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# Thunee Man Naidoo

• ### Should I do push ups with tricep pain?

I just got back into gyming and did my first arms day after about a year or so. It's been 2 days and my triceps still hurt. Should I do push ups today or will the strain on my triceps overwork my muscles and negate the work I did on arms day.

1 AnswerDiet & Fitness5 years ago
• ### Friction question (determining if a system will move, will one block slide over another)?

Two blocks mA =10kg and mB = 20kg are stationary on a flat surface, block A on top of block B, when a force F = 220N is applied to block B. The coefficients of static and kinetic friction are 1/3 and 1/4 respectively.

a)Show that the system will start moving immediately

b)Determine whether blocks A and B will move together as a unit or whether block A will slide over block B. Find the accelerations of both blocks. (answers given as : A will slide over B, acceleration of A =2.5m/s^2 and acceleration of B =6m/s^2)

My working:

a) For block A

Fy = NA -mA(g) = 0 (assume equilibrium)

Fx = f (between A and B) =NA(coefficient of friction)

For block B

Fy = NB - NA -mB(g) - mA(g) =0

Fx = F - f(between A and B) - f (between B and ground) =0

f (between B and ground) = NB (coefficient of static friction)

NA = 100 (from eqn for Fy of block A)

NB = 100 + 200+100 =400

f = 400(1/3)

=133.3N

which is less than 220N given therefore the system will move

Now I'm not sure if my working is correct, if it isn't could you please explain the right method to get the answer. Also I'm not sure at all at how to go about b) so if anyone can help it'd be really appreciated :)

• ### Volume of a solid (by integrating the area)?

Question given: Let R be the region bounded by the ellipse of x^2/12 + y^2/16 = 1

and the lines of x=1 and x=3. If a solid has R as it's base and cross sections perpendicular to the x-axis yield triangles being where 1/x is the distance of the cross-section from the origin. Find the volume of the solid:

My working:

Area = 1/2 * 2y *h

y^2/16 =1 - x^2/12

y^2 = 16 - 16x^2/12

y = sqrt(16 - 16x^2/12)

Therefore Area = 1/2 * 2 sqrt(16 - 16x^2/12) *1/x

= sqrt(16 - 16x^2/12) *1/x

Therefore Volume = the integral of this area on the interval of 1 and 3

My question is: Is my working right so far? if so how would I go about integrating this?

Any help is greatly appreciated :)

Mathematics7 years ago
• ### Volume of a solid (by integrating the area)?

Question given: Let R be the region bounded by the ellipse of x^2/12 + y^2/16 = 1

and the lines of x=1 and x=3. If a solid has R as it's base and cross sections perpendicular to the x-axis yield triangles being where 1/x is the distance of the cross-section from the origin. Find the volume of the solid:

My working:

Area = 1/2 * 2y *h

y^2/16 =1 - x^2/12

y^2 = 16 - 16x^2/12

y = sqrt(16 - 16x^2/12)

Therefore Area = 1/2 * 2 sqrt(16 - 16x^2/12) *1/x

= sqrt(16 - 16x^2/12) *1/x

Therefore Volume = the integral of this area on the interval of 1 and 3

My question is: Is my working right so far? if so how would I go about integrating this?

Any help is greatly appreciated :)

• ### Evaluate the integral (confirm/complete my working)?

The integral given is that of 1/(x^2-9) dx on the interval of 4 and infinity (this is an improper integral but that's not the part I'm having trouble with, so we'll just ignore that for now)

My working:

let x=3sect

therefore dx = 3sect*tant

Sub back into integral you get

3sect*tant/9sect^2-9

= 3sect*tant/9(sect^2 -1)

= 3sect*tant/9tant^2

take out the constants

= sect*tant/tant^2

=sect/tant (I haven't written them but assume the constants are outside the integral)

= 1/cost * cost/sint

= 1/3 (the integral of 1/sint) (subbed back in the constants)

My question is: Is my working correct so far? and if so how would I go on from here?

The reason why I doubt my working is because the question is only for 3 marks and it seems like quite a bit of working for so few points

Of course if my working is correct there's no other choice but to soldier on

Any help is greatly appreciated :)

• ### Volume of a solid (by integrating the area)?

