Marianne owes $56 for tickets to the school play. If each ticket cost $4, how many tickets did she buy?
1 answer:
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Let 
represent the number of bacteria after 
hours.
so
is the number of bacteria after 0/2 = 0 hours
is the number of bacteria after 1/2 hours
is the number of bacteria after 2/2 = 1 hours and so on
so if we list a few terms of this sequence, we have:
so clearly,, the number of bacteria after hours, is equal to 
.
is the number of bacteria after
hours.
Thus, we calculate, which is 
.
Answer: the number of bacteria after 24 hours is.
so
so if we list a few terms of this sequence, we have:
so clearly,
Thus, we calculate
Answer: the number of bacteria after 24 hours is
Answer:
(a) 2.79 seconds after its release the bag will strike the ground.
(b) At a velocity of 73.28 ft/second it will hit the ground.
Step-by-step explanation:
We are given that a balloon, rising vertically with a velocity of 16 feet per second, releases a sandbag at the instant when the balloon is 80 feet above the ground.
Assume the acceleration of the object is a(t) = −32 feet per second.
(a) For finding the time it will take the bag to strike the ground after its release, we will use the following formula;
Here, s = distance of the balloon above the ground = - 80 feet
u = intital velocity = 16 feet per second
a = acceleration of the object = -32 feet per second
t = required time
So,
Now, we will use the quadratic D formula for finding the value of t, i.e;
Here, a = 1, b = -1, and c = -5
Also, D = =
= 21
So,
We will neglect the negative value of t as time can't be negative, so;
= 2.79 ≈ 3 seconds.
Hence, after 3 seconds of its release, the bag will strike the ground.
(b) For finding the velocity at which it hit the ground, we will use the formula;
Here, v = final velocity
So,
v = 16 - 89.28 = -73.28 feet per second.
Hence, the bag will hit the ground at a velocity of -73.28 ft/second.