Calculus

here is 150 digits of pi by memory;

3.14159265358979323846264338327950288419716939937510582097494459230781640

628620899862803482534211706798214808651328230664709384460955058223179408128

Think of this a 12 x-rays + 5 x-rays

Makes 17 x-rays.

12x+5x=17x

this is an equation of a line. it has a slope of 4/3 and a y-intercept of 5

You would write it as 93

it is equal to 6y plus y

16 times 7 equals 112.

Think of ln 1 as "e to what power will given me 1." Anything to the zero power will give you 1. So, ln 1 = 0, and 0/2 = 0

it is 2400

3 many =Saturday

3X7 many =21 is also Saturday

So 20 many is one day before Friday.

Three quarters of 4 is three

While 3 is a number multiplying, it's a coefficient. That has x as is its factor.

11

3x - y = -1

x = -2

3(-2) -y = -1

-6 - y = -1

-y = 5

y = -5

Yes.

The abbreviation for degrees is a little circle written above the numerical value (somewhat like an exponent). It looks a little like this: 98o (98 degrees).

Despite my serious qualms with the wording of your question, I am assuming it to be the factoring of x2-2x+3

This is not factorable. As long as there is a positive 3 in the position of the constant element, there can only be -4 or 4 for the coefficient of the single x. Perhaps you made an error in entering the question, so I will provide some likely alternatives.

If the trinomial read as x2-2x-3, then it would be factorable and would be (x-3)(x+1)

If the trinomial read as x2-4x+3, then it would be factored as (x-3)(x-1)

If the trinomial read as x2+4x+3, then it would be factored as (x+3)(x+1)

1 meter = 1000 millimeters

1 millimeter = 0.001 meter

4x - 5y = 4 & 6x - 7y = 10

This is a pair of simultaneous equations. Re-write as

4x - 5y = 4

6x - 7y = 10

To find the value of 'x; we need to eliminate 'y'

To do this multiply the top eq'n by '-7' and the bottom equation by '5' . This brings the coefficients of 'y' to the same value, but one is plus(+) and the other is negative(-).

Hence

-28x + 35y = -28

30x - 35y = 50

Add the two eq'ns, this will eliminate 'y'

2x = 22

x = 11

x^2 - 4 = 0

What you have to recognise is that the constant '4' is a 'squared number.

4 = 2^2

So we can write

x^2 - 2^2 = 0

Next remember that two squared terms with negative between then, factors.

Hence

x^2 - 2^2 = 0

=>

( x - 2)(x + 2) = 0

NB Note the plus (+) sign in the second bracket.

Hence

x - 2 = 0

x = 2

&

x + 2 = 0

x = -2

So 'x' can take two values, they are '(+)2, & -2'.

NB Note that two squared terms with a plus(+) between then , does NOT factor. e.g. the Pythagorean equation. c^2 = a^2 + b^2

It is not possible to answer this question because people find different things easy or difficult. What you find easy I might find difficult, and conversely.

30 ml is equal to 30 ml. You have not given us any other unit to convert, so that's the answer.

f(x) = 1/3x3

f'(x) = ∫ 1/3x3 dx

f'(x) = 1/3∫ x3 dx

f'(x) = 1/3 * 3 * x2

f'(x) = x2

When finding an antiderivative, substitution can be very helpful. In your integral expression, look for a term that, if you took the derivative and perhaps manipulated it a bit, would give you another term in the same equation. For example, if your integral is ∫tanxdx or ∫((sinx)/(cosx))dx , you can choose cosx as your arbitrary variable (often u or w). If u=cosx, du=-sinxdx. Therefore, your expression using u becomes -∫du/u. We know that the antiderivative of 1/u is ln (absolute value x) +C. So, our answer with u is -ln (abs. val. u) +C. But BE CAREFUL, this is not your final answer. You must plug in the value you originally designated as u. Therefore, the final answer is -ln (abs. val. cosx) +C, with C as an arbitrary constant.

12 x 5 = 60

That's because 12 x 100 = 600

12/2 = 6