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12

12 * 12 = 144

if a, b, and c are integers between -10 and 10, and a cubed plus b cubed = c cubed, what does a, b, c, represent if as to get the greatest possible sum for a+b+c

\(a^3+b^3=c^3\\ \)

This will only happen if a or b = 0 and the other one =c

Let b=0

a=c

maximum value of a+b+c = 10+0+10 = 20

400·1,03^x = 1000  Solve for x

Divide both sides by 400

1.03^x =2.5 Take the log of both sides

x. log(1.03) =log(2.5)

x =log(2.5) / log(1.03)

x=~31.....

thats all brov

More info needed ://

I have no idea what you are on about.   ://

1.25

Draw some triangles on a peice of paper and see if you can work this one out for yourself :)

Try to draw a triangle where the 2 short sides added together are less  than the length of the long side...

In any trinagle,

The largest angle is always opposite the longest side

and the smallest angle is always opposite the shortest side.

I suspect you mean asin.  Press the 2nd button first.

| cos0 -sin0 | = |  1 - 0 |  = 1

| sin0 cos0 | = |  0 * 1  | =  0

You got it Alan

No.1 maths detective trophy goes to Dr. Alan   :))

I think this means:  5^m = 605  Find m.   (rays to = raised to!)

"How much heat (in kJ) is required to warm 13.0 g of ice, initially at -13.0 ∘C, to steam at 112.0 ∘C? The heat capacity of ice is 2.09 J/g⋅∘C and that of steam is 2.01 J/g⋅∘C, the heat of fusion for water is 6.02 kJ/mol, and the heat of vaporization for water is 40.7 kJ/mol."

Latent heat of fusion = 334 kJ/kg    Latent heat of vaporisation = 2264.76 kJ/kg  

Specific heat capacity of water = 4.18 J/(gK)

Ice from -13 to 0°C                E₁ = 13*2.09*13 J → 353.21 J →  0.353 kJ

Ice to water at 0°C                 E₂ = 0.013*334 kJ →                    4.342 kJ                        (Note: 13g = 0.013 kg)

Water at 0 to 100°C               E₃ = 13*4.18*100 J → 5434 J →  5.434 kJ

Water to steam at 100°C       E₄ = 0.013*2264.76 kJ →           29.442 kJ

Steam from 100 to 112°C      E₅ = 13*2.01*12 J → 313.56 J → 0.314 kJ

I'll leave you to add up the five energies!

.

200Kj

I do not understand this question.  ://

1 3/5x1 2/5

you can put it into the Web2 calc as 

(1+3/5)*(1+2/5) =

cos( pi) = -1

NOT     cos(2)

A particle moving back and forth along a straight line has position function given by x(t)=sin(π(t−1)) with t in sec.

(a) Estimate its instantaneous velocity at t=1 sec using a table of values (up to two decimal places).

You have not given us a table so I will use calculus.

\(x(t)=sin(\pi(t-1))\\ \dot{x}(t)=\pi cos(\pi(t-1))\\ \dot{x}(1)=\pi cos(\pi(1-1))\\ \dot{x}(1)=\pi cos(0)\\ \dot{x}(1)=\pi *1\\ \dot{x}(1)=\pi\\ \dot{x}(1)\approx3.14\)

So instantaneous velocity when t=1 is  pi 

(b) Using part (a), what can you say about the limit limx→0sin(πx)/x ?

I am really not sure what you are being directed to do here but this is the answer.

Using L'Hopital's rule

\(\displaystyle\lim_{x\rightarrow 0}\;\frac{sin(\pi x)}{x}\\ =\displaystyle\lim_{x\rightarrow 0}\;\frac{\frac{d}{dx}sin(\pi x)}{\frac{d}{dx}x}\\ =\displaystyle\lim_{x\rightarrow 0}\;\frac{\pi cos(\pi x))}{1}\\~\\ =\pi \)

in a circle radius 6 miles the length of the arc that subtends a central angle of 6 radians is

\(Arc=\frac{6}{2\pi}\;\times 2*\pi * r\\ Arc=\frac{6}{2\pi}\;\times 2*\pi * 6\\ Arc=\frac{6}{1}\;\times 6\\ Arc=36miles\)

That is most of the circle  :)

what is 3 times the square of a number x.

\(3x^2\)

You are being asked for he biggest number that goes into 9 and into 45

What numbers go into 9?     lets see   1*9  and 2*3  so the factors are   1,3 and 9

Which is the biggest of these that also goes into 45?

That will be your answer. :)

This is an interesting question  :)

Assume that the maximum speed your car will go is a linear function of the steepness of the hill it is going up or down. suppose that the car can go a maximum of 55 mph up a 5° hill, and a maximum of 104 mph down a 2° hill.

a) whats the equation for expressing maximum speed in terms of steepness?

Think of it like this.

Let k be the maximum speed on flat land - that when the angle is 0 degrees.        

(0,k)  is one point on the linear function.

If the angle is +5 degrees then the max speed is 55mph     so     (5, 55) is another point.

If the angle is -2 degrees then the max speed is 104mph     so     (5-2, 104) is another point.

Let the linear function be

        \(S=m\theta+k\\ we\;\;have\\ 55=5m+k \qquad(1)\quad and\\ 104=-2m+k\qquad (2)\\ (1)-(2)\;\;gives\\ -49=7m\\ m=-7\\ \text{substituting back in we get}\\ k=90\\ \text{So the equatoin is}\\ S=-7\theta+90 \)

b) what does the slope represent?

   The speed will drop by 7 mph for each 1 degree increase in the slope of the road.

Here is the graph that might help you understand

what do you need "dimentional analysis" for something as simple as a leaking pipe?

I American gallon =128 fluid ounces

12 fluid ounces are leaking per minute, therefore:

12 x 60 =720 fluid ounces of water leaking in 1 hour.

720 / 128 =5.625 gallons of water leaking in 1 hour.