Calculus

3x - x = (3 - 1)x

= 2x

The surface area of a sphere is 4 x pi x radius2 - exactly 4 times the area of the circle you get when you cut the the sphere right through the center.

eight hundred twelve thousand

x^(3) +x^(2) - x = 0

Factor

x(x^(2) + x - 1) = 0

First part of the answerr is x = 0

Second part of the answer

x^(2) + x - 1 = 0

Use Quadratic Eq'n.

x = { -1 +/- sqrt[1^(2) - 4(1)(-1_]} / 2(1)

x = { -1 +/- sqrt[1 + 4]} / 2

x = ( -1 +/- sqrt)5)} / 2

x = =1 +/- 2.236...} / 2

x = -1/2 +/- 2.236.../2

X = -0.5 +/- 1.118...

x = - 1.618.... & x = 0.618....

So the three values of x that satisfy the equ'n are

x = 0 , -1.618.... & 0.618....

Salute, Salutations

2x + 7 = 79

Subtract '7' from both sides/

Hence

2x = 72

Divide both sides by '2'

Hence

x = 36 .

20 x 7.5 = 150

x^(2) - 2x - 3 = 0

This is a Quadratic Equation.

There are three methods to solve.

#1 ; Factor

#2 ; Complete the Square

#3 ; Use the Quadratic Equation.

Use #1 , which is the simplest method.

We note that 'x^(2) ' has a coefficient of '1' (not Shown).

We also note that the constant is '-3' . So write down the factors of '3', which are 1, & .3.

From '1' & '3' we add/subtract to make '2' the coefficient of the middle term. Hence 1 - 3 = -2

Writing up our brackets

( x 1)(x 3) = 0

Since the sign of the constant '3' is negative (-), it means that the two signs in the brackets are different (+/-)

Since the '2' is negative, then the larger number in the brackets is the negative term.

Hence

( x + 1)(x - 3) = 0

Equating each bracket to zero.

x + 1 = 0 Hence x = -1

&

x - 3 = 0 Hence x = 3

So the two solutions for 'x' are '-1' & '3'.

No. A centimeter is defined as 1/100 of a meter. Thus, 100 centimeters in a meter. Envisioning a cube with sides of 1 meter is 1x1x1 meter, or 100x100x100 (Or 1,000,000 cubic centimeters.)


Thus, 1000 cubic centimeters=1/1000 of a cubic meter.


On a side note, 1000 cubic decimeters is a cubic meter.

2,100 square meters.

Eight squared is like saying you take eight multiplied by eight. In this case it equals out to sixty four.

The anti-log of what ??? If log(12) = 1.07918, then antilog(1.07918) = 12 Did you want the anti-log of 12 ? That's 1,000,000,000,000.

No. The log of a quotient is the log of a denominator subtracted from the log of the numerator.

Yes!!! True!!!

The axes are x, y, & z.

Any given point is denoted by ( x,y,z).

87

Derivative of natural log x = 1/x

The derivative of cosine of x is simply the negative sine of x. In mathematical terms

f'(x) = d/dx[cos(x)] = -sin(x)

y^(2) + 9y - 52 #

Write down all the factors of '52'

Hence

1, 52 ; 2 , 26 ; 4 , 13 ;

By addition or subtraction, select a pair of factors that 'add' to '9'

They are, '4' & '13' ; Hence 13 - 4 = 9

Set up ther brackets , without the signs

Hence

( y 4)(y 13)

Since '52' is negative (-) , then the two signs are different.

Since '9' is positive then the larger factor is positive(+).

Hence inserting

(y - 4)(y + 13)

Factored!!!!

Done!!!!

x^(3) + 125 =>

x^(3) + 5^(3)

This factors to

(x + 5)(x^(2) - 5x + 5^(2) ) or (x + 5)(x^(2) - 5x + 25)

NB The clue is to spot that the constant (125) is a cubic numbers ( 5^(3)).

Similarly with other 'cubic factorings'.

Calculus was created in order to calculate volume and area. Everything in our world is not able to be measured by straight lines and 90 degree angles. Its roots can be traced back the the ancient Egyptians. You can read more about the history of calculus at the link provided below.

Since a square is a 2 dimensional object, it does not have a volume. You can however calculate the area of a square = length x width. Squares are also very useful in trigonometry.

However, you can calculate the volume of a cube (6 squares arranged edge to edge to form a box)

The volume of a cube = length x width x height

pi/4 radians = 45 degrees.

2pi radians = 360 degrees

pi radians = 180 degrees

pi/2 radians = 90 degrees

pi/4 radians = 45 degrees

pi/3 radians = 60 degrees.

et seq.,

-3

You don't say whether they've to be added or multiplied!

103 + 104 = 207; 207 = 3 x 3 x 23 so there is no solution in integers.

Applying the systematic method, we get:-

3x-5+5=20-5(cancelling -5 from both sides)

3x=15

3x/3=15/3

Therefore, x=15