Question

Helppppp pleaseeee!!! Its 5 Marks

Answer 1

As the picture shows, we have

V = (x+5)(x-2)x =30x

<=> x(x^2+3x-10) =30x

<=> x^3 + 3x^2-10x-30x = 0(*)

<=> x^3 +3x^2 -40x = 0

<=> x(x-5)(x+8) =0

Solve for (*), there are 3 solution :

5,

0(invalid),

-8(invalid)

=> 3 dimensions of rectangular box: 5, 3, 10

Answer 2

5, 10 and 3

Explanation:

We know that that to find the volume of a cuboid you have to multiply the length by width by the height so we can set up an equation to work out the value of x

→ Form equation

( x + 5 ) × ( x - 2 ) × ( x ) = 30x

→ Expand out the brackets

( x² - 2x + 5x - 10 ) × ( x ) = 30x

( x ) × ( x² + 3x - 10 ) = 30x

x³ + 3x² - 10x = 30x

→ Minus 30x from both sides to make an equation

x³ + 3x² - 40x = 0

→ First factor 'x' out of the equation

x ( x² + 3x - 40 ) = 0

→ Now we have to solve the equation

x ( x + 8 ) ( x - 5 ) = 0

( x + 8 ) = 0 so x = -8

( x - 5 ) = 0 so x = 5

We have 2 solutions but since we are finding the volume of a cuboid we don't use the negative value since it isn't logical to have negative number side length's so we discard -8. The true value of x is 5. Now we have to substitute 5 into all of the x length's and the volume to make sure the solution is correct

→ Substitute x = 5 into ( x ), ( x + 5 ), ( x - 2 ) and 30x

→ 5 , 10 , 3 and 150

We know that the side lengths are 5, 10 and 3 and we know that volume is 150 so we multiply the 3 numbers together to make that value of x = 5 is correct so,

5 × 10 × 3 = 50 × 3 = 150

So the value of x = 5 is correct