Answer:
Step-by-step explanation:
The work is define as the integral of the force times distance. So we have:
Now, we can write the force in terms of density.
V is the volume (V=2*1*1=2 m³)
So the work will be:
The limit of integration is between 0 and 0.5 because we want to pump half of the water out of the aquarium.
I hope it helps you!
The piece-wise linear functions can be written as follows:
A linear function is modeled by:
y = mx + b
In which:
For x equal or less than -2, the line passes through (-3,-3) and (-2,-2), hence the rule is:
.
For x greater than -2 up to 1, the y-intercept is of -7, and the line also passes through (1,-8), hence the rule is:
.
For x greater than 1, the function goes through (2,-5) and (3,-3), hence the slope is:
m = (-3 - (-5))(3 - 2) = 2.
The rule is:
y = 2x + b.
When x = 2, y = -5, hence:
-5 = 2(2) + b
b = -9.
Hence:
.
More can be learned about linear functions at brainly.com/question/24808124
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Answer:
Q7. 11.3 inches (3 s.f.)
Q8. 96.2 ft
Q9. 36.4cm
Step-by-step explanation:
Q7. Please see attached picture for full solution.
Q8. Let the length of a side of the square be x ft.
Applying Pythagoras' Theorem,
Thus, the perimeter of the square is
Q9. Equilateral triangles have 3 equal sides and each interior angle is 60°.
Since the perimeter of the equilateral triangle is 126cm,
length of each side= 126÷3 = 42 cm
The green line drawn in picture 3 is the altitude of the triangle.
Let the altitude of the triangle be x cm.
sin 60°=
(to 3 s.f.)
Therefore, the length of the altitude of the triangle is 36.4cm.
