Simplified answer,, -12v^2+2504v+2095
Answer:
The value of double derivative at x=4.834 is negative, therefore the trough have a maximum volume at x=4.834 inches.
Step-by-step explanation:
The dimensions of given metal strip are
Length = 160 inch
Width = 20 inch
Let the side bend x inch from each sides to make a open box.
Dimensions of the box are
Length = 160-2x inch
Breadth = 20-2x inch
Height = x inch
The volume of a cuboid is
Volume of box is
Differentiate with respect to x.
Equate V'(x)=0, to find the critical points.
Using quadratic formula,
The critical values are
Differentiate V'(x) with respect to x.
The value of double derivative at critical points are
Since the value of double derivative at x=4.834 is negative, therefore the trough have a maximum volume at x=4.834 inches.
F(x)=(2/3)x^1.5
The centroid position along the x-axis can be obtained by
integrating the function * x to get the moment about the y-axis,
then divide by the area of the graph,
all between x=0 to x=3.5m.
Expressed mathematically,
x_bar=(∫f(x)*x dx )/(∫ f(x) dx limits are between x=0 and x=3.5m
=15.278 m^3 / 6.1113 m^2
=2.500 m
Answer:
x = - 2
Step-by-step explanation:
The equation of a circle in standard form is
(x - h)² + (y - k)² = r²
where (h, k) are the coordinates of the centre and r is the radius
To obtain this form use the method of completing the square
Given
x² + y² + 4x - 6y = b ( collect x and y terms together )
x² + 4x + y² - 6y = b
add ( half the coefficient of x/ y terms )² to both sides
x² + 2(2)x + 4 + y² + 2(- 3)y + 9 = b + 4 + 9
(x + 2)² + (y - 3)² = b + 13 ← in standard form
with (h, k) = (- 2, 3)
Thus x- coordinate of centre is x = - 2