Solving for real roots / evaluating functions

[KimmyDean]

I am having trouble getting started on this word problem:

1) The amount of money Jim spends fishing is dependent upon the average temperature during any month. It varies according to the function: m= 5t^(3/5) + 45. If the average temperature last July was 87.45 degrees, how much did he spend fishing?

I get a very high number. My work:

. . .87.45 = 5t^(3/5) + 45

. . .87.45 = 150t^(1/5) + 45

. . .42.45 = 150t(1/5)

This just doesn't seem right to me!

Also:

2) Solve for all real roots: (x - 4)^2 = 36

I got x = 26, but I don't think I even started it right!

 

[skeeter]

m = 5t^3/5 + 45

87.45 is the temperature, not the money, plug it in for t ...

m = 5(87.45)^3/5 + 45

get out your calculator ...

m = ?
---------------------------------------------------

use some common sense for the second problem ...

if (x - 4)² = 36

wouldn't (x - 4) be equal to 6 or -6 ?

 

[stapel]

1) You didn't include any definitions of the variables, but I would guess that "m" stands for "money" and "t" stands for "temperature". As such, the temperature "87.45" should probably be plugged in for "t", not for "m".

Note: To solve for the value of a variable, you need to get "(that variable) = (some value)". The equation "42.45 = 150t^1/5" isn't solved for anything.

2) Since ([26] - 4)² = 22² = 484, it is unlikely that "x = 26" is a valid solution. How did you arrive that this value?

Please be specific. You took the square root of each side, putting the "plus-minus" on the numerical side, you added 4 to both sides, you simplified the two values given by the "plus-minus", and... then what? How did you get just one value, and "26" at that? Thank you.

Eliz.

 

[KimmyDean]

Thanks for the reality check. Math gets me rattled!

m = 5t^3/5 + 45

87.45 is the temperature, not the money, plug it in for t ...

m = 5(87.45)^3/5 + 45

get out your calculator ...

m = ?

1) That makes sense now that M = Money and T = Temp Duh me sorry.

Okay so if I do (5)(87.45)^3/5 + 45
I get M = 437.25^3/5 + 45
then M = $668819.10 which seems quite high!

2) For the other prob (x - 4)² = 36 I got it equal to (6, -6)

 

[skeeter]

Thanks for the reality check. Math gets me rattled!

m = 5t^3/5 + 45

87.45 is the temperature, not the money, plug it in for t ...

m = 5(87.45)^3/5 + 45

get out your calculator ...

m = ?

That makes sense now that M=Money and T=Temp Duh me sorry.

Okay so if I do (5)87.45)^3/5+45
I get M=437.25<sup>3/5>+45
nope ... remember the order of operations (exponents first, then multiply, finally add)?
then M= $668819.10 which seems quite high!

For the other prob (x-4)²=36 I got it equal to (6,-6)

 

[KimmyDean]

okay I think I got it now...

would it equal $26795.96?

 

[skeeter]

no. still too high for fishin'

87.45^3/5 = 87.45^.6 = 14.62365...

times 5 ...

73.12

plus 45 ...

$ 118.12

 

[KimmyDean]

Thanks

so was this correct?

For the other prob (x-4)2=36 I got it equal to (6,-6)

 

[stapel]

For the other prob (x-4)2=36 I got it equal to (6,-6)

How did you get that?

You were given the step-by-step instructions, and provided the hint that x - 4 should be something that, when squared, equalled 36. How did you then arrive at "x = 6, x = -6" for your answers?

Please show all of your steps. Thank you.

Eliz.

 

[KimmyDean]

I was going off of the advice of the poster before you! Sorry.

If I do x-4=36 and x+4=36

I get x=34 and x=40


Now I know that doesn't seem right since ([10]-4)²=36

So I would say it should be -10,10

 

[skeeter]

x - 4 = 6
x = 10 ... o.k.

but ...

x - 4 = -6

x = ? big hint ... it's not -10.