The length (L) of the rectangle can be written as a function of the width (W)
:
Now since we know Area = Width*Length, we can write the area as a function of the width:
Distributing the W inside the parentheses we have:
We know the area is 54 ft^2, so we can rewrite it as:
Now solve for W by factoring (or by applying the quadratic formula):
Factor out a common 2W from the first two terms and a 9 from the last two terms:
Regroup the terms to get our fully factored equation:
This gives us the roots W = 6 and W = -9/2, but width can't be negative so we have width = 6 ft. Then remember that the length L = 2W - 3, so our length is:
So now we know that our rectangle is 9 feet long and 6 feet wide.
1 km = 0.621371 miles
5 km = 5 x 0.621371 = 3.106855 miles
1 mile = 5,280 feet
3.106855 miles x 5,280 = 16,404.1944 feet
1 foot = 12 inches
16,404.1944 feet x 12 = 196,850.3328 inches
Answer:
$ 3051
Step-by-step explanation:
Original cost = $ 1000
Marked up Price = Original cost + 170% of 1000
= 1000 + 1.7 * 1000
= 1000 + 1700
= $ 2700
Sales tax = 13% of 2700
= 0.13 * 2700
= 351
Total cost paid by Bernie = 2700 + 351 = $ 3051
Segment 0-A: accelerating
Segment A-B: constant speed
Segment B-C: decelerating
Segment C-D: at rest
Segment D-E: accelerating
Segment E-F: constant speed
Answer:
32π is the volume of the larger sphere
Step-by-step explanation:
The volume of a sphere is V = 4/3πr³. The smaller sphere is V = 4π. This means r³ divided by 3 was 1. So r³ = 3. For the larger sphere, substitute r = 2r into the volume formula.
V = 4/3πr³
V = 4/3π(2r)³
V = 4/3π8r³
We know from the previous problem that r³ = 3.
So the volume formula simplifies to V = 4π(8) = 32π