<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>
Answer:
i will say 12 i think so
Step-by-step explanation:
Answer:
a. 1 inch = 3 feet
b. 1 inch
Step-by-step explanation:
In the figure attached the drawing of the bench is shown correctly.
a.
The drawing shows that the width of the bench is 2 inches. To get the scale we need to divide actual width by drawing width, in mathematical terms:
scale = 6 feet/2 inches = 3 feet/inch
b.
If actual height is 3 ft and every inch represents 3 feet, then, the height of the scale drawing is 1 inch
Answer:
<em> y = 4.25x</em>
Step-by-step explanation:
Given that:
After 2 week he has used 8 1/2 cups of dog food after 5 week he has used 21 1/4 cups, we can write this in coordinate form (x, y) where;
y is the amount of dog food
x is the time in weeks
The coordinates are (2, 8 1/2) and (5, 21 1/4)
get the slope m:
m = y2-y1/x2-x1
m = (21 1/4 - 8 1/2)/5-2
m = (85/4-17/2)/3
m = (85-34/4)/3
m = 51/12
m = 4.25
Get the intercept c:
Substitute any of the points say (2, 17/2) and m = 51/12 into the equation
y = mx+c
17/2 = 51/12(2) + c
17/2 = 51/6 + c
c = 17/2 - 51/6
c = 51-51/6
c = 0
Get the required equation:
substitute m - 4.25 and c = 0 into y = mx+c
y = 4.25x + 0
<em>Hence the required equation is y = 4.25x</em>
<em></em>
Answer: The similar figures are 1,4,6. The figure 2 and 5 have different shape. The figure 3 have different ratio of side lengths.
Explanation:
The given figure is a rectangle with length 6 yd and width 2 yd.
The figure 2 shows a triangle and figure 5 shows a parallelogram, therefore the figure 2 and 5 have different shape.
Two figure are called same if their corresponding sides have same proportion.
The figure 1 and 4 have two sides having length 2 yd and 6 yd, So, the figure 1 and 4 shows the similar figure.
The figure 6 have sides 4 and 12 which is twice of side length of given figure, therefore the sides increased by same proportion 2.
Thus, the figure 1,4,6 shows the figure similar to given figure.
In figure 3 the length is 6 and width is 3. The length is same but the width is different.
Therefore the figure 3 have different ratio of side lengths.