Answer:
1 ≥ t ≤ 3
Step-by-step explanation:
Given
h(t) = -16t² + 64t + 4
Required
Determine the interval which the bar is at a height greater than or equal to 52ft
This implies that
h(t) ≥ 52
Substitute -16t² + 64t + 4 for h(t)
-16t² + 64t + 4 ≥ 52
Collect like terms
-16t² + 64t + 4 - 52 ≥ 0
-16t² + 64t - 48 ≥ 0
Divide through by 16
-t² + 4t - 3 ≥ 0
Multiply through by -1
t² - 4t + 3 ≤ 0
t² - 3t - t + 3 ≤ 0
t(t - 3) -1(t - 3) ≤ 0
(t - 1)(t - 3) ≤ 0
t - 1 ≤ 0 or t - 3 ≤ 0
t ≤ 1 or t ≤ 3
Rewrite as:
1 ≥ t or t ≤ 3
Combine inequality
1 ≥ t ≤ 3
so every 3 orange picks there are 2 green picks so 6 orange picks leads to 4 green pick and just keep adding to each side. 9 orange picks is 6 green picks, 12 orange picks is 8 green picks. Therefore you add 3 to 12 and get 15 which means 15 orange picks is your answer.
Answer:
No solutions
Step-by-step explanation:
Isolate the absolute value:
|x−1| + 5 = 2
Subtract 5 from both sides:
|x-1| = -3
Since an absolute value can never be equal to a negative number, there are no solutions.
Answer:
x ≤ -15
Step-by-step explanation:
-x / 3 ≥ 5
multiply by 3
-x ≥ 15
add x to both sides and subtract 15 from both sides
-15 ≥ x or x ≤ -15
Answer:
RS ≈ 5.83 units
Step-by-step explanation:
Calculate RS using the distance formula
d = √ (x₂ - x₁ )² + (y₂ - y₁ )²
with (x₁, y₁ ) = R(- 3, 1) and (x₂, y₂ ) = S(2, 4)
RS = 
= 
= 
=
≈ 5.83 ( to 3 significant figures )