21. แดง ซื้อผ้าตัดชุด ยาว 2 เมตร 15 เซนติเมตร ผ้าผืนนี้ยาวกี่เซนติเมตร ก. 2.15 ข. 21.5 ค. 215 ง. 2,115

Q 7. Find the values of the other five trigonometric (i) \( \cot \theta=\frac{12}{5}, \theta \) in quadrant III

If a crane worker lifts a crate with a mass of 120 kg from the ground to a shipping container that is 30 meters off the ground, by how much has the worker increased the gravitational potential energy of the crate? (Recall that g \( =9.8 \mathrm{~m} / \mathrm{s}^{2} \) )

candi3.5- 26

19. \( 1+2+3+4+5+\ldots+n=\frac{n(n+1)}{2} \) (a) i) Show that this formula is true for the sum of the first 8 natural numbers. ii) Find the sum of the first 400 natural numbers. (b) i) Show that \( 2+4+6+8+\cdots+2 n=n(n+1) \). ii) Find the sum of the first 200 even numbers. iii) Find the sum of the first 200 odd numbers. (c) i) Use the formula at the beginning of the question to find the sum of the first \( 2 n \) natural numbers. ii) Find a formula, in its simplest form, for \( 1+3+5+7+9+\cdots+(2 n-1) \).

Suppose that you are going to program a computer to carry out an iterative calculation of motion involving nonconstant forces. Which of the following calculations should be done before starting the repetitive "loop" calculations? Specify the initial (vector) momentum of each object. Define constants such as \( G \). Specify an appropriate value for the time step. Specify the initial (vector) position of each object. Update the (vector) position of each object.