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...
Find parametric equations for the tangent line at the point (cos(-4pi/6),sin(-4pi/6),-4pi/6) on the curve x=cost, y=sint,z=t
x(t) = _________
y(t) = _________
z(t) = _________
r'(t) = <-sin(t), cos(t), 1>
r'(0) = <0,1,1>
my answer:
x = cos(-4pi/6) + 0t
y = sin(-4pi/6) +1t
z =...
Find the limit:
lim, t->0 < \frac{e^{-5t} - 1}{t}, \frac{t^{13}}{t^{14}-t^{13}}, \frac{6}{5+t}>
answer: <__,__,__>
well, what i did is just plug in zero for t which i get <0,0, 6/5> which is incorrect. am i missing something? or actually it should be <undefined,undefined, 6/5>
Find the domain of the vector functions, r(t), listed below
a.) r(t) = <ln(6t), sqrt(t+14), 1/sqrt(16-t)>
i don't extactly know how to approach this, can someone give me a hint or two
Find an equation of a plane through the point (-1, -2, -3) which is orthogonal to the line x=5+2t,y=-3-5t,z=2-2t
in which the coefficient of x is 2.
______________________________=0
i don't get this problem at all, but here's what i came up with after sitting here at the computer for a...
1+6t=2+4t
t=1/2
and when i plug that 1/2 back in for the x and y equation, i get the wrong answer. I'm not understanding what you are trying to tell me.
Consider the line which passes through the point P(-3, -4, 3), and which is parallel to the line x=1+6t, y=2+4t,z=3+1t
Find the point of intersection of this new line with each of the coordinate planes:
xy-plane:(_,_,_)
yz-plane:(_,_,_)
yz-plane:(_,_,_)
to find xy-plane, I am...
List the first 10 trems of each of these sequences.
i need help with this one:
1.) the sequence whose nth term is the sum of the first n positive integers
1,2,3,6,12,24,48,96...
i'm not really sure if this is correct. what I am doing is just adding the previous numbers together to get...
thanks alot, dividing by 2 worked. i had the -6 in on my paper, but when i typed it on here, everything was messed up including the answer i gave at the end. i was really sleepy awhile i was typing it, thanks agian for the help
Find a vector orthogonal to both <-3,2,0> and to <0,2,2> of the form
<1,_,_> (suppose to fill in the blanks)
well i thought the cross product would do the trick, but i keep getting the wrong answer.
I|2 0| - j |-3 0| + k |-3 2|
|2 2| |0 2| |0 2|
(format is kinda messed up...
A proton is on the x-axis at x= 1.6nm. An electron is on the y-axis at y=0.85nm. Find the net force the two exert on a helium nucleus (charge + 2e) at the orgin.
there's a solution from the book, but i don't really understand it:
k = 9X10^9 N*m^2 and e=1.6*10^-19
Coulomb force of the...
A typical lightning flash delivers about 35 C of negative charge from cloud to ground. How many electrons are involved?
Im not extactly sure how to approach this question. it should be an easy one since it's one of the first problems from the book.
Im thinking i might need to use this...
A child walks due east on the deck of a ship at 1 miles per hour.
The ship is moving north at a speed of 1 miles per hour.
Find the speed and direction of the child relative to the surface of the water.
speed = sqrt(2)
im having trouble finding the direction
The angle of the...
Find the equation of the sphere centered at (-6,-7,-1) with radius 9.
well i got (x+6)^2 + (y+7)^2 + (z+1)^2-9^2 which is correct.
now for the next question:
Give an equation which describes the intersection of this sphere with the plane z=0.
i don't understand how to do the second...
You're speeding at 85 km/h when you notice that you're only 10m behind the car in front of you, which is moving at the legal speed limit of 60 km/h. You slam on your brakes, and your car decelerates at 4.2 m/s^2. Assuming the car in front of you continues at constant speed, will you collide? if...
A Standing Vertical Jump. Basketball player Darrell Griffith is on record as attaining a standing vertical jump of 1.2 m (4 ft). (This means that he moved upward by 1.2 m after his feet left the floor.) Griffith weighed 890 N (200 lb).
1.) Use Newton's laws and the results of part (B) to...
can microsoft word or excel set up hot keys for the greek letters(+-) symbol? what about super/sub scripts? can mircosoft or excel do any of that? I am trying to write my physics lab report and i need to input a lot of symbols. if mircsoft word/excel can't do it, is there any program that can? i...
i got the answer now, i don't know what i was thinking setting A + B =7, i should of set it to 1, because i already took out the 7 in the beginning
7/2(-ln|x-1| + ln|x+1|) is my answer... and it's correct, but cal101.com gets
7/2*(-log(x+1) + log(x-1))
they said that the integral of...
"7\int -7/2(x-1) + 7\int 7/2(x+1)"
when i took out the 7's, i added it for some reason. ok now i just took out the 7/2
49/2 (-ln(x-1) + ln(x+1))
but its still the wrong answer.
k i took the derivative of it, and know it's the wrong answer. but i can't really fix it cause i don't...
yea, but at the end, it should be equal to each other.
when i use maple, i get "-7*arctanh(x)"
and it's correct(submitted online already), maple has always been the best tool, but it doesn't show you step by step on how it does it. it would be awesome if it did. but i would still like to...
i thought it was pretty cool, but after looking at their answer, it was wrong lol. i submit my homework online, so it checks my answer.
"In one of your steps you mistakenly replaced x+1 with x-1"
"7\int -7/2(x-1) + 7\int 7/2(x-1)"
ok changed that to
7\int -7/2(x-1) + 7\int 7/2(x+1)...
i will use "\int" as a integral sign since latex is down.
\int (7)/(x^2-1)*dx
using partial fractions...
took out the 7...
7\int (1)/(x+1)(x-1)
A(x-1) + B(x+1) = 7
if x = 1, B=7/2
if x = -1, A= -7/2
ok it's time to set up my integral function:
7\int -7/2(x-1) + 7\int...
yes, but I am not trying to solve for the mass of the watermelon on earth, that was another question, but i already got the answer. it's 4.99 kg
im trying to solve for the mass on the surface of Io. here's what i done:
F= m*a
49 = m*1.81
m = 27.07kg
that's the mass of Io that i got...
At the surface of Jupiter's moon Io, the acceleration due to gravity is 1.81m/s^2 . A watermelon has a weight of 49.0N at the surface of the earth. In this problem, use 9.81m/s^2 for the acceleration due to gravity on earth
1.) What is its mass on the surface of Io?
2.) What is its...