A ladder is leaning against a house at an angle inclined 45 degrees from the ground. If the ladder touches the house 7 m height from the ground, how far is the base of the ladder from the house?

There is a 90 degree triangle (right-angled triangle) formed between the house, the ground, and the ladder. We are given that the angle at which the ladder inclines is 45 degrees, so given any dimension of the triangle, we can determine the other dimensions, using the trigonometric ratios. Since we are given the dimension opposite the angle in question, and we need to find the length adjacent to the angle, we can use the tangent property, ie tan 45 degrees = 7/x where x is the distance of the ladder base from the house. Since tan 45 = 1 then 7/x=1, ie x =7 m. so the ladder is 7 m from the house.

At 100 C, for the following reaction: 2NOBr (g) <======> 2NO (g) + Br2 (g) Kp =60.6 One hour after NOBr was introduced into the reaction vessel, the contents were analyzed, and it was found that the reaction quotient Q was 30.3. In which direction is it likely that the reaction will proceed?

The reaction quotient Q is less than the equilibrium constant Kp, so this suggests that the ratio of products to reactants is less than what it is at equilibrium. The reaction will then move so as to bring the state to equilibrium i.e. supply more products, by moving in the forward direction.

Solve for x,y and z. 2x - 3y + z = 14 A x + 2y - 3z = -7 B 4x - y + 10z = 21 C

From B, x = 3z-2y-7 D Substituting in A gives: 6z - 4y - 14 - 3y + z =14, Giving 7z - 7y = 28, or z - y = 4 z = 4 + y E Substituting back in D gives: x = 3(4 + y) - 2y - 7 = 12 + 3y - 2y - 7 = y + 5 x = y + 5 F Substituting E and F into C gives: 4(y+5) - y + 10(4 + y) = 4y + 20 - y + 40 + 10y = 21 13y + 60 = 21 y =(21 - 60)/13 = -3 G Substituting G into E gives: z = 4 - 3 = 1 Substituting G into F gives: x = -3 + 5 = 2 Hence solution is x = 2, y = -3, z = 1