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0 <= -x**2 -3x - 70, so x**2 + 3x + 70 >+ 0. Now the discriminate of this quadratic is negative, so it has no real root. Hence it is either always >+ 0 or always <= 0. Since it it >= 0 when x = 0,...

As Capuchin says, divide the first equation by 3 to get
x + 2y = -2. And the second equation is
5x - 2y = 14. Add these two equations to get
6x = 12, so x = 2,and fro the first equation we have...

h(-4) = -1/3(-(-4)+5) = -1/3(9) = -3
gh(4) = g(-3) = (4(-3)+4)5 = (-8)5 = -40

Of course g(4)=g(4), As Adam is the same as Adam. What do you mean by the inverse of this?

f(g(x)) = g(x)^2 - 3 = (-1 - x)^2 - 3 = 1 + 2x + x^2 - 3 =
x^2 + 2x - 2

This is not a composite function. If you are asking about
f(g(x)) = 7g(x) + 49 = 7(x + 3) + 49 = 7x + 70 or
g(f(x)) = f(x) + 3 = (7x + 49) + 3 = 7x + 52,
in either case the domain is the...

That post I made in answer to the question was a year ago. Step by step is in the post. If you have any problemms with this post let me know and I'll try to clarify it.

I'm with you, Oranges!

52<n+26, so (subtracting 26 from both sides) 26<n

Cost is at loelast $60.

I'm only answering the questions that have been incorrectly answered before. In this question outward bound the pilot flies 600 mph for 1 hour and travels 600 * 1 = 600 miles; inward bound he...

out rate = 600 mph, in rate = 400 mph, total time = time = 2 hours, 30 min = 2 1/2 hours = 5/2 hours. If he flies outbound for t hours, his outbound distance is 600t and his inbound distance is...

Volume = V = pi * r^2 * h, so h = V/(pi * r^2).
Ssurface area = S = 2 * pi * r^2 + 2 * pi * r * h = 2 * pi * r^2 + 2 * pi * r * V / (pi * r^2)
= 2 * pi * r^2 + 2 * V / r....

4^(1/3) + 4^(1/4) = 4^((1/3) +1/4)) = 4^(7/12) = (2^2)^7/12) =2^(2*(7/12)) = 2^(7/6)

1 is a quarter of 4

There are four such points, with coordinates ((+-)sqrt6,(+-)sqrt6)

z = 3 + I = sqrt (10) e^(I arc tan(1/3)) = 10^(1/2) e^(I arc tan(1/3)), so sqrt z =
10^(1/4) e^(I(1/2)arc tan(1/3)).

d/dx(sinx/x) = (sin x - x cos x)/x^2 < 0 iff sin x - x cox s < 0 iff sin x < x cos x iff tan x < x, which is not true in this range. In fact the opposite is true: tanx >= x in this range, so sin...

If you mean x^3 - 2x^2 - 4x + 8, then this equals
x^2(x-2) - 4(x-2) = (x^2 - 4) (x-2) = (x+2)(x-2)^2

(a) The probability of getting no 1 is (5/6)^3, so the probability of getting at least one 1 is
1 - (5/6)^3

(b) The probability of getting a 1 on one particular die and not a 1 on the other two...

Speaking of tricks there is one that I find helpful in checking my arithmetic. It's caslled "casting out 9's" and it seems to be becoming lost.

What it is is that in any arithmetic operation you...

The tangent line is vertical when the denominator of dy/dx = (3x**2 y ? y**2)/(2xy -x**3) is zero. i.e. when 0 = 2xy - x**3 = x(2y-x**2). This happens when x=0 or when y = x**2/2. In this case 6 =...

Such a relation is surely not linear, depending on the thickness of the tape, what the counter is really measuring, etc. Your best bet (I've actually done this) is to let the tape run and record the...

The trouble with your solution for A is, is the resulting sequence bounded?

As for B, there is no increasing bounded sequence of natural numbers. This is because, if a sequence is bounded, say by...

(x/y)**4 (y/x)**4 (8x7x6x5)/(4x3x2x1) = 70

Speaking as a retired math teacher my advice would be as follows.

I think it is a great mistake to try to understand math at an inappropriate level. Mathematics is different from most subject in...

at a point (x,y) we have 2(x-h) + 2(y-k)der of y = 0, so der of y = -(x-h)/(y-k) = slope of a tangent line at this point. A radial line goes through (x,y) and (h,k), so its slope is (y-k)/(x-h),...

sqrt (4 - x**2) = sqrt (4 - (2 cos theta)**2) = sqrt (4 - 4 cos**2 theta) =
sqrt (4 (1 - cos**2 theta)) = sqrt (2**2 sin**2 theta) = 2sin theta

log a 16 = log a 2**4 = 4 log a 2 = 4.. 4307 = 1.7228

Calling the heighth of the tree x, the distance to the first measurement y, the first angle a=36.7, and the second angle b=22.2, we have cot a=y/x, so y=x cot a. Also cot b = (y+50)/x = (x cot a +...

Can I convert a text file--presumably ASCII--to a format I can burn to and played on an ordinary CD?