Answer:
Step-by-step explanation:
<u>Given equation:</u>
<u>Factorize it in steps:</u>
- 3x² + 5x + 2 = 0
- 3x² + 3x + 2x + 2 = 0
- 3x(x + 1) + 2(x + 1) = 0
- (x + 1)(3x + 2) = 0
<u>The roots are:</u>
- x + 1 = 0 ⇒ x = - 1
- 3x + 2 = 0 ⇒ 3x = - 2 ⇒ x = - 2/3
Answer:
Step-by-step explanation:
Given the surface
G(x, y, z) =2z²
Over the hemisphere
x² + y² + z² = 36. For z≥0
Using polar coordinate
x=sin Φ cos θ,
y = sin Φ sin θ,
z = cos Φ
0 ≤ Φ ≤ π/2, 0 ≤ θ ≤ 2π
Therefore
r(Φ, θ) = sin Φ cos θ i + sin Φ sin θ j + cos Φ k
Also, dS= |rθ×rΦ|= sinΦ
dS=sinΦdΦdθ
Then we want to compute the volume integral of
∫ ∫ₛ G(x, y, z) dS
G(x, y, z) =2z²
Therefore in polar forms
G(x, y, z) =2(cos Φ)²
G(x, y, z) = 2cos²Φ
Given that dS=sinΦdΦdθ
∫ ∫ₛ G(x, y, z) dS
∫ ∫ 2cos²ΦsinΦdΦdθ at 0 ≤ Φ ≤ π/2,
0 ≤ θ ≤ 2π
∫ 2cos²ΦsinΦ •θdΦ from 0 ≤ θ ≤ 2π
2∫cos²ΦsinΦ •(2π-0)dΦ
4π∫ cos²ΦsinΦ dΦ from 0 ≤ Φ ≤ π/2
Let U = cosΦ
dU/dΦ =-sinΦ
-dU/sinΦ =dΦ
4π∫ U²sinΦ(-dU/sinΦ) 0 ≤ Φ ≤ π/2
-4π∫ U² dU
-4π U³/3, then U=cosΦ
[-4πcos³Φ / 3 ] from 0 ≤ Φ ≤ π/2
[-4π cos³(π/2)/3 - [-4π cos³(0)/3]
0+4π/3
4π/3
4π/3 unit²
A, because n is having 19 taken from it
Answer:
Initial velocity (u)=o m/s
Final velocity (v)=27m/s
Time taken to attain velocity is(t)=5m/s
As we know v=u+at
Substitute above values in the given equation
27=0+a(5)
27/5=a
a=5.4 m/s^2
Step-by-step explanation:
Answer:
35
Step-by-step explanation:
Let number = x
(1/5 of x) + (3 * x) = 42 + (2 * x)
x/5 + 3x = 42 + 2x
1/5x + 3x - 2x = 42
1 1/5x = 42
6/5 x = 42
x = 42 ÷ 6/5
x = 42 * 5/6
x = 210 / 6
x = 35
The number is 35
