<span>Answer: To set up the integral, we divide the upper half of the aquarium into horizontal slices,
and for each slice, let x denote its distance from the top of the tank and ∆x denote
2
its thickness. (We choose horizontal slices because we want each drop of water in a
given slice to be the same distance from the top of the tank.) Using the formulae at
the beginning of this handout, we see that the work taken to pump such a slice out of
the tank is
work for a slice = W
= F · d
= (m · a) · d
= (ρ · V ) · a · d .
Since the length, width and thickness of the slice are given by 2 m, 1 m and ∆x m,
respectively, its volume is 2 · 1 · ∆x m3 = 2∆x m3
. Thus, the equation above becomes
work for a slice ≈
force
z }| {
mass
z }| {
(1000 kg/m
3
)
| {z }
density
(2∆x m
3
)
| {z }
volume
(9.8 m/s
2
)
| {z }
gravity
(x m)
| {z }
distance
= (1000)(9.8)(2)x · ∆x (kg · m/s
2
) · m
= (1000)(9.8)(2)x · ∆x N · m
= (1000)(9.8)(2)x · ∆x J .
Summing over our slices, this is
total work for top half of aquarium ≈
X(1000)(9.8)(2)x · ∆x J ,
where the sum is over the slices in the top half of the aquarium; that is, from distance
x = 0 to x = 1/2. As we refine our slices, this becomes the integral
total work = Z 1/2
0
(1000)(9.8)(2)x dx J
= (1000)(9.8)(2) Z 1/2
0
x dx J
= (1000)(9.8)(2)(1/8) J
= 2450 J .</span>
Mrs. Malone would earn 512 hours of paid vacation time if she works of 81 days
Answer: <em>third from the top</em>
Step-by-step explanation:
<em>The correct answer is third from the top.</em>
<em>Arranging numbers in ascending order: </em>
<em>15 17 17 17 18 18 18 19 19 19 21 21 22 23 24</em>
<em>Let's count how many times each number occurs in this series of numbers.</em>
<em>row of numbers</em>
<em>15 </em>+
<em>16 not</em>
<em>17 </em>+ + +
<em>18 </em>+ + +
<em>19 </em>+ + +
<em>20 not</em>
<em>21 </em>+ +
<em>22 </em>+
<em>23 </em>+
<em>24 </em>+
<em>25 not</em>
Answer:
3.25, I don't know, I'm in like 1st grade
Step-by-step explanation:
(1) The train travels 4 miles per gallon.
(2) The slope of the graph is 
Explanation:
(1) The miles that train travels per gallon is given by
Dividing, we have,
Thus, the train travels 4 miles per gallon.
(2) To determine the slope, let us consider two points from the graph.
The coordinates are 
and 
Thus, substituting the coordinates in the slope formula, we get,
Simplifying, we have,
Thus, the slope of the graph is
