1. An open box is to be made from a sheet of card 40cm by 30cm. A square of side x cm is to be cut from each corner, as shown in the diagram, and then the sides will be folded up so that the
depth of the box will be x cm.

(a) Find in terms of x the length and width of the base of the box (ie AB and AD).
(b) The volume of the box is y. Write down an equation expressing y in terms of x.​

Step-by-step explanation:

AB = DC = 40 - 2x

AD = BC = 30 - 2x

there is not more explanation possible, I think.

we cut off from each side 2 pieces of x cm. so, AB, DC, AD, BC are the the remaining lengths.

the volume of the box is ground area times height (x is the length of the remaining flaps after the cut, so, when folding up these flaps/sides, they will be x cm high).

Volume = y = AB×AD×x

=> y = (40-2x)×(30-2x)×x = (1200 - 60x - 80x + 4x²)×x =

= (1200 - 140x + 4x²)×x = 4x³ - 140x² + 1200x

9.55 degrees.

step-by-step explanation:

the given angle is

1 cycle is equal to 2π radians. so 4π will be equal to two cycles.

5.166667π-4π = 1.166667π

hence, this angle goes a little more than negative x axis.

1.166667π-π= 0.166667π

hence, the reference angle is 0.166667π radians.

1 radian = 57.2958 degrees

now, in degrees, this should be equals to 9.55 degrees.

the multiples of 15 are 15, 30,45, 60, 75, 90, 105, 120, 135, 150, 165, 180, 195,   210, 225, 240, 255, 270, 285, 300, 315, 330, 345, 360, 375,   390, 405, 420, 435, 450, 465, 480, 495, 510, 525, 540, 555, 570, 585, 600, 615, 630, 645, 660, 675, 690, 705, 720, and 735.

the factors of 15 are 1, 3, 5, and 15.

hope that , fam!

-une, your fren : )