10.) ¿Cuál de los siguientes puntos NO pertenece al gráfico de la función \( h(x)=1-\times 2 \) A) \( (0,1) \) B) \( (1,0) \) C) \( (-1,0) \) D) \( (\sqrt{ } 2,-1) \) E) \( (1,1) \)

Classify the given function as a polynomial function, rational function, or root function, and then fi \( f(x)=\sqrt{x^{2}-3 x-18} \)

Exercise \( 7.11 \mathrm{Q} 1(2012) \) (d)A proton travelling with a velocity of \( 3.00 \times 10^{7} \mathrm{~m} \mathrm{~s} \) collides with an oxygen nucleus, of mass \( 2.56 \times 10^{-26} \mathrm{~kg} \) that is at rest, and is scattered through an angle of 90 r . Calculate the velocity and direction of the oxygen nucleus using Newtonian mechanics. [12] (l)A rescue helicopter of mass 810 kg , supports itself in a stationary position by imparting a downward velocity, v , to the air in a circle of radius 4.0 m . The density of the air is 1.20 kg \( \mathrm{~m}^{-3} \). Calculate: (i)the value of v (ii)the power, P , required to support the helicopter [5]

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 \( 1+3+5+7+9+\cdots+(2 n-1) \).

An unknown compound has the following chemical formula: where \( x \) stands for a whole number. Measurements also show that a certain sample of the unknown compound contains 4.2 mol of chlorine and 1.41 mol of aluminum. Write the complete chemical formula for the unknown compound.

There are two functions that can be used to describe the percent of Americans 25 and older who have completed an associate's degree or higher. For both functions \( f(x)=0.72 x+35.2 \) and \( g(x)=0.04 x^{2}+0.47 x+34.9, x \) is the number of years since 2010, and any \( y \) (or \( f(x) \) or \( g(x)) \) is the percent of Americans 25 and older who have completed an associate's degree or higher. Assume that the trend of \( g(x) \) continues. Find \( g(18) \) and describe in words what this means.