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Answer:
The maximum height it reaches is 20 meters
The time taken by it to reach the height is 2 seconds
Step-by-step explanation:
The formula of the height of the stone is h = u t - g t², where
- t is the time to reach the height h
- u is the initial velocity
- g is the acceleration of gravity
∵ A stone is thrown vertically upwards with an initial velocity of 20 m/s
∴ u = 20 m/s
∵ g = 10 m/s²
→ Substitute them in the equation above
∴ h(t) = 20t - (10) t²
∴ h(t) = 20t - 5t²
→ Arrange the terms of the right side according to the greatest power of t
∴ h(t) = -5t² + 20t
To find the maximum height and the time of it find the vertex of the quadratic function (m, k), where m = and k is the value of h at t = m, a is the coefficient of t² and b is the coefficient of t
∵ The coefficient of t² is -5
∴ a = -5
∵ The coefficient of t is 20
∴ b = 20
→ Use them to find h
∵ m = =
= h
∴ m = 2
→ Substitute it in the equation above to find k
∵ h(m) = k
∵ k = -5(2)² + 20(2)
∴ k = -5(4) + 40
∴ k = -20 + 40
∴ k = 20
∴ The coordinate of the vertex of the function are (2, 20)
→ m represents the time of the maximum height and k represents
the maximum height
∴ The maximum height it reaches is 20 meters
∴ The time taken by it to reach the height is 2 seconds
Answer:
1). Option (b)
2). Option (d)
3). Option (d)
Step-by-step explanation:
Question (1)
For Pythagoras triplet,
(Largest number)² = (Number 1)² + (Number 2)²
a). 5² = 5² + 2²
25 = 25 + 4
25 = 29
Not True.
b). 5² = 3² + 4²
25 = 9 + 16
25 = 25
True.
c). 10² = 1² + 5²
100 = 1 + 25
100 = 26
Not true.
d). 2² = 2²+ 2²
4 = 4 + 4
4 = 8
Not true.
Therefore, Option (b) is correct.
Question (2)
1 - =
=
=
Therefore, Option (d) is the answer.
Question (3)
Property of triangle → Sum of lengths of two sides of a triangle should be greater than the measure of third side.
a). 6 + 3 > 2 ⇒ 9 > 2 [True]
6 + 2 > 3 ⇒ 8 > 3 [True]
2 + 3 > 6 ⇒ 5 > 6 [False]
Triangle is not possible.
b). 2 + 8 > 3 → 10 > 3 [True]
8 + 3 > 2 → 11 > 2 [True]
2 + 3 > 8 → 5 > 8 [False]
Triangle is not possible.
c). 5.5 + 2.5 > 2.5 → 8 > 2.5 [True]
5.5 + 2.5 > 2.5 → 8 > 2.5 [True]
2.5 + 2.5 > 5.5 → 5 > 5.5 [False]
Triangle is not possible.
d). 3 + 6 > 7 → 9 > 7 [True]
3 + 7 > 6 → 10 > 6 [True]
7 + 6 > 3 → 13 > 3 [True]
These are the sides of a triangle.
Therefore, Option D is the answer.