Hi May I know how to solve this question with step by step explanation please
1 answer:
Answer:
a = 1, b = - 2
Step-by-step explanation:
The points that lie on the curve and straight line satisfy the corresponding equations.
Substitute the points into their corresponding equations, that is
(1, - 1 ) → - a = 1² + b = 1 + b ( multiply both sides by - 1 )
a = - 1 - b → (1)
(3, 3 ) → =
( cross- multiply )
- 3ab = 6 ( divide both sides by - 3 )
ab = - 2 → (2)
Substitute a = - 1 - b into (2)
(- 1 - b)b = - 2 , distribute left side
- b - b² = - 2 ( multiply through by - 1 )
b² + b = 2 ( subtract 2 from both sides )
b² + b - 2 = 0 ← in standard form
(b + 2)(b - 1) = 0 ← in factored form
Equate each factor to zero and solve for b
b + 2 = 0 ⇒ b = - 2
b - 1 = 0 ⇒ b = 1
Substitute these values into (1) for corresponding values of a
b = - 2 : a = - 1 - (- 2) = - 1 + 2 = 1
b = 1 : a = - 1 - 1 = - 2
Thus a = - 2, b = 1 or a = 1, b = - 2
Given that a > b then a = 1, b = - 2
You might be interested in
The paper would be 112589991 km thick if folded 50 times.
Step-by-step explanation:
Step 1; The sheet is mm thick which equals 0.1 mm. Every time it is folded it doubles in thickness. So if folded once it becomes 0.2 mm thick, if folded thrice it becomes 0.4mm thick.
Thickness if folded once = × 0.1 mm
thickness if folded twice = × 0.1 mm
Thickness if folded thrice = × 0.1 mm.
So if the paper is folded nth fold it would be × 0.1 mm thick.
Step 2; Using the above formula, if the paper is folded 50 times the thickness would be equal to × 0.1 mm = 112,589,990,684,262.4 mm.
1 km is equivalent to mm so 112,589,990,684,262.4 mm = 112,589,990.6842624 km which is rounded off to 112589991 km.