answer:We know that the point (-4, -7) lies on line n, so we can substitute these values into the equation of line n to find k. -7 = k(-4) - 7 -7 = -4k - 7 0 = -4k k = 0 Therefore, the value of k is 0. The answer is: 0

answer:Fabian walks for 3 hours and covers 5 kilometers per hour, so in 3 hours, he covers 3 x 5 = 15 kilometers. To reach a total of 30 kilometers, Fabian needs to walk 30 - 15 = 15 more kilometers. Since Fabian covers 5 kilometers per hour, he needs to walk 15 / 5 = 3 more hours. 3 The answer is: 3

answer:To find the points of intersection, we set the two equations equal to each other: [4cos theta = 8 sin theta.] Dividing both sides by 4 gives cos theta = 2 sin theta. Dividing both sides by sin theta (we can do this because sin theta is not zero) gives cot theta = 2. Since cot theta = frac{cos theta}{sin theta}, we can rewrite this equation as frac{cos theta}{sin theta} = 2. Using the identity cot theta = frac{1}{tan theta}, we can rewrite this equation as frac{1}{tan theta} = 2. Taking the reciprocal of both sides gives tan theta = frac{1}{2}. The solutions to this equation are theta = frac{pi}{6} and theta = frac{7pi}{6}, since the tangent function has a period of pi and the tangent function is positive in the first and third quadrants. Therefore, there are boxed{2} points of intersection between the two graphs. The answer is: 2

answer:To find the cross product of two vectors, we can use the formula begin{pmatrix} a b c end{pmatrix} times begin{pmatrix} d e f end{pmatrix} = begin{pmatrix} bf-ce cd-af ae-bd end{pmatrix}. Using this formula, we have begin{pmatrix} 5 2 -6 end{pmatrix} times begin{pmatrix} 1 1 3 end{pmatrix} = begin{pmatrix} (2)(3)-(-6)(1) (-6)(1)-(5)(3) (5)(1)-(2)(1) end{pmatrix} = begin{pmatrix} 12 -21 3 end{pmatrix}. Therefore, the cross product is boxed{begin{pmatrix} 12 -21 3 end{pmatrix}}.The answer is: begin{pmatrix}12-213end{pmatrix}