Question

Q4. In the AABC given below BC=5cm, ZC 40° and ZB = 50°, then answer the у - following questions (i) Is AB=AC ? If not, why ? (ii) Which one is longer side, AB or AC ? (iii) The largest side is opposite to the smallest angle or to the largest angle?​

Answer 1

Answer:

I assume that this box does not need a lid.

Suppose we cut a square of side x out each corner of the piece of cardboard, and then turning up the sides. The dimensions of the resulting box will be:

height = x

width = 15–2x

length = 24–2x

So volume = V = x(15–2x)(24–2x)

Multiplying out the brackets gives V = 4x³ - 78x² + 360x

We need to find the value of x that maximises V. We can do this by differentiation:

dV/dx = 12x² - 156x + 360

At the maximum, dV/dx = 0, so 12x² - 156x + 360 = 0

Dividing both sides of this equation by 12 gives x² - 13x + 30 = 0

Factorising gives (x-3)(x-10) = 0

We have a multiplication giving an answer of 0, so either (x-3)=0 or (x-10)=0

So x=3 or x=10

x=3 gives V=3(15–6)(24–6)=486

x=10 gives V=10(15–20)(24–20)=-200, which is a silly answer.

So the answer is that the maximum volume is 486 cubic inches, and this is achieved by cutting a square of side 3 inches from each corner.

Step-by-step explanation: