All Answers

snape9303:
A truck accelerating at 0.0083 meters/second2 covers a distance of 5.8 × 10Ê4 meters. If the truck's mass is 7,000 kilograms, what is the work done to reach this distance?

First you need the force, which is mass*acceleration. Then you need Work done = Force*distance.

So: Force = 0.0083*7000 N and Work done = 0.0083*7000*5.8*10 ⁴ Joules

AlanMar 21, 2014

+893

If you just want to know the result then using the scientific calculator is fine. If however you would like to know how the result is arrived at, that's different.
Here's a route through to the result, (and sorry, I don't know the best way of entering this maths stuff, maybe Melody could point me in the right direction ?)

int (cos ^-1x) ² dx = int (cos ^-1x) ².1.dx ,
(and integrating by parts,)
= x.(cos ^-1x) ² + int x.2cos ^-1x /sqrt(1 - x ²) dx
(Note that the negative sign from the parts formula is multiplied by a negative sign from the derivative of cos ^-1x .)

For this new integral, use the substitution u = cos ^-1x.
From that, du = -1/sqrt(1 - x ²) dx,
in which case the (new) integral becomes int (-1).2u.cos(u) du.

Integrating that by parts gets you (-2){u sin(u) - int sin(u) du} = (-2){u sin(u) + cos(u)},
(where again you have two negative signs giving you a positive sign.)

Now notice that if u = cos ^-1x, then cos(u) = x, so sin(u) = sqrt(1 - x ²).

So, substituting for u and putting this with the first term from the original integration by parts, we arrive at

x.(cos ^-1x) ² - 2sqrt(1 - x ²)cos ^-1x - 2x, (plus a constant of integration, or substitute in your limits).

BertieMar 21, 2014

+118728

ThaKidd:
How do I put 5 degrees and 15 minutes in a calculator

Alan has shown you how to do it using the Web2 calc

If you want to know how to do it on most hand held calculators you use the degrees, minutes, seconds button. (DMS for short)
It looks like this
degrees min secs calculator pic.jpg

so you would press 5 DMS 15 DMS

You can use this button for time calculations as well

MelodyMar 21, 2014

+118728

*
Alan just showed us how to do an indefinite integral

int(acos(x)^2)

AND a definite integral

int(acos(x)^2,x=0..1)

Now Alan has shown us how to factor polynomias. He is a wealth of information.

factor(x^2-2x-3)

Samgelinas whas shown us how we can solve a quadatic equation.

[input]solve(24^2+b^2=25^2, b)[/input]

MelodyMar 21, 2014

+33666

ThaKidd:
How do I put 5 degrees and 15 minutes in a calculator

If the calculator is in degree mode then put 5+15/60 or 5+1/4 or 5.25, as there are 60 minutes in one degree.

AlanMar 21, 2014

+118728

It is not a problem Sam,
Don't worry about it.
I like to see you answer so many questions.

MelodyMar 21, 2014

+142

Melody:
CountryGirl333:
Find the height of a triangular prism with a base length of 10 yards, a base height of 20 yards, and a volume of 600 cubic yards.

Sorry Sam but it is a prism NOT a pyramid so you have used the wrong formula.

The volume of any prism is the area of the cross section (that stays the same) times by the depth, or height or whatever you want ot call it.

I think it is the height of the triangle that is missing although the question could be interpreted differently. The area of a triangle is (1/2)*base*height = (1/2) * 10 * h = 5h yards squared

so
5h*20=600
and you can finish it.