1). Simplify: |8 – 3|
2 answers:
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The <em><u>correct answer</u></em> is:
Explanation:
An exponential function is of the form
, where a is the initial population, b is 1 plus the amount of yearly change, and x is the number of years.
For our problem, a, the initial population, is 1500.
The yearly change is 6.3%; 6.3% = 6.3/100 = 0.063. Since it is decreasing, this is negative; 1+(-0.063) = 0.937.
We use t as the number of years.
This gives us
Answer:
Identity property of multiplication
Step-by-step explanation:
From step 5:
Here, to solve for x so that the variable x stands alone, Alberto uses the identity property of multiplication, which justifies what he has in step 6.
Step 6:
According to the identity property of multiplication, any value you multiply by 1 gives you that same value.
Therefore, 1x = 1 × x = x.
The variable x multiplied by 1 will give you x.
Answer:
Exercise (a)
The work done in pulling the rope to the top of the building is 750 lb·ft
Exercise (b)
The work done in pulling half the rope to the top of the building is 562.5 lb·ft
Step-by-step explanation:
Exercise (a)
The given parameters of the rope are;
The length of the rope = 50 ft.
The weight of the rope = 0.6 lb/ft.
The height of the building = 120 ft.
We have;
The work done in pulling a piece of the upper portion, ΔW₁ is given as follows;
ΔW₁ = 0.6Δx·x
The work done for the second half, ΔW₂, is given as follows;
ΔW₂ = 0.6Δx·x + 25×0.6 × 25 = 0.6Δx·x + 375
The total work done, W = W₁ + W₂ = 0.6Δx·x + 0.6Δx·x + 375
∴ We have;
W =
The work done in pulling the rope to the top of the building, W = 750 lb·ft
Exercise (b)
The work done in pulling half the rope is given by W₂ as follows;
The work done in pulling half the rope, W₂ = 562.5 lb·ft