Arrange the systems of equations that have a single solution in increasing order of the x-values in their solutions.
2x + y = 10
x − 3y = -2
x + 2y = 5
2x + y = 4
x + 3y = 5
6x − y = 11
2x + y = 10
-6x − 3y = -2
Answers
Step-by-step explanation:
Given :
Swati walks in a circle of radius 20m and minal walks in a circle of radius 40m.
Both complete one circle in same time.
To Find :
Relation between their speeds.
Solution :
❒ Speed is defined as the ratio of distance travelled to the time taken.
It is a scalar quantity having only magnitude.
SI unit : m/s
Distance covered by body after completing one round of circle will be equal to the perimeter of circle.
Let time taken by them to complete one round of circle be t..
A. Speed of swati :
➛ v = 2πr / t
➛ v = 2π(20) / t
➛ v = 40π / t .......... (I)
B. Speed of minal :
➛ v' = 2πr' / t
➛ v' = 2π(40) / t
➛ v' = 80π / t .......... (II)
From equation (I) and (II),
➠ v / v' = (40π/t) / (80π/t)
➠ v / v' = 1 / 2
➠ v' = 2v
∴ (c) Speed of minal is twice the speed of swati.Given :
Efficiency of the carnot engine changes from 1/6 to 1/3 when source temperature is raised by 100K.
To Find :
Temperature of sink.
Solution :
❒ Efficiency of carnot's engine (an ideal heat engine), is given by
η = 1 - T'/T
where,
T' denotes temp. of the sink
T denotes temp. of the source
Case - I :
➛ 1/6 = 1 - T'/T
➛ T'/T = 1 - 1/6
➛ T'/T = 5/6
➛ T = 6T'/5 .......... (I)
Case - II :
In this case temperature of the sink is raised by 100K..
➛ 1/3 = 1 - T'/(T + 100)
➛ T'/(T + 100) = 2/3
➛ 3T' = 2T + 200
From the equation (I),
➛ 3T' = 12T'/5 + 200
➛ 15T' - 12T' = 1000
➛ T' = 1000/3
➛ T' = 333.33kQuestion :
A geyser of 2kW is used to heat 20kg of water. Calculate the time taken in raising the temperature of water by 30°C. Specific heat of water is 4,200 J/kg °C
Given :
Power of geyser = 2kW = 2000W
Mass of water = 20kg
To Find :
Time taken by geyser to raise temperature of water by 30°C.
Solution :
❒ Specific heat capacity of substance is defined as the heat required to increase temperature of 1kg substance by 1°C.
Mathematically, H = m × c × ∆T
H denotes heat energy
m denotes mass
c denotes specific heat
∆T denotes change in temperature
First of all we need to find heat required to raise temperature of water..
By substituting the given values i. above formula, we get;
➠ H = m × c × ∆T
➠ H = 20 × 4200 × 30
➠ H = 252 × 10⁴ J
★ We know that, power is measured as the energy consumed per unit time.
➛ P = H / t
➛ 2000 = 252 × 10⁴ / t
➛ t = 2520/2
➛ t = 1260 s
60 s = 1 min
∴ 1260 s = 1260/60 = 21 min
Final answer :- 21 min