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Given the vectors u = 3i - 2j + k, v = i + 2j - 4k, w = -2i + 4j - 5k use vector methods to answer the following:
(a) Prove u, v and w can form the sides of a triangle;
(b) Find the vector projection of u on v;
(c) Find the angle between u and v (to nearest degree);
(d) Find a unit vector normal (perpendicular) to the plane of the triangle in (a).
How many integers satisfy (sqrt n- sqrt 8836)^2 Solution) sqrt 8836 = 94 , let sqrt n=x the equation becomes... (x-94)^2 (x-94)^2 - 1 (x-95)(x-93) hence 93 8649 the number o
Proper and Improper Fractions: Example: 3/8 proper fraction 8/3 improper fraction 3/3 improper fraction Here an improper fraction expressed as the sum of an in
How long does it take for an amount of money P to double itself if it is invested at 8% interest compounded 4 times a year?
Indeterminate form : The 0/0 we initially got is called an indeterminate form. It means that we don't actually know what it will be till we do some more work. In the denominator
By the method of completion of squares show that the equation 4x 2 +3x +5 = 0 has no real roots. Ans: 4 x 2 +3 x +5=0 ⇒ x 2 + 3/4 x + 5 = 0 ⇒ x 2 + 3/4 x +
Differentiate following functions. (a) f ( x ) = 15x 100 - 3x 12 + 5x - 46 (b) h ( x ) = x π - x √2 Solution (a) f ( x ) = 15x 100 - 3x 12 + 5x - 46 I
Suppose that the number of hours Katie spent practicing soccer is represented through x. Michael practiced 4 hours more than 2 times the number of hours that Katie practiced. How l
Graph f ( x ) = |x| Solution There actually isn't much to in this problem outside of reminding ourselves of what absolute value is. Remember again that the absolute value f
Q. Show Frequency Tables? Ans. A frequency table is used to show how often a piece of data occurs. Example: Michelle decides to keep track of the number of phone call
Determine the linear approximation for f(x)= sin delta at delta =0
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