Lv 16 points

# Nigel Jefferds

• ### Derivative Question?

I need help taking the derivative of a function that includes the dot product of vectors. r is the position, v is velocity, and a is acceleration. An arrow denotes a vector. A period ( . ) denotes a dot product. Please help me solve this!

d/dt [ (r⃗^2 . v⃗) - (r⃗ . v⃗) r⃗ ]

• ### Volume Question?

Find the volume of the solid enclosed by the paraboloids

z=1(x^2+y^2) and z=8−1(x^2+y^2)

• ### Cylindrical Coordinates Question?

Use cylindrical coordinates to calculate :

∫∫∫ x^2+y^2dV

W

W: x^2+y^2≤36, 0≤z≤18

• ### Calculus Problem?

Find the average value of

f(x,y)=7e^y(sqrt(x+e^y)) over the rectangle R=[0,6]×[0,5].

• ### Calculus Question about Centroids?

Find the centroid of the region bounded by:

y=5x^2+3x, y=0, x=0, and x=5

x=

y=

• ### Calculus Question about volume?

A cylindrical drill with radius 2 is used to bore a hole through the center of a sphere of radius 5. Find the volume of the ring shaped solid that remains.

• ### Hard Double Integration Question?

Find the volume of the solid bounded by the planes x = 0, y = 0, z = 0, and x + y + z = 9.

• ### Double Integral Question?

8 64

∫ ∫ ysin(x^2)dxdy

0 y^2

I tried to format it the best I could. The integral is from 0 to 8 (dy) and the second integral is y^2 to 64 (dx).

• ### Trig Substitution Question?

For each of the indefinite integrals below, select which of the following trig substitutions would be most helpful in evaluating the integral.

A. x=5tanθ

B. x=5sinθ

C. x=5secθ

1. ∫(x^2)/sqrt(25+x^2) dx

2. ∫sqrt(x^2−25) dx

3. ∫(x^2)/sqrt(25−x^2) dx

4. ∫(x^2−25)^(5/2) dx

5. ∫1/(25−x^2)^(3/2) dx

• ### Double Integral Question?

3 e^3

∫ ∫ x/ln(x) dxdy

0 e^y

I tried to format it the best I could. I really cannot figure out this double integral! I will give 10 points out to whoever can help me here.

• ### Calculus Question About Volumes?

Using geometry, calculate the volume of the solid under z=sqrt(81−x^2-y^2) and over the circular disk x^2+y^2≤81.

• ### Partial Derivatives Question?

The voltage, V (in volts), across a circuit is given by Ohm's law: V=IR, where I is the current (in amps) flowing through the circuit and R is the resistance (in ohms). If we place two circuits, with resistance R1 and R2, in parallel, then their combined resistance, R, is given by:

1/R=1/R1+1/R2.

Suppose the current is 3 amps and increasing at 0.03 amps/sec and

R1 is 3 ohms and increasing at 0.4 ohms/sec, while R2is 3 ohms and decreasing at 0.2 ohms/sec. Calculate the rate at which the voltage is changing.

• ### Calculus Question on Partial Derivatives?

Calculate the derivative using implicit differentiation:

∂w/∂z = ?

x^6w+w^4+wz^2+7yz=0

• ### Calculus Question on Partial Derivatives?

If z=sin(x^2+y^2),x=vcos(u),y=vsin(u), find ∂z/∂u and ∂z/∂v. Simplify your answers as much as possible. The variables are restricted to domains on which the functions are defined.

• ### Calculus Question? (Really need help)?

The voltage, V (in volts), across a circuit is given by Ohm's law: V=IR, where I is the current (in amps) flowing through the circuit and R is the resistance (in ohms). If we place two circuits, with resistance R1 and R2, in parallel, then their combined resistance, R, is given by:

1/R=1/R1+1/R2.

Suppose the current is 3 amps and increasing at 0.03 amps/sec and

R1 is 3 ohms and increasing at 0.4 ohms/sec, while R2is 3 ohms and decreasing at 0.2 ohms/sec. Calculate the rate at which the voltage is changing.

• ### Calculus Question About Intervals?

Find all the values of x such that the given series would converge.

∑ (((−1)^n)(10^n)(x^n))/(√n+2)

n=1

The series is convergent from x= to x=

• ### Calculus Series Question?

How many terms of the series do we need to add in order to find the sum to the indicated accuracy? (Your answer must be the smallest possible integer.)

∑ ((-1)^(n−1))(8/(n^4)), |error|<0.0006

n=1

• ### Polar Equation Question?

How do you convert (xy)^6=9 into a polar equation with r and theta?