Let the speed of the train be x km/h and the time has taken be y h. The total distance is then xy km. Case1: Speed increases by 10 km/h and the time taken reduces by 2 hours. The distance traveled remains xy km. (x+10)(y−2)=xy Therefore, xy−2x+10y−20=xy ⇒−2x+10y−20=0 ⇒−2x+10y=20 ---------- (1) CaseRead more
Let the speed of the train be x km/h and the time has taken be y h.
The total distance is then xy km.
Case1:
Speed increases by 10 km/h and the time taken reduces by 2 hours.
The distance traveled remains xy km. (x+10)(y−2)=xy
Therefore, xy−2x+10y−20=xy ⇒−2x+10y−20=0 ⇒−2x+10y=20 ———- (1)
Case 2:
Speed decreases by 10 km/h, then the time taken increases by 3 hours.
However, the distance remains,xy km. (x−10)(y+3)=xy
Therefore, xy+3x−10y−30=xy ⇒3x−10y−30=0 ⇒3x−10y=30 ———- (2) ⇒x=50 km/h
Using this in (2), we get 150−10y=30 ⇒y=12
Therefore, the distance is 50×12=600 km
The distance between the two points can be measured using the Distance Formula which is distance formula = √ [(x₂ - x₁)2 + (y₂ - y₁)2] Let the points be A(0, 0) and B(36, 15) Hence, x₁ = 0, y₁ = 0, x₂ = 36, y₂ = 15 We know that the distance between the two points is given by the Distance Formula, =Read more
The distance between the two points can be measured using the Distance Formula which is distance formula
= √ [(x₂– x₁)2 + (y₂ – y₁)2]
Let the points be A(0, 0) and B(36, 15)
Hence, x₁ = 0, y₁ = 0, x₂ = 36, y₂ = 15
We know that the distance between the two points is given by the Distance Formula,
= √ [(x₂– x₁)2 + (y₂ – y₁)2]….(1)
= √ (36 – 0)2 + 15 – 0)2
= √ [(1296) + (225)]
= √1521
= 39
Yes, it is possible to find the distance between the given towns A and B.
The positions of towns A & B are given by (0, 0) and (36, 15), hence, as calculated above, the distance between town A and B will be 39km
Solve the following quadratic equation: √2x²+7x+5√2=0.
1
1
See lessA train covered a certain distance at a uniform speed. If the train would have been 10 km/h faster, it would have taken 2 hours less than the scheduled time. And, if the train were slower by 10 km/h; it would have taken 3 hours more than the scheduled time. Find the distance covered by the train. Q.3
Let the speed of the train be x km/h and the time has taken be y h. The total distance is then xy km. Case1: Speed increases by 10 km/h and the time taken reduces by 2 hours. The distance traveled remains xy km. (x+10)(y−2)=xy Therefore, xy−2x+10y−20=xy ⇒−2x+10y−20=0 ⇒−2x+10y=20 ---------- (1) CaseRead more
Let the speed of the train be x km/h and the time has taken be y h.
The total distance is then xy km.
Case1:
Speed increases by 10 km/h and the time taken reduces by 2 hours.
The distance traveled remains xy km.
See less(x+10)(y−2)=xy
Therefore, xy−2x+10y−20=xy
⇒−2x+10y−20=0
⇒−2x+10y=20 ———- (1)
Case 2:
Speed decreases by 10 km/h, then the time taken increases by 3 hours.
However, the distance remains,xy km.
(x−10)(y+3)=xy
Therefore, xy+3x−10y−30=xy
⇒3x−10y−30=0
⇒3x−10y=30 ———- (2)
⇒x=50 km/h
Using this in (2), we get
150−10y=30
⇒y=12
Therefore, the distance is 50×12=600 km
In a ∆ABC, AD is the bisector of ∠A, meeting side BC at D. If BD = 2 cm, AB = 5 cm and DC = 3 cm, find AC
1
1
See lessIn a ∆ABC, AD is the bisector of ∠A, meeting side BC at D. ) If AD = 5.6 cm, BC = 6 cm and BD = 3.2 cm, find AC
1
1
See lessIn the figure, AE is the bisector of the exterior ∠CAD meeting BC produced in E. If AB = 10 cm, AC = 6 cm and BC = 12 cm, find CE.
The external bisector of an angle of a triangle divides the opposite side externally in the ratio of the sides containing the angle.
Check whether AD is the bisector of ∠A of ΔABC in each of the following:AB = 6 cm, AC = 8 cm, BD = 1.5 cm and CD = 2 cm
1
1
See lessFind the distance between the points (0, 0) and (36, 15). Can you now find the distance between the two towns A and B discussed in Section 7.2. Q.2
The distance between the two points can be measured using the Distance Formula which is distance formula = √ [(x₂ - x₁)2 + (y₂ - y₁)2] Let the points be A(0, 0) and B(36, 15) Hence, x₁ = 0, y₁ = 0, x₂ = 36, y₂ = 15 We know that the distance between the two points is given by the Distance Formula, =Read more
The distance between the two points can be measured using the Distance Formula which is distance formula
= √ [(x₂ – x₁)2 + (y₂ – y₁)2]
Let the points be A(0, 0) and B(36, 15)
Hence, x₁ = 0, y₁ = 0, x₂ = 36, y₂ = 15
We know that the distance between the two points is given by the Distance Formula,
= √ [(x₂ – x₁)2 + (y₂ – y₁)2]….(1)
= √ (36 – 0)2 + 15 – 0)2
= √ [(1296) + (225)]
= √1521
= 39
Yes, it is possible to find the distance between the given towns A and B.
The positions of towns A & B are given by (0, 0) and (36, 15), hence, as calculated above, the distance between town A and B will be 39km
See lessIn s triangle ABC AD bisects ∠A, AB = 12 cm, AC = 20 cm, and BD = 5 cm, determine CD.
1
D and E are the points on sides BC, CA and AB respectively. of a ΔABC such that AD bisects ∠A, BE bisects ∠B and CF bisects ∠C. If AB = 5 cm, BC = 8 cm, and CA = 4 cm, determine AF, CE, and BD.
A
What is the formula for the length of an arc?
Arc Length Formula (if θ is in degrees) s = 2 π r (θ/360°) Arc Length Formula (if θ is in radians) s = ϴ × r