Question given: Let R be the region bounded by the ellipse of x^2/12 + y^2/16 = 1

and the lines of x=1 and x=3. If a solid has R as it's base and cross sections perpendicular to the x-axis yield triangles being where 1/x is the distance of the cross-section from the origin. Find the volume of the solid:

My working:

Area = 1/2 * 2y *h

y^2/16 =1 - x^2/12

y^2 = 16 - 16x^2/12

y = sqrt(16 - 16x^2/12)

Therefore Area = 1/2 * 2 sqrt(16 - 16x^2/12) *1/x

= sqrt(16 - 16x^2/12) *1/x

Therefore Volume = the integral of this area on the interval of 1 and 3

My question is: Is my working right so far? if so how would I go about integrating this?

Any help is greatly appreciated :)

• ### Partial Fractions (please confirm/complete my working)?

The question given is: Evaluate the integral of x^3/(x^2 +6x +10)^2 using partial fractions.

My working so far:

(Ax + B)/(x^2 +6x +10) + (Cx+D)/(x^2+6x+10)^2 = x^3/(x^2 +6x +10)^2

Therefore: (Ax + B)(x^2 +6x +10) + (Cx+D)(1) = x^3

Therefore we get eqns:

Ax^3 = x^3

6A + B = 0

10A + 6B = 0

10B + D = 0

Therefore:

A = 1

B = -6A = -6

C = -10A -6B = -10 +36 =26

D = -10B = 60

And we get eqns:

The integral of (x-6)/(x^2 +6x +10) + the integral of (26x +60)/(x^2+6x+10)^2

I know next we just have to integrate but I'm sure how to do that for these terms. If anyone could check (and possibly correct) and finish my working it'd be greatly appreciated :)

• ### Partial Fractions integration (please confirm/ complete my working)?

The question given is: Evaluate the integral of x^3/(x^2 +6x +10)^2 using partial fractions.

My working so far:

(Ax + B)/(x^2 +6x +10) + (Cx+D)/(x^2+6x+10)^2 = x^3/(x^2 +6x +10)^2

Therefore: (Ax + B)(x^2 +6x +10) + (Cx+D)(1) = x^3

Therefore we get eqns:

Ax^3 = x^3

6A + B = 0

10A + 6B = 0

10B + D = 0

Therefore:

A = 1

B = -6A = -6

C = -10A -6B = -10 +36 =26

D = -10B = 60

And we get eqns:

The integral of (x-6)/(x^2 +6x +10) + the integral of (26x +60)/(x^2+6x+10)^2

I know next we just have to integrate but I'm sure how to do that for these terms. If anyone could check (and possibly correct) and finish my working it'd be greatly appreciated :)

• ### Parametric curvs: why does the interval change?

The parametric curve given is formed by the eqns x=t-1 and y=ln(t) on the interval of tE[1,2].

The question given is: write the curve in terms of x and y only.

The model answer gives the answer of t=x+1 and y=ln(x+1) on the interval of xE[0,1]

My question is why does the interval change when we write the eqns in terms of x and y?

• ### Components of forces question?

Hi :) I'm having some trouble with this problem in my textbook and any help would be greatly appreciated :)

A particle with charge 9.50×10−8C is moving in a region where there is a uniform magnetic field of 0.700T in the +x-direction. At a particular instant of time the velocity of the particle has components vx = −1.68×104m/s , vy = −3.10×104m/s , vz = 5.80×104m/s.

a) What is the x-component of the force on the particle at this time?

b) What is the y-component of the force on the particle at this time?

c) What is the z-component of the force on the particle at this time?

Like I said, I'd really value any help :)

• ### Weakest possible magnitude?

A straight 15.0-g wire that is 2.00 m long carries a current of 8.00 A. This wire is aligned horizontally along the west-east direction with the current going from west to east. You want to support the wire against gravity using the weakest possible uniform external magnetic field.

a) Which way should the magnetic field point?

b)What is the magnitude of the weakest possible magnetic field you could use?

I've already worked out that the magnetic field should point from south to north for a) but am having trouble working out the magnitude for b). Any help is greatly appreciated :)

• ### Energy Density (Capacitance Question)?

An air-filled capacitor is formed from two long conducting cylindrical shells that are coaxial and have radii of 32 mm and 83 mm. The electric potential of the inner conductor with respect to the outer conductor is -828 V (k = 1/4πε 0 = 8.99 × 109 N · m2/C2) The maximum energy density of the capacitor is closest to:

a) 5.4×10−4 J/m3.

b) 1.2×10−4 J/m3.

c) 1.1×10−3 J/m3.

d) 5.4×10−3 J/m3.

e) 1.0×10−3 J/m3.

