Evaluate the line integral \int x^5*z*ds where C is the line segment from (0,3,5) to (4,5,7)
so first thing i did was found the parametric equations
the parametric equations are:
x= 4t
y= 3+2t
z= 5+2t
how do i find out what t is? i totally forgot how to do that and i can't seem to...
Find the volume of the solid enclosed by the paraboloids z= 16(x^2 +y^2) and z=32-16(x^2+y^2)
i'm not sure how i would find the x bounds for this triple integral. here's my work:
16x^2+16y^2 = 32-16x^2+16y^2 => simplifies to y = +- sqrt(1-x^2) (the y-bounds)
z bounds is already given...
Evaluate the triple integral \int \int \int xy*DV where E is the solid
tetrahedon with vertices (0,0,0), (4,0,0),(0,1,0),(0,0,7)
first I'm going to find n:
AB= <-4,1,0>
AC= <-4,0,7>
AB X AC = <7,28,4> = n
so i get this equation: 7(x-4) + 28y + 4z = 0
=> 7x+28y+4z = 28
so the...
Find the volume of the ellipsoid x^2 + y^2 + 10z^2 = 16
solve for z... z=sqrt((16-x^2-y^2)/(10))
z = sqrt((16-r^2)/10)
so to find the volume, my integral looks like this:
latex doesn't seem to be working, so this could look messy...
2*int (from 0-2pi)*int(from 0-1)*...
Using geometry, calculate the volume of the solid under z = sqrt(9- x^2-y^2) and over the circular disk x^2 + y^2 <= (greater than or equal to sign) 9
how extactly would i do this? i have no clue and don't know where to start
Consider the solid that lies above the square (in the xy-plane) R= [0,1] X [01]
and below the elliptic paraboloid z= 64 -x^2 +4xy -4y^2
Estimate the volume by dividing R into 9 equal squares and choosing the sample points to lie in the midpoints of each square.
i'm not sure how you...
chain rule agian - check my work please
w = -xy-5yz+3xz, x = st, y = exp(st), z = t^2
dw/ds(5,-2) = ________________________
here's what i did:
dw/ds = dw/dx*dx/ds + dw/dy*dy/ds + dw/dz*dz/ds
dw/ds = (3z-y)*(t) + (-x-5z)(exp(st)*t) + (3x-5y)(0)
plug in x,y and z...
dw/ds =...
Suppose w = x/y + y/z
x = exp(t), y=2+sin(5t), and z= 2+cos(7t)
A.) Use the chain rule to find dw/dt as a function of x, y, z, and t. Do not rewrite x, y, and z in terms of t, and do not rewrite exp(t) as x. I got this one right, the answer is 1/y*exp(t) +(- x/y^2+1/z)*(5*cos(5t)) +...
Surface Area of a Rectangular = 2xy + 2yh + 2xh
DV = (2y)(dx) + (2h)(dy) + (2x)(dh)
(2)(50)(0.2) + (2)(100)(0.2)+(2)(70)(0.2) = 88 which is also wrong, did i miss something agian?
The dimensions of a closed rectangular box are measured as 70 centimeters, 50 centimeters, and 100 centimeters, respectively, with the error in each measurement at most .2 centimeters. Use differentials to estimate the maximum error in calculating the surface area of the box.
Answer...
If sin (2x+4y+z) = 0 , find the first partial derivatives \frac{dz}{dx} at the point (0,0,0)
A.) \frac{dz}{dx}(0,0,0) = _________________
isnt this saying get the derivative of z, respect to x? I'm just kinda confuse since the variable 'z' is also in the problem.
well i got the...