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algebra regarding logs (answer)

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...

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what is the inverse function of f(x)=6x+11 (answer)

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...

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Solve the initial value problem? (answer)

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...

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Find the general solution? (answer)

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...

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Rewrite the following equation in standard form. y = -2x + 8 (answer)

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...

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how do you factor the expression 4x²+29x+30 (answer)

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. For example...

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Help me with Differential Equations? (answer)

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)

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p – 5 – 13p = 150 – 11 (answer)

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

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How do you input this on a Ti-89 calculator? (answer)

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...

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Problem Solving Questions - Help? (answer)

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...

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what's midpoint of (-2,2) and (6,4) (answer)

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)

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how do i simplify (2ab^-2c^-4)^-5 /(16a^-3bc^5)^2 (answer)

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 3. Power...

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What is the significance of composite functions? (answer)

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. In others...

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overlap between rates (answer)

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...

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Help me with this integral? (answer)

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...

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