Calculus

There are 10C4 = 10*9*8*7/(4*3*2*1) combinations of 4 digits that are all different. That is, 210 of them, and I have no inclination to list them.

This equation does not equal a number, but it can be factorised.

x2-xy-20y2=(x-5y)(x+4y)

1522

Writing x instead of theta, cos2x = 1 - (12/13)2 = 1 - 144/169 = 25/169 = (5/13)2

So cos(x) = ± 5/13

so that x = cos-1(5/13) or cos-1(-5/13)

And then, depending on the range of x, you have solutions for x. A calculator will only give you the principal solutions, though.

of course. As long as it doesn't cause you to divide by 0

Are you for real?! Just substitute it. 17 plus 23 is 40.

yes, 1 million times bigger

x - 5y = -4

x + 8y = -4

The first equation gives x = 5y - 4

SUBSTITUTE this value for x in the second equation:

(5y - 4) + 8y = -4

Simplify: 13y = 0 so that y = 0

Then x = 5y - 4 gives x = -4

4.5

The derivative of 10x is 10. This is irrespective of the value of x.

No. An "x term" normally means a term containg x to the power of one. Depending on the context of the question, it may include any powers of other variables and numerical constants.

if y=7/(x^3)-4/x
then
by the quotient rule
y'=(((0)(x^3)-(7(3x^2))/((x^3)^2))-(((0x)-(4))/(x^2))

3,978,000

u can't solve it because there has to be one variable to solve and equal sign, ex. 4x=20.

U can simifly though distrubute the n to 4 and -x. ur answer is 4n-nx

y+50 = 600

y = 600-50

y = 550

Yes, for some functions A, and not for others.

3

No one single point corresponds to y = 7 - x, but a whole straight line of them do.

eg the points (0, 7), (1, 6), (1.5, 5.5), etc all do.

It is the line of gradient -1 that crosses the y axis at 7 (and the x-axis at 7).

350 x 2.336 = 817.6

4

Use integration by parts. integral of xe^xdx =xe^x-integral of e^xdx.

This is xe^x-e^x +C. Check by differentiating. We get x(e^x)+e^x(1)-e^x, which equals xe^x. That's it!

There are 8 ounces to a cup.

So 32 ounces is 4 cups.

And there are 2 cups to a pint.

So 2 pints.

And 1 quart for every 2 pints.

The given equation is y = x - 4x + 2

which can be written as y = -3x + 2

This is an equation of a straight line. Therefore it has no vertex and so cannot be written in vertex form.

2

The ordered pair is (3, 2).