how is the relationship between the central angle theta and the depth of an amount of liquid in a cylinder tank on its side h= r(1-cos(theta/2)?

how is the relationship between the central angle theta and the depth of an amount of liquid in a cylinder tank on its side h= r(1-cos(theta/2)?

dy/dx= (2cx-x^-1)/((y^-1)-2cy) the c's are constants of integration. I am trying to find a differential equation for the family of curves: ln(xy)=c(x^2+y^2) and can't figure out...

integrate √[ (1+y)/(1-y) ]dy from -1 to 0 the answer is: (pi/2) -1

2xy^2 + 4 = 2(3-x^2y)y' ; y(-1) = 8 Note: The "y" is not part of the exponent in "2(3-x^2y)" My answer to this problem is "6y - x^2y^2 = -16"...

A road running north to south crosses a road going east to west at the point P. Car A is driving north along the first road, and an airplane is flying east above the second road. At a particular time...

y=x^(1/2)+cx I can't seem to get the right answer :(

I need help with this question

find f'(a)

find f'(a)=

the parent is f(x) = log x

Answer in ____ ft/s

log base(ab) [2log base(ab)(√a)-1/2log base(ab)√ab(b)]=(log base(ab) (a))^2-(log base(ab)(b))^2 I do not know

y=(x3+1)(x4+7)(x5+8)4

y=x(x5+4)/√x+4

complex numbers in cartesion form

I have a problem on limits. The graph shows two very different equations approaching the same point, but at that point (x=4) there is a hole. Below the hole there is a point at (4,2). What is the...

Joe decides to construct a new toy. He takes a solid fuel rocket engine from his model rocket kit and a flat bed rail car from his train set . He straps the engine to the back of the rail car. He...

The plane of equation x + y = 1 intersects the cone of equation z = 4 − √((x^2)+(y^2)) in a parabola. Verify that the point of coordinates (3/7, 4/7, 23/7) is...

Find the length s of the arc of a circle of radius 48 centimeters subtended by the central angle one eighth radian 1/8 radian.

y'=(x^2-y^2)xy, with y(1)=2