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Vector Form of the Equation of a Line We have, → r = → r 0 + t → v = (x 0 ,y 0 ,z 0 ) + t (a, b, c) This is known as the vector form of the equation of a line. The lo
Integrate following. ∫ -2 2 4x 4 - x 2 + 1dx Solution In this case the integrand is even & the interval is accurate so, ∫ -2 2 4x 4 - x 2 + 1dx = 2∫ o
In her last gymnastics competition Keri scored a 5.6 on the floor exercise, 5.85 on the vault, and 5.90 on the balance beam. What was Keri's total score? Keri's three scores re
If cos?+sin? = √2 cos?, prove that cos? - sin? = √2 sin ?. Ans: Cos? + Sin? = √2 Cos? ⇒ ( Cos? + