In order to answer this problem you need to be able to convert from log form to exponential form. In general if you have loga(b) = c then the exponential form of that would be ac = b.
So in your problem you have log3(log(3x)) = 1. Here a = 3, b = log(3x) and c = 1 so to convert this to exponential...
The easiest way to find the inverse of a function in my opinion is to first change the f(x) back into y and swap your x's and y's. Doing these things gives you:
x = 6y + 11. After you do this simply solve for y and your answer will be the inverse.
start by substracting 11 on both sides...
Here we have 2 distinct roots to the characteristic equations r = -1, 2 so the general solution becomes:
y(t) = C1e-t + C2e2t
plugging in our initial conditions we get:
y(0) = C1 + C2 = a
y'(0) = -C1 + 2C2 = 2
After solving this 2 X 2 linear system (preferably using...
Since this is not a linear system I think the best route to take is to set each equation equal to each other. So this gets us:
2x + 2 = (1/2x) + 5
Multiplying this equation by 2x will get rid of the fraction and leave us with:
4x2 + 4x = 1 + 10x
Now we have a quadratic...
What you did to get 17/0 is correct but that doesn't equal 0, 0/17 = 0. When you get a 0 in the denominator your slope is undefined.
I think you meant simplify the 1st and evaluate the 2nd. If that is the case then for the 1st problem you begin by distributing the m and the 3, this should give you:
m(2 + n - m) + 3(3n + m2 - 1) = 2m + nm - m2 + 9n + 3m2 - 3.
Next combine like terms, this...
1st thing we do in this problem is put it in a form that will allow us to find an integrating factor. We do this by multiplying the entire equation by (1/t), this gives us y'-(1/t)y=te-t
From here we see that our integrating factor is g(t)=e-∫(1/t)= 1/t.
Multiplying the equation by the integrating...
Keeping in that csc(t) = 1/sin(t), distribute that csc(t) and you get csc(t)(sin(t) + cos(t)) = 1 + cot(t)
Right now your equation is in what is called the slope-intercept form y=mx+b where m is the slop and b is the y intercept.
You job is to put it in the for Ax+By=C where A is a positive whole number and B and C are integers. We look at these 2 forms and we ask ourselves what is the difference...
Roman and Herb's method of factoring by grouping works fine. There is a slight variation to that which can save a few steps.
Once you have determined your 2 numbers simply divide them by the leading coefficient and you can immediately put those number into your factored form.
When you get complex roots a ± bi, the general solution becomes y(t) = eatcos(bt) + eatsin(bt). So for this problem you get y(t) = cos(2t) + sin(2t)
We start this proof by letting a, b, c be non zero real numbers and we assume a+b+c=0. This implies that a = -(b+c), b = -(a+c), c = -(a+b). Plugging these into the expression we need to work with we get:
(b+c)2/(bc) + (a+c)2/(ac) + (a+b)2/(ab). Notice...
By combining like terms we get -12p - 5 = 139
Add 5 to both sides we get -12p = 144
Dividing by -12 we get p = -12
Well I'm not sure how to check this on a calculator but for any type equation (differential equations included) if you want to check your work simply plug it back into the original problem. For exact equations like this just take the partial derivatives and they should match up with your original...
For question one 1 we need to use the fact that distance d is given by the equation d = rt. The problem is saying that the total distance, 600km, is broken into 2 parts (one being the distance he travels going 75 km/h and the other being the distance going 110 km/h) we will call these 2 parts d1...
Using the midpoint formula ((x1+x2)/2 , (y1+y2)/2) we get that the x coordinate of the midpoint is (-2+6)/2 = 2 and the y coordinate is (2+4)/2 = 3.
so the midpoint is the ordered pair (2,3)
Any problem that involves simplifying exponents requires a good understanding of the exponent rules. There are several rules that you should know but I'll just go over the ones which we will use for this problem.
1. Product Rule: anam = an+m
2. Quotient Rule: an/am = an-m
What Steve said is spot on. In addition to the horizontal line test there is an algebraic way to determine one to one
You start by assuming 2 arbitrary range values are equal, if we show that their corresponding domain values are equal then we get that the function is one to one.
Are you asking how to calculate the % of how many users are performing exactly one activity? If so then you find out what % among all users are performing whichever activity you would like to start with then subtract that from the percent of those performing both tasks.
This type of question...
This is what I think. I hope it isn't too late.
You have already found that the new region in terms of u, v, and w is u2 + v2 + w2 ≤ 1 and u2 + v2 ≥ w2. In words, the region is inside the sphere of radius 1 and outside the cone.
Since you have to find the integral I would strongly...