if x+1/x=9 and x²+1/x²=53 find the value of x-1/x.
Answers
Given
x+1/x=9 and x^2+1/x^2=53
In my view this is not possible because
x+1/x=9
=>(x+1/x)^2=81
=>x^2+1/x2+2=81
=>x^2+1/x^2=79
but given 53 in question instead of 79.
However if we assume x-1/x=A then
(x+1/x)(x-1/x)=9A
=>x^2–1/x^2=9A and
x^2+1/x2=53
=>(53+9A)/2 = 2/(53–9A)
(53)^2-(2)^2 = 81A^2
=>81A^2=55*51
A=(1/9)√(2805).
My conclusion is that question needs some correction..
Ask if u hv any further doubt..!
Hope this helps u………
Answer:
a) V₀ = 13.5m/s
a) V₀ = 13.5m/sb) a = 2.1 m/s²
Explanation:-
1) Convert velocities to m/s
i) 20 km/h × 1000m/kg × 1h/3600s = 5.556m/s
ii) 40km/h = 11.111m/s
2) Red car, time elapsed to reach position x = 44.5m
Constant velocity ⇒ x = V×t ⇒ t = x / V
⇒ t₁ = 44.5m / 5.556m/s = 8s
3) Red car, time elapsed to reach position x = 77.6m
t₂ = 76.6m / 11.111/s = 6.9s
4) Green car, distance run at t₁ = 8s, x = 44.5m
i) uniform acceleration equation d = V₀t + at² / 2
ii) d = 220m - x = 220m - 44.5m = 175.5m = V₀ (8) + a (8)² /2
175.5 = 8V₀ + 32a ↔ equation (1)
5) Green car, distance run at t₂ = 6.9s, x = 76.6m
i) d = 220m - x = 220m - 76.6m = 143.4
ii) 143.4 = V₀t₂ + at₂² / 2
143.4 = V₀ (6.9) + a(6.9)² / 2
143.4 = 6.9V₀ + 23.8a ↔ equation (2)
6) Solve the system of equations:
175.5 = 8V₀ + 32a ↔ equation (1)
143.4 = 6.9V₀ + 23.8a ↔ equation (2)
V₀ = 13.5m/s
a = 2.1 m/s²