For which value of 0 is cot (0) undefined?
90°
180°
270°
450°

The value of cot theta is undefined for all the options

Step-by-step explanation:

I think the best way to go about this is by the use of a calculator.

All that needs to be done is to input the individual values to see where we have an answer that is out of it.

Now, moving away from the calculators, we know quite well that cot is a derivative of tan.

By knowing the values at which we have tan as undefined, we can appropriately see values where cot too would be undefined.

On a normal scientific calculator, there is no cot functionality.

The way around this is to express

Cot theta as 1/tan theta

Thus cot 90 = 1/cot(90) = calculation error

Cot 180 = 1/tan (180) = calculation error

Cot 270 = 1/tan 270 = calculation error

Cot 450 = 1/tan (450) = calculation error

This shows that the value of cot is undefined for all of these options

Formula for pyramid's volume: V = 1/3 * l² * h

Knowing that V = 560, l = 10 and h = 14, we can write it down as:

560 = 1/3 * 10 * w * 14
560 = 3 1/3w * 14
560 = 10/3w * 14
560 = 140/3w                      / * 3 (both sides)
1680 = 140w                       / ÷ 140 (both sides)
w = 12

Doublecheck:

560 = 1/3 * 10 * 12 * 14
560 = 1/3 * 120 * 14
560 = 1/3 * 1680
560 = 560

So it's correct :)