Dakota

Verify by substitution that the given function is a solution of the differential equation.

y'=y+2e^(-x) ; y=e^(x)-e^(-x)

Tried substituting the y=e^(x)-e^(-x) into the differential equation and it gave me back y=e^(x)+e^(-x).

I had to switch my courses and because of this, I missed the first week of class. The first homework is due in a few days. I just need to know how to solve problems like this and I should be good. Please and thank you!

A particle travels along a straight line with a velocity of v=(4t-3t^2)m/s, where t is in seconds. Determine the position of the particle when t=4s. s(position) is 0 when t=0

I don't think this is as easy as plugging in 4 for t and solving...

Switch S in in the figure is closed at time t = 0, to begin charging an initially uncharged capacitor of capacitance C = 16.6 μF through a resistor of resistance R = 23.3 Ω. At what time is the potential across the capacitor equal to that across the resistor?

Recently finished Calculus 3 and got a B-, I just want to get an idea of what I will be getting myself into next fall so I can better prepare.

F=⟨0,3,x2⟩ , hemisphere x2+y2+z2=36, z≥0 , outward-pointing normal

Most likely finding T with respect to u

T with respect to v

and n

Compute the surface integral over the given oriented surface:

F=⟨0,0,e^(y+z)⟩,

boundary of the cube

0≤x,y,z≤2,

outward-pointing normal

∬_S F⋅dS=

5star best answer for CORRECT answer!

Use Green's Theorem to evaluate the line integral ∮_C y^2dx+x^6dy

where C is the boundary of the square −1≤x≤1, −1≤y≤1 oriented counterclockwise.

∮_C y^2dx+x^6dy

Tried to set bounds from 0 to 7 and 0 to 7 integrating vsqrt(4u^2+1)dudv by using x=u and z=v but had no luck... I came out to 14553sqrt33/8 but apparently thats wrong...

Calculate ∬Sf(x,y,z)dS For

y=3−z2, 0≤x,z≤7

f(x,y,z)=z

∬_S f(x,y,z)dS=

Let G be the map G(x, y)=(x+y, y−2x) from the xy-plane to the uv-plane. Let D be the domain

D= { (x, y): 6≤x+y≤6, 6≤y−2x≤12}

Compute ∫∫_D e^(x+y) dA using Change of Variables Formula with the map G^−1.

(Use symbolic notation and fractions where needed.)

Use the Change of Variables Formula to compute ∫∫_D (x+3y) dxdy,

where D is the region bounded by x+2y=4, x+2y=5, y=10, y=10 .

(Use symbolic notation and fractions where needed.)

Let Φ(u,v)=(4u+5v,9u+4v) be a map from the uv-plane to the xy-plane.

Describe the image of the line v=4u under Φ in slope-intercept form.

Use the Divergence Theorem to evaluate the surface integral ∬_S F⋅dS .

F=⟨x^3,8,z^3⟩, S is the sphere x^2+y^2+z^2=49.

∬_S F⋅dS= ?

Use spherical coordinates to calculate the triple integral of f(x, y, z)=y over the region x^2+y^2+z^2≤9, x, y, z≤0.

Use spherical coordinates to calculate the triple integral of f(x, y, z)=√(x^2+y^2+z^2) over the region x^2+y^2+z^2 ≤ 2z.

(Use symbolic notation and fractions where needed.)

∫∫∫_W √(x^2+y^2+z^2) dV=

Please show as many steps as possible!

The surface z=7x−3y can be described in cylindrical coordinates in the form

r=f(θ,z)=

Note: Write theta in your answer wherever θ is appropriate.

Evaluate ∫∫∫Wf(x, y, z) dV for the function f and region W specified.

f(x, y, z)=e^61z; W: x+y+z≤1, x≥0, y≥0, z≥0

∫∫∫_W e^61z dV

Just need the limits and how to get to them. I can integrate it. Thank you!!

Evaluate the integral

∫∫_D e^(x+y)dA

Over the domain D defined by

x≥4, y≥4, x+y≤10

(Use symbolic notation and fractions where needed.)

Tried setting the limits of both dx and dy from top 6 to bottom 4 but that didn't seem to work...

I am a mechanical engineering student currently going for my B.M.E and currently taking University Physics II passing with about a B average, University Physics 1 I got a C- barely passed! In an effort to get done with school as quick as possible I opt to take summer courses. I am currently signed on to take a 6 week Statics course and feel very unsure about this decision. I had to take Calculus II twice and the second time I got a B+ it was also a 6 week summer course so I have a little experience with them. I haven't researched much into Statics and don't really know what it entails? It is a 3 credit course vs UPhy I and II being 5 credit but what I really want to know is what the course is about and how difficult is/was it if you have taken it before? Would taking a 6 week course 3 days a week for Statics likely benefit or hurt me? I work a full time job at night and go to school part time during the day.