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1. The logo, for a company that makes chocolate, is a secto...

1. The logo, for a company that makes chocolate, is a sector of a circle of radius 2cm, shown as shaded in the diagram. The area of the logo is 3ncm2. diagram not to scale (a) Find, in radians, the value of the angle 0, as indicated on the diagram. (b) Find the total length of the perimeter of...

Part-A 1. The function f is defined by f(x) = e "...

Part-A 1. The function f is defined by f(x) = e "cos.r+x-1. By finding a suitable number of derivatives of f. determine the first non-zero term in its Maclaurin series. 2. Consider the functions f and g given by = 2 e (a) Show that f'(x)=g(x) and g'(x)=f(x). (b) Find the first thre...

1. In the diagram, ABD = BBC = 90°, AB = 4. Three point...

1. In the diagram, ABD = BBC = 90°, AB = 4. Three points A. B and are on level ground, 4.2 cm. BD = 5.8 cm and BCD = 37.6°. A is due south of B and C is 25 m due east of Calculate the following: B. BT is a vertical flagpole. (a) BAD. (b) CD. (a) If the angle of elevation of T from C ...

In this question, you given that 0053-1-1- 1 and sin T are ...

In this question, you given that 0053-1-1- 1 and sin T are The displacement of an object from a fixed point, o is given by s (t)=1-sin 2t - for OSISH (a) Find s'(t). In this interval, there are only two values of t for which the object is not moving. One value is (b) Find the other value. (...

Exercise 5A 1. Find the vector and cartesian equations of t...

Exercise 5A 1. Find the vector and cartesian equations of the (a) Show that L and M intersect and find their straight line joining the points A and B, whose point of intersection. coordinates are (-2, 1, 4) and (1, 7,6) respectively. (b) Show that L and N do not intersect. (c) Do M and N int...

Question 5 Standard KAPS Investigate graphs in the form of...

Question 5 Standard KAPS Investigate graphs in the form of y = a(x + k1)(x + k2)(x + k3) (x +kn) where a is L any non-zero constant. What effect does a have on the graphs of the polynomials? Justify your answer fully Question 6 C Standard MAPS There is an infinite number of functions which have...

Problem 1 Find the distance between two lines r1(t) = &l...

Problem 1 Find the distance between two lines r1(t) = <4t,t,2t>, and r2(s) = <0,1,0> + s <1, 1, 1>. The distance between two lines r1 and r2 is defined by the smallest length of PQ where P is on r1 and Q is on r2. Hint: Use cross product to find a plane con...

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