step-by-step explanation:
a + b + c = 36
a = b
a = 2c
then:
c = a/2
a + a + a/2 = 36
2a + a/2 = 36
4a/2 + a/2 = 36
5a/2 = 36
a = 2*36/5
a = 72/5
a = 14.4
a = 2c
14.4 = 2*c
c = 14.4/2
c = 7.2
a = b
b = 14.4
Check:
14.4 + 14.4 + 7.2 = 36
Distribute 3
6t+15=5t+25
subtract 5t from 6t
t+15=25
subtract 15 from both sides
t=10
Using the cube formula for volume I got V=3.38cm^3
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:
x = 30m
Step-by-step explanation:
<u>GIVEN :-</u>
There are 2 right-angled triangles.
In the triangle on the right side ,
- Hypotenuse = 26m
- Base = 10m
In the triangle on the left side ,
<u>TO FIND :-</u>
- Length of the common perpendicular to both triangles.
- Length of the hypotenuse of the triangle on the left side.
<u>FACTS TO KNOW BEFORE SOLVING :-</u>
.
<u>SOLUTION :-</u>
In the triangle on the right side ,
⇒ Perpendicular of the triangle on right side = Perpendicular of the triangle on left side.
In the triangle on the left side ,
∴ x = 30m
