Please answer these two 10th grade math Questions...
Answers
Question : Find the valuenof k in the system of equations
• kx + 3y = k + 3
• 12x + ky = k
Solution : Bringing equations in form of ax + by + c,
→ kx + 3y - (k + 3) = 0
→ 12x + ky - k = 0
When two equations have no solution then it means that,
→ a₁/a₂ = b₁/b₂
→ k/12 = 3/k
→ k² = 3 × 12
→ k = 6
Answer : Value of k is 6.
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Question : A boat take 5 hrs to go 300 km downstream. It takes time to go 150 km upstream.
• Calculate speed of boat in still water.
• Calculate speed of stream.
Solution : Let speed of boat be x and stream be y.
Then, Time = Distance/Speed
→ 300/(x + y) = 5
→ 150/(x - y) = 5
Let 1/(x + y) be u and 1/(x - y) be v.
→ 300u = 5
→ u = 5/300 = 1/60
→,150v = 5
→ v = 5/150 = 1/30
→ Therefore x + y = 60 and x - y = 30
On adding both equations weget,
→ x = 45 and y = 15
Hence speed of boat is 45 km/h in still water and speed of stream is 15 km/h.
I have given the answer to the first question along with the second one...
Hope it helps!
