True of false: 1+1 has the same answer as 1x1
2 answers:
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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.
(9)^4 × (27)^3 × (81)^2 / (3)^24 = 3.
Explanation:
- All the numbers in the numerator i.e. 9, 27, 81 are multiples of 3.
- 9 = 3 × 3 = 3², 27 = 3 × 3 × 3 = 3³, 81 = 3 × 3 × 3 × 3 =
.
= (3^2)^4, 27³ = (3^3)^3, 81^2 = (3^4)^2.
- According to the power rule, (a^x)^y = a^xy.
- So the given numbers can be written as follows
- According to the product rule, (a^x) × (a^y) = a^xy.
- So the numerator can be written as
- So the fraction becomes 3^25 / 3^24 = 3 × 3^24 / 3^24 = 3.