This topic deals with implicit differentiation for which I am sure your textbook has a lot to say.
I assume that you are expected to find y'(x) = dy/dx since nothing is specified in the text of the problem and that is usually what is done, i.e., we are working as if y=y(x).
Look...

Well, if you invest K today, and the annual interest is r, then using simple interest, at time t, your investment is worth
A = K(1+r*t).
We want A = 4K and r=5%. Thus:
4K = K(1+.05*t)
or
4 = (1+.05*t)
which...

By definition the rate of change is
f(c+h)-f(c) [-(c+h)^2+2(c+h)-3] - [- c^2 +2c-3]
------------- = ----------------------------------------------
c+h - c ...

(3.7-1.2)=c/2 In fact we knew that before adding 1.2 gallons the bucket was half full (c/2) and, clearly, if now we have 3.7 gallons after adding extra 1.2, before adding there were (3.7-1.2)=2.5 gallons of water in the bucket.
Hence,
c = 2*(3.7-1.2)=2*2.5 = 5, i.e. the...

To find the domain of the function assigned, the natural log, you need to specify for which values of x, the function is well defined. We know that for logarithms in general, natural or in any base, we need the argument to be positive, i.e.,
x^2 - 3x - 4 > 0
Now...

Ana,
The domain of definition of a function is the set of values of x for which the assigned function exists. In this case you are given a ratio of two second degree polynomials. However, if you factor both numerator and denominator, you get
...

Variables are
m = number of cars;
n = number of buses;
max: Profit = 2.50*m +7.50*n
s.t.: 6*m+30*n <= 600 (we can use 60% of the total 20x50=1000 sqm parking lot)
n+m <= 60 ...

The easiest, and perhaps the only way, to solve this kind of problems is to write
y = g(x) = x+1
and solve this equation as a function of y, i.e.,
x = y-1.
Therefore, the inverse function you are looking for is given by g-1(x) = x-1...

Let x be the number of rows.
Leo plants x+29 trees in each row. Hence the number of rows is given by
912 x
------ =
x+29
i.e., after simple algebraic manipulations, 912=...

The probability that a police officer is physically assaulted on the job can be estimated as 560/14,000 = 0.04 or 4%. But what does this have to do with postal workers and the probability of one of them being assaulted on the job? Comparing pears to apples
here. Also, over what period of time...

This problem can be done by hand, of course, but it requires a lot of computations as you have a multiple regression. Are you allowed to use a calculator such as the TI-83 or higher graphing calculator? If you are, the answers are not too difficult to
get.
1) Put the data in L1,...

Yousaf, you need to compare how much John is going to pay under either alternative:
1) 3.2% simple interest rate. What John pays to borrow $500,000 for 3 years is equal to
$500,000*3.2%*3 = $48,000
2) 1.6% compound interest...

Suppose that the statement is true for n, i.e., 2n >= n+1 (inductive assumption)
Then, for n+1, one finds using the inductive assumption, that
2(n+1) = 2n+2 >= (n+1)+2 > (n+1)+1.
Since the statement obviously holds for n=1...

You have 15 freshmen, 15 sophomores, 15 juniors, and 15 seniors available.
We assume that the order in which the students are chosen within each "standing" is irrelevant, i.e., we only care about who they are and not the position they were picked.
So, there are 15C4...

Hi Shola,
I assume that you are supposed to perform this calculation without a calculator. Well, the point to start from is to recognize that
13.568/.4 does not change if you multiply both 13.568 and .4 by 10 or by 100 or even by 1000 and so on.
So
13.568/...

Eme, something is missing in the expression you wrote above. In any case, let's assume that we had
3c3(5c+2cq) where q is any integer (or even just any real number as a matter of fact). Then you would have
3c3*5c + 3c3*2cq where we used the distributive property of multiplication...

xsin(x)[cos(x)ln(x) + sin(x)/x].
You can write the function y =xsin(x) as
y = exp(log(xsin(x)))= esinx*log(x),
then dy/dx = [sin(x)/x + ln(x)cos(x)]esin(x)log(x) = [sin(x)/x + ln(x)cos(x)]xsin(x) .

In case of continuously compounded interest, the relevant formula is
A = Pert.
In this case you want to achieve A=225,500, r=8.15% or 0.0815 and t = 8+145/365 =8.39726 years.
So, you can find the amount of money that you want to invest today, P, to achieve A in 8 years and...

Sun, I am afraid that this is not a "simple" inverse Laplace transform problem. it is not terribly difficult, but it requires quite a bit of calculations.....
The answer is e(1-i)t[(2-i)+(2+i)e2it]
and it requires that you use complex numbers. Note that the solutions...

Jerri, you are given a polynomial, x3-14x2+49, and that is "what it is", but what are you exactly asked to do with it? What do they mean by "what is?"