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
Answer:
8:30 PM
Step-by-step explanation:
Let's say that x is minutes since 6:20 PM, and y is position in miles.
Since Jonathan drives at a constant rate, the position vs time graph is linear. Two points on the line are (0, 75) and (20, 85). The slope of the line is:
m = Δy / Δx
m = (85 − 75) / (20 − 0)
m = ½
So the equation of the line is:
y = ½ x + 75
We want to find x when y is 140.
140 = ½ x + 75
65 = ½ x
x = 130
So 130 minutes after 6:20 PM is when Jonathan's position will be 140 miles. 130 minutes is 2 hours and 10 minutes. So the time will be 8:30 PM.
Answer:
in a region with a letter
Step-by-step explanation:
For a certainty, then probability is 1.
That means sum of probability of all events in the sample space.
This means P(A)+P(B)+P(C)+P(D)=1
This is equivalent to:
P(A or B or C or D)=1
Hence for certainty, the region must be:
A or B or C or D
So the correct answer is in a region with a letter.
Answer:
r can be any number -1.5 to 9.4999999
Step-by-step explanation:
6 / (2/3)
= 6 * 3/2
= 18/2
= 9
answer
there are 9 (2/3 cup) servings in 6 cups of yogurt
