<h3>
Answer: 51 square inches</h3>
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Explanation:
There are a few ways to do this. One way is to divide the figure as shown in the diagram below. I divided it into a rectangle and a triangle. Find the area of the rectangle and triangle, then add up those areas to get the final answer.
A = area of rectangle
A = length*width
A = 7*6
A = 42
B = area of triangle
B = 0.5*base*height
B = 0.5*(6-3)*(13-7)
B = 0.5*3*6
B = 1.5*6
B = 9
C = total area
C = A+B
C = 42+9
C = 51 square inches
Volume is a three-dimensional scalar quantity. The volume of concrete that will have to be poured into the pool deck is 6.0185 cubic yards.
<h3>What is volume?</h3>
A volume is a scalar number that expresses the amount of three-dimensional space enclosed by a closed surface.
Since an inch is equal to 1/12 of a foot. Therefore, the thickness of the pool deck is,
3 inches = 0.25 foot
If a pool deck of 650 square feet is to be laid with concrete 3" thick, then the volume of concrete that will be needed is,
Volume of concrete = 650 ft² × 0.25 ft = 162.5 ft³
Now, one yard is equal to 3 feet, therefore,
1 cubic foot = 1/27 cubic yards
162.5 cubic feet = 6.0185 cubic yards
Hence, the volume of concrete that will have to be poured into the pool deck is 6.0185 cubic yards.
Learn more about Volume:
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Answer:
27/9
Step-by-step explanation:
Let f(x) = p(x)/q(x), where p and q are polynomials and reduced to lowest terms. (If p and q have a common factor, then they contribute removable discontinuities ('holes').)
Write this in cases:
(i) If deg p(x) ≤ deg q(x), then f(x) is a proper rational function, and lim(x→ ±∞) f(x) = constant.
If deg p(x) < deg q(x), then these limits equal 0, thus yielding the horizontal asymptote y = 0.
If deg p(x) = deg q(x), then these limits equal a/b, where a and b are the leading coefficients of p(x) and q(x), respectively. Hence, we have the horizontal asymptote y = a/b.
Note that there are no obliques asymptotes in this case. ------------- (ii) If deg p(x) > deg q(x), then f(x) is an improper rational function.
By long division, we can write f(x) = g(x) + r(x)/q(x), where g(x) and r(x) are polynomials and deg r(x) < deg q(x).
As in (i), note that lim(x→ ±∞) [f(x) - g(x)] = lim(x→ ±∞) r(x)/q(x) = 0. Hence, y = g(x) is an asymptote. (In particular, if deg g(x) = 1, then this is an oblique asymptote.)
This time, note that there are no horizontal asymptotes. ------------------ In summary, the degrees of p(x) and q(x) control which kind of asymptote we have.
I hope this helps!
Answer:a) 1,2,6,24,120
Step-by-step explanation:
The formula for the nth term of the sequence is expressed as
n=(n+1)!/n+1
For the first term, n = 1. Therefore,
(1+1)!/(1+1) = 2!/2 = (2×1)/2 = 1
For the second tern, n = 2. Therefore,
(2+1)!/2+1 = 3! /3 = (3×2×1)/3 = 6/3 = 2
For the third term, n = 3, therefore
(3+1)!/3+1 = 4!/4 =(4×3×2×1)/4 = 6
For the fourth term, n = 4. Therefore
(4+1)!/4+1 = 5!/5 = (5×4×3×2×1)/5 = 24
For the fifth term, n = 5. Therefore
(5+1)!/5+1 = 6!/6 = 6× 5×4×3×2×1)/6 = 120
