Question

what is the value of p in x= -1/8y^2

Answer 1

I don't see any p's in that equation... Can you be a bit more specific in what you want answered?

Answer 2

we are dealing with parabolas and that is all the question says...my teacher says that in a normal parabola it is y= 1/4p x^2

Answer 3

According to this page

http://www.mathwords.com/f/focus_parabola.htm

It states that the general form for parabolas that open left/right is

4p(x-h) = (y-k)^2

where p is the focal distance and (h,k) is the vertex.

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So we need to get x= -1/8y^2 into that form

x= -1/8y^2

-8x= y^2 ... Multiply both sides by -8.

-8(x-0) = (y-0)^2

-4*(2)(x-0) = (y-0)^2

So p = 2 which means the focal distance is 2 units

Answer 4

so then this would be false the focus of x = -1/8y^2 is (-2,0)

Answer 5

p = 2 is just the distance the focus is away from the center

Answer 6

because x= -1/8y^2 opens to the left, we start at the vertex (0,0) then move 2 units along the axis of symmetry y = 0 to land on the focus of (-2,0)

So it's actually true

Answer 7

oh ok that is making more sense now thanks can you help with some more math problems with midterm review?

Answer 8

Sure I can do a few more

Answer 9

ok solve the equation for x round to nearest thousandth

\[10^{x+5} -2\]

Answer 10

wait that was a typo hold on

Answer 11

\[10= 3^{x+5} -2\]

Answer 12

would i add 2 to 10 and then divide by 3 giving us 4=x+5?

Answer 13

You do add 2 to both sides, but you cannot divide both sides by 3

Answer 14

ok then what would i do with the 3?

Answer 15

We now have

\[\Large 3^{x+5} = 12\]

we then convert to logarithmic form to get

\[\Large x+5 = \log_{3}(12)\]

and then subtract 5 from both sides to isolate x

\[\Large x = \log_{3}(12)-5\]

Answer 16

That last equation is the exact answer. Use a calculator to evaluate that to get the approximate answer (make sure you use the correct base)

Answer 17

You will use the change of base formula

\[\Large \log_{b}(x) = \frac{\log(x)}{\log(b)}\]

Answer 18

i am confused with what to plug into that equation what is log base b of x

Answer 19

well the last thing I posted is just a general form

In this case, b = 3 (base is 3), x = 12

So....

\[\Large \log_{b}(x) = \frac{\log(x)}{\log(b)}\]

turns into

\[\Large \log_{3}(12) = \frac{\log(12)}{\log(3)}\]

after the proper replacements are made

Answer 20

ok thanks that makes sense

Answer 21

so what do you get as a final answer?

Answer 22

2.262

Answer 23

So that means

\[\Large \log_{3}(12) \approx 2.262\]

which is correct. Now you must subtract off 5

Answer 24

Since we found above that

\[\Large x = \log_{3}(12)-5\]

Answer 25

-2.738

Answer 26

perfect

Answer 27

thanks do u still have time to be on here?

Answer 28

Yes I do

Answer 29

mind helping me with more logarthims stuff

Answer 30

sure I can help, go ahead

Answer 31

i stink at logarithims lol but what is the range of the funtion show below
f(x)= log base 5 (x+2) i believe it would be all real numbers i dont think there are any y restrictions

Answer 32

You are correct. Nice work.

Answer 33

thank you now for this one what is domain of f(x)= log base 5 (x-3) i believe it would be greater than or equal to -2

Answer 34

that is incorrect

Answer 35

hint: you cannot take the log of a negative number or the log of 0

Answer 36

all real numbers greater than 3?

Answer 37

Good,

x-3 > 0

x-3+3 > 0+3

x + 0 > 3

x > 3

Answer 38

thanks so much...i dont wanna keep you any longer. when do you think you will be on here again?

Answer 39

I should be on later tonight

Answer 40

it is after 8pm here i am going to try and work on my midterm packet more...maybe you could help me tomorrow or thursday?

Answer 41

Sure that works for me

Answer 42

ok sounds good talk to you tomorrow or thursday