Walt

2 Questions
22 Answers

0

885

1

+56

Complicated functions

If f(x)+2f(8-x)=4 for all real x values, find f(2).

Walt Jan 22, 2014

0

1571

15

+56

Teacher trying to flunk me with these math questions! Help

Given that f(x)+2f(8-x)=4 for all real x values find f(2).
What is the smallest positive integer with exactly 768 divisors.

●●●●●●●●●●●●●●●

Walt Jan 19, 2014

+56

0

Well if you have the formula just plug in 50 for the F and solve.

WaltJan 20, 2014

+56

0

To do a factorial all you have to do is multiply all numbers that come before. So if you wanted to do 4 factorial it would be 4*3*2*1, or 6 factorial would be 6*5*4*3*2*1.

WaltJan 20, 2014

+56

0

I'm assuming you meant y^7 on the last part.

14x(4xy^14)(-4x^-10y^7)

14x(4)(xy^14)(-x^-10y^7)

56x(xy^14)(-y^7/x^10)

56x(xy^7/x^10)

56y^7/x^8

WaltJan 20, 2014

+56

0

Hey Nobody Special

I remember that to undo a cosine you use the arccos of your answer. I think you'll have to put it into a calculator to get your answer because the only other way I know how to do it is by drawing right triangles which I'm not sure will be simple with the number you got for your cosine.
Hope this helps.

WaltJan 20, 2014

+56

0

Ok so, paul shoveled x sidewalks in the first day. Each day after that he shoveled 3 more sidewalks so the equation is x+(x+3)+(x+6)+(x+9)=26 Solve that and you got your answer.

WaltJan 20, 2014

+56

0

You should be a little more thorough in your question but if you have a number like say .5 all you would have to do is multiply it by 100, or move the decimal two places to the right, to get it into a percentage which would make it 50%.

WaltJan 20, 2014

+56

0

If you were to plot this on a graph it would be an exponential curve and the formula for an exponential curve is y=a*(r)^x where a is the y intercept and r is the common ratio. To help you out, a is the original number you started with which was 1 cent and to find r all you have to do is divide the money you earned one day by the money you got the day before. So (4/2) or (2/1) which both equal 2 so that's your common ratio. Now that you have both a and r you plug them into your equation and you get y=1*2^x Y is the money you've gotten and x is the number of days you've worked there. Oh and by the way just so you don't get confused, day 1 would appear as 0 on the x axis, day 2 would be 1 and so on.

WaltJan 20, 2014

+56

0

This is a simple Foil problem. Foil stands for First-Outer-Inner-Last.
You multiply the first terms, then the outer terms , than the inner terms, then the last terms and combine like terms.

First terms (1*1)=1

Outer terms (1*9x)=9x

Inner terms (-7x*1)=-7x

Last terms (-7x*9x)= -63x^2

Then just combine like terms
-63x^2 +2x +1

WaltJan 20, 2014

+56

0

Melody:
Walt:
To find the largest possible square that would fit into your garden, we would have to find the largest perfect square that will divide into 6912, which is the area of the garden. 256 is the largest perfect square to divide into 6912 and when you divide you get 27. This means that you could make 27 squares with equal areas that would fit inside your garden. Because a square's length and width are always the same, you just find the square root of 256 and you got your sides. So, 16 feet.

a garden measures 64 ft by 108 ft. the gardener wishes to subdivide the garden into congruent squares. what is the side length of the largest squares possible?

But Walt, 108 divided by 16 = 6.75 so there is not a 'whole' number of squares in the length.

For the moment, this question has got me stumped. I don't have a lot of time to think about it today, I definitely want to play with this question.

Sorry for the moment.
Melody.

Good point Melody, I failed to see this. Ok so I think this is the right way,
To find the side lengths of the largest possible squares then you would have to find the greatest common factor of both 64 and 108 which is 4. Here is the why:

Another way to look at the length and width of this rectangle is that it tells you that you could fit 64x108 tiny boxes, all with side lengths of 1, inside the rectangle. If the side lengths of your overall rectangle have a common factor that means you could group up the little unit boxes into bigger ones. The biggest boxes you could possibly group them into will have side lengths of your greatest common factor which in this case is 4. If you draw yourself a picture in your head you'll see how it all works out.

WaltJan 20, 2014

+56

0

Lol this is a great question that I'm not exactly sure I know how to answer, but I think if you were going the same exact speed as your lights then you would not be able to notice them moving, they would look like they're completely still. But in reality to go the speed of light you would need an infinitely large mass, so that means its impossible.

WaltJan 19, 2014