# Thread: Having trouble with these two questions!

1. ## Having trouble with these two questions!

"A container built to hold statures is based on a rectangular cuboid"

The volume in cubic meters is given by the formula V=x^3 + 6x^2 + 8x

a) Show that the sides have lengths x,x+2 and x+4 meters.
b)An expresssion for the surface area of the container is 6x^2 + 24x +16
If the surface are of the container is 142m^2, what is the volume?

Last one:

"A rectangular garden has a perimeter of 22m and an area of 21.84m^2. The width of the garden is x meters and the length is y meters.

a) Write two equations for this situation in terms of x and y
b) Solve the equations simultaneously and state the dimensions of the garden

Any help would be great!

2. Originally Posted by krinkle
"A container built to hold statures is based on a rectangular cuboid"

The volume in cubic meters is given by the formula V=x^3 + 6x^2 + 8x

a) Show that the sides have lengths x,x+2 and x+4 meters.

factor x^3 + 6x^2 + 8x

b)An expresssion for the surface area of the container is 6x^2 + 24x +16
If the surface are of the container is 142m^2, what is the volume?

solve the quadratic equation 6x^2 + 24x + 16 = 142 for x ... then substitute the solution that makes sense in the context of the problem into the expression for V.

Last one:

"A rectangular garden has a perimeter of 22m and an area of 21.84m^2. The width of the garden is x meters and the length is y meters.

a) Write two equations for this situation in terms of x and y

2(x+y) = 22

xy = 21.84

b) Solve the equations simultaneously and state the dimensions of the garden

do it.
...

3. 2(x+y) = 22

xy = 21.84

What are the answers to these?

4. Also how to solve quadratic equation 6x^2 + 24x + 16 = 142 for x ... I thought the formula always ended in 0?

5. Originally Posted by krinkle
Also how to solve quadratic equation 6x^2 + 24x + 16 = 142 for x ... I thought the formula always ended in 0?
try subtracting 142 from both sides and then using the quadratic formula

6. Originally Posted by krinkle
2(x+y) = 22
x+y =11
y=11-x

xy = 21.84
x(11-x)=21.84

Can you continue from here?

.

7. Originally Posted by linalg123
.
Lol,
No... does y = 11-x too?

8. Originally Posted by linalg123
try subtracting 142 from both sides and then using the quadratic formula
Both sides of what?
Deeply confused!
any solutions so i can work backwards?

9. Originally Posted by krinkle
Also how to solve quadratic equation 6x^2 + 24x + 16 = 142 for x ... I thought the formula always ended in 0?
subtracting 142 from both sides of the equation gives us
6x^2 + 24x + 16 - 142 = 142 - 142
6x^2 + 24x - 126 = 0
taking a common factor of 6 gives us 6( x^2 + 4x - 21) = 0
this is now in the correct form to use the quadratic equation. Can you do this?

2(x+y) = 22
x+y =11
y=11-x

xy = 21.84
x(11-x)=21.84
11x - x^2 = 21.84
x^2 - 11x + 21.84 = 0
this is also now in the correct form to use the quadratic equation

10. Originally Posted by linalg123
subtracting 142 from both sides of the equation gives us
6x^2 + 24x + 16 - 142 = 142 - 142
6x^2 + 24x - 126 = 0
taking a common factor of 6 gives us 6( x^2 + 4x - 21) = 0
this is now in the correct form to use the quadratic equation. Can you do this?

2(x+y) = 22
x+y =11
y=11-x

xy = 21.84
x(11-x)=21.84
11x - x^2 = 21.84
x^2 - 11x + 21.84 = 0
this is also now in the correct form to use the quadratic equation

For the first quadratic im getting -7 and 3 - which one is right?

11. Originally Posted by krinkle
For the first quadratic im getting -7 and 3 - which one is right?
remember x is a length. It doesn't make sense to have a negative length

12. 2(x+y) = 22
x+y =11
y=11-x

however, what are the values for x and y?

13. Originally Posted by krinkle
2(x+y) = 22
x+y =11
y=11-x

however, what are the values for x and y?

subbing this into your other equation xy= 21.84 gives
xy = 21.84
x(11-x)=21.84
11x - x^2 = 21.84
x^2 - 11x + 21.84 = 0 (which has the form a(x^2) + bx + c = 0)

so you use the quadratic formula to solve for x. Do you know how to do this?
once you have solved for x, you plug that value into x+y=11 and solve for y.