Afew precalc problems which i'm having problems with

[kevin12345]

i will try and post the question and tell you how far i got and hopefully some nice guy/girl out there will show me what i did wrong and help me solve the problems before the test tomorrow

1-The heat experienced by a hiker at a campfire is proportional to the amount of wood on the fire, and inversely proportional to the cube of his distance from the fire. If he is 15 feet from the fire, and someone triples the amount of wood burning, how far from the fire would he have to be so that he feels the same heat as before?

okay here is what i did
hiker = k*wood/distance^3
hiker = k(3*wood)/distance^3

but now I'm stuck i feel like I'm missing something that is very important to solve this problem and i don't know what it is..

2-F(x) is given asf(x)=x^(1/5) , and the indicated transformations are applied to its
graph in the given order. Write the equation for the final transformed graph.

a) shift upward 6 units and to the left 7 units
(x^(1/5) +7) +6
b) shift right 4 units, shrink horizontally by a factor of 1/5 and shift downward 2 units
(5x^(1/5) -4)-2
c) reflect over the y-axis, stretch vertically by a factor of 3 and shift upward 1 unit
3(-x^(1/5))+1
d) reflect over the x-axis, stretch horizontally by a factor of 5 and shift left 7 units
-(5x^(1/5)+7)


i gave the equation for all 4 questions but i don't know if all are correct so please help

9. An open box with a square base is to have a volume of 19 ft^3. Find a function that models the surface area, A(x), of the box, where x is the length of the base. Find the box dimensions that minimize the amount of material used to make the box. Round your dimensions to the nearest hundredth.

not only do i not know how to start this well i dont

thank you in advance

 

[Mindscrape]

Okay, the second one is definitely right unless I missed something glancing over. Why do you have variable "k" in the first one? Is that your constant? If so it should be that the constant k=(w)/(d^3) then you find out what has to be done to the equation if to keep the same constant when the wood is tripled.

For the third one, I suspect you are supposed to use a graphing calculator since this is pre-calc. So, for most volumes you find the cross-sectional area and multiply it by a height. A box is very easy to do, especially if it is a square base (which I think it must be since they don't provide any other limitations). Then you would want to take the function of volume and graph it to find the minimum value of the curve.

 

[HallsofIvy]

i will try and post the question and tell you how far i got and hopefully some nice guy/girl out there will show me what i did wrong and help me solve the problems before the test tomorrow
1-The heat experienced by a hiker at a campfire is proportional to the amount of wood on the fire, and inversely proportional to the cube of his distance from the fire. If he is 15 feet from the fire, and someone triples the amount of wood burning, how far from the fire would he have to be so that he feels the same heat as before?
okay here is what i did
hiker = k*wood/distance^3
hiker = k(3*wood)/distance^3
but now I'm stuck i feel like I'm missing something that is very important to solve this problem and i don't know what it is..

It would help you a lot if you would write out specifically what your variables meant! "hiker" is not a person but is "the heat felt by the hiker" and is the same number in both equation ("he feels the same heat as before"). "wood" is the amount of wood on the fire and since your write "3*wood" is also the same number in both equations. "distance" is the distance the hiker is from the fire and is NOT the same number in both equations. Write d1 and d2 for the two numbers and divide one equation by the other.

2-F(x) is given asf(x)=x^(1/5) , and the indicated transformations are applied to its
graph in the given order. Write the equation for the final transformed graph.

Well, no, F(x) is given as F(x)= x^(1/5)!
In particular, if x= 1, then y= 1.

a) shift upward 6 units and to the left 7 units
(x^(1/5) +7) +6

As a check, if x= 1- 7= -6 (left 7 units from 1), what is y? Is it 1+6= 7?
In general, a change in x (horizontal) is applied before the function is applied, a change in y (vertical) is applied after the function.
Suppose y= (x+7)^(1/5)+ 6 and x= -6, what is y?

b) shift right 4 units, shrink horizontally by a factor of 1/5 and shift downward 2 units
(5x^(1/5) -4)-2

Same thing: shift right 4 units (subtract 4) and shrink (multiply by 1/5) before taking the fifth root.

c) reflect over the y-axis, stretch vertically by a factor of 3 and shift upward 1 unit
3(-x^(1/5))+1

I would prefer "(-x)^(1/5)" but since 5 is odd, that's correct.
[\quote]d) reflect over the x-axis, stretch horizontally by a factor of 5 and shift left 7 units
-(5x^(1/5)+7)[\quote]
Multiply x by 5 before taking the fifth root!

i gave the equation for all 4 questions but i don't know if all are correct so please help
9. An open box with a square base is to have a volume of 19 ft^3. Find a function that models the surface area, A(x), of the box, where x is the length of the base. Find the box dimensions that minimize the amount of material used to make the box. Round your dimensions to the nearest hundredth.
not only do i not know how to start this well i dont
thank you in advance

An "open box" means that the box has a bottom but no top. Start by looking for surface area as a function of two variables, A(x,y), where x is the length of the base and y is the height of the box. In that case the length and width of the base are x and the height is y. The base is a square x by x ft. What is its area (in terms of x)? The box has 4 sides each a rectangle x by y ft. What is the area of each side (as a function of x and y)? What is the total area of the box?
The volume is V= x*x*y= x²y= 19 ft³. You can use that equation to eliminate y from A(x,y) to get just the A(x) you want.
I presume you know how to find a max or min of a function.