Any help is greatly appreciated :)

• ### Capacitance Question?

Two thin-walled concentric conducting spheres of radii 5.0 cm and 10 cm have a potential difference of 100 V between them. (k = 1/4πε0 = 8.99 × 109 N · m2/C2)

a) What is the capacitance of this combination?

b) What is the charge carried by each sphere?

• ### Calculating Potential Energy in a Capacitor?

A cylindrical capacitor is made of two thin-walled concentric cylinders. The inner cylinder has radius 7mm , and the outer one a radius 10mm . The common length of the cylinders is 155m . What is the potential energy stored in this capacitor when a potential difference 4V is applied between the inner and outer cylinder?

Options Given Are:

a) 1.7×10−6J

b) 1.9×10−7J

c) 3.1×10−8J

d) 2.2×10−7J

e) 4.8×10−8J

I tried using the eqn C = ε0*A/d to find capacitance then use U = 1/2*C*V^2 to find potential energy but I really don't know how to calc A between the two cylinders.

Any help is greatly appreciated :)

P.S: If my method above is wrong please correct me and show the right way to work out this problem

• ### Calculating capacitance (when plate diameter and separation are doubled)?

An ideal air-filled parallel-plate capacitor has round plates and carries a fixed amount of equal but opposite charge on its plates. All the geometric parameters of the capacitor (plate diameter and plate separation) are now DOUBLED. If the original capacitance was C0, what is the new capacitance?

Options given are:

a) C0/2

b) C0

c) 4C0

d) C0/4

e) 2C0

Any help is greatly appreciated :)

• ### Evaluate the integral (inverse substitution)?

Evaluate the integral of x^2 dx/(-x^2+2x+2)^(3/2)

To type all my working would be quite difficult for you to read as well as for me to type so please take the time to confirm/correct my working here as well as complete it (I've posted a picture):

As you can see both the bottom and top have a sqrt(3cos^(theta)) which hopefully means I'm on the right track however I don't know where to go from there.

Also, I posted this question a couple days ago and got quite a few different answers. All of them were really complicated and non corresponded with another so I couldn't deduce which was right. The method I used in my working is the same Salman Khan from KhanAcademy used in his videos on the subject and seemed much simpler compared to what others gave me.

Any help would be greatly appreciated :)

For interest sake here's a link to when I previously posted the question: http://answers.yahoo.com/question/index;_ylt=AjlOv...

The question is evaluate the improper integral: (e^(-1/x))/x^2 dx on the interval -1 and 0

however I think to type out my working would be quite complicated for me to type and for you to read. So if you can please follow the link to a pic of my working and confirm/correct my working

Any help is greatly appreciated :)

Please not I posted the same question earlier except I said that the question was e^(1/x)/x^2 by mistake (I left out the negative sign). Please ignore that one but thanks to Ray for answering that question

The question is evaluate the improper integral: (e^(1/x))/x^2 dx on the interval -1 and 0

however I think to type out my working would be quite complicated for me to type and for you to read. So if you can please follow the link to a pic of my working and confirm/correct my working

Any help is greatly appreciated :)

• ### Evaluating improper integrals (please confirm my working and/or complete the question)?

Find the integral of (2x/(x^2-16)) - (1/(x-4)) dx on the interval of 5 and infinity

What I did:

separate the eqn into the integral of 2x/(x^2-16) dx minus the integral of 1/(x-4) dx (both on the interval 5 and infinity)

for 2x/(x^2-16)

let x^2-16 =u

therefore du = 2x dx

Therefore the entire eqn becomes the integral of 1/u du - the integral of 1/(x-4) dx (both on the interval 5 and infinity)

= ln |u| - ln |x-4| on the interval 5 and infinity

subst u back in:

=ln |x^2-16| - ln|x-4| on the interval 5 and infinity

This however is where I get stuck and don't know how to proceed. I'm also unsure of whether all my calculations above are correct. If anyone could check/correct my work and also complete the calculations that would be greatly appreciated :)

Note: If you're having trouble understanding my working in text form here's a link to a pic of what I actually did: https://twitter.com/LukeshNaidoo/status/3690642739...

Also, I know infinity cannot be directly substituted in the eqns because it isn't actually a number but for ease sake I left it as it is so the text doesn't become too confusing (instead of subbing it out for a variable and letting the limit of the variable approach infinity.