I understand the question to mean that when somebody gives you the volume of the sphere (V), you want to be able to find its radius (R). When you have the radius, you calculate the volume with V = 4/3 pi R3, so we'll just solve this equation for R. V = 4/3 pi R3 (3V)/(4 pi) = R3 R (radius) = cube root of [ (3V) / (4 pi) ] R = 0.6203 times the cube root of ( Volume )

To find the CUBE root , we note that 27 is 3^(3) . So '3' is the cube root of '27'.

Also 8 = 2^(3) . so '2' is the cube root of '8'.

So the cube root of 26 is between '2' & '3'.

Since it is very close to '3' ; (by 26 & 27) they we can try 2.9^3

2.9^(3) = 24.389 (2.9 is too low) So try 2.95

2.95^(3) = 25.67.. ( Still too low) Try 2.975

2.975^(3) = 26.333 .. ( Now too high) So try 2.97

2.97^(3) = 26.198 ( Too high Try 2.968

2.968^(3) = 26.145... (Too high ; try 2.965

2.965^(3) = 26.065... (Too high : try 2.964

2.964^(3) = 26.0396 (Too high )

You keep trying like this. Until you find the root to the required number of decimal places.

However on the calculator 26^(1/3) = 2.962496068....

Simplyfy means reduce to its lowest/smallest terms.

e.g.

6/12 simplified is = 1/2

a^3 / a^2 = 'a' simplified to its lowest tertms.

Sin(30) = 0.5 or (1/2)

Trigonometric data is integrated in your scientific calculator.

'42' being an even number will divide by '2'

Hence

2)42 = 21

3)21 = 7

7 ) 7 = 1

So the prime factors of '42' are 2^(1) X 3^(1) x 7^(1).

#NB the '1' is the exponent. 2,3, & 7 are the primes.

As you were copying the question, did you notice the drawing alongside it ?

Well, see, that sketch is actually part of the question; anybody who wants to

try and answer it needs to see that drawing.

YES!!!!

However, y = x^(3) does not have a vertex , but an horizontal point at the origin.

However, y = ax^(3) + bx^(2) + dx + c will have vertices , and they are found by differemntiating, and equating to zero.

The equation is: (x+3)^2 + (y+4)^2 = 4

The Classical Exmple is C = pi d ; The circle circumference and 'd' the diameter. 'pi' is the constant of proportion.

However if given a set of data , that is directly proportional , then we say

y is directly proportional to 'x'

We now equate this by inserting a constant of proportion(k)

Then

Hence

y = kx

Then k = y/x

This is how 'pi' was found.

e.g.

C = 6.2831....

d = 2

Hence

k(pi) = 6.2831... / 2 = 3.141592....

Other sonstants of proportion are

y is inversely proportional to the square of 'x'

Hence

y = k X 1/x^(2)

k = yx^(2)

et.seq.

Hope that helps!!!!

3

NO!!!

sqrt(1512 = 38.88444.... Since it is a decimal , its 'squaring is not perfect.

'x' times '2y' is written as '2xy'.

In Algebra.

Addition is shown as 'a + b' '.

Subtraction is shown as 'a - b'

Multiplication is shoewn as 'ab' (NB no multiplication sign 'x', as it might be confused with the unknown 'x'.

Division is showen as a/b ( like a fraction).

NB '2y' means '2' Times 'y' So overall 2 X y X x = 2xy . Notice ; for clarity ,I have put in 'capital ' 'x' for multiplication. However, hopefully you can see that it may become unclear which is the unknown 'x'.

5.6 = 5 6/10 = 5 3/5 = 28/5 (as an Improper Fraction).

The PYRAMIDS at Giza in Egypt.

Hence the name 'pyramid'.

'Step ladder' to find the factors.

3)57 = 19

19. 19 = 1

&

3)69 = 23

23)23 = 1

The Only and greatesty common factor (GCF) is '3' .

NB '19' & '23' are prime numberd and have no common factors.

6*6*6*6 is the same as 64 in exponential terms

16

The answer will range between '2' & '-2'

Reason; The Sine function ranges between '1' & '-1' , so if it has a coefficient of '2', this will increase the range to '2' & '-2'.

The definitive answer is 'pH = -log(10) [H^(+)]

In words, ' pH is the negative logarithm, to the base ten, of the hydrogen ion concentration.

As an example

If H^(+) is 0.002

Then

pH = -log(10)[0.002]

On the calculator using the 'log' button

pH = -(-2.69897...)

pH = 2.69897...

pH = 2.70

NB This would be an acidic pH

NNB pH is always quoted to 2 d.p. only.

NNNB Do NOT use the 'ln' button on a calculator.

0.052 least

0.52

5.2 greatest

y^(3) - 2y^(2) + 4y

Factor out 'y'

Hence y(y^2 - 2y + 4)

This will not factor any further.

intersection.

-1/2 X -2 = -- 2/2 = (+) 1 = 1

x^(2) = 5x + 2

x^(2) - 5x - 2 = 0

This does NOT factor so apply the Quadratic Eq;n

x = { - - 5 +/- sqrt[(-5)^2 - 4(1)(-2) }} / 2(1)

x = { 5 +/- sqrt[25 + 8]} / 2

x = { 5 +/- sqrt(33)} / 2

x= { 5 +/- 5.7445... } / 2

x = 10.7445... / 2 = 5.37228....

&

x = -0.7445626... / 2 = -0.37228...

Tan = o/a

Tangent of an angle = opposite over adjacent.

Here are the other Trig. functions.

SINe(angle) = opposite/hypotenuse

COSine(angle) = adjacent/hypotenuse

COTangent(angle) = adjacent/opposite

Cosecant(CSC)(angle) = hypotenuse/oppositre

SECant(angle) = hypotenuse/ adjcent.