A)24 boards/1 * 47.5 inch/boards * 1 ft/12in = 95 ft.
according to dimensional analysis the answer is 95 ft.
b) 95/8 is approximately 12 so 12 boards are needed.
Answer:
V=3.098 yd³
Step-by-step explanation:
To answer this question we need to work with formula of the Volume of rectangular prism, the patio. Once it is required 1 inch deep. Some relations will be useful.
As 1 yard = 1 feet/3
1 yard = 1 inch/36
1 feet=12 inches
a) 23 feet 9 inches
23 ft 9''=23 +9/12=23.75 ft
b)10 feet 1 inch
10 feet 1" = 10ft + 1/12=10.083 ft
c)4 inches: 4/12 =0.33
V= w.l.h
V=23.75*10.083*0.33=79.025 ft³
Converting from cubic yard to cubic feet:
V≈79.025 : 27 yd³=2.926 yd³
Considering the possible spillage due to uneven base. ( adding 5%of V)
V≈ 2.92+0.05*(2.92)=3.098 yd³
The slope of the tangent line to the curve at (8, 2) is given by the derivative 
at that point. By the chain rule,
Differentiate the given parametric equations with respect to 
:
Then
We have 
and 
when 
, so the slope at the given point is 
.
The normal line to the same point is perpendicular to the tangent line, so its slope is +4. Then using the point-slope formula for a line, the normal line has equation
Alternatively, we can eliminate the parameter and express 
explicitly in terms of 
:
Then the slope of the tangent line is
At 
, the slope is again 
, so the normal has slope +4, and so on.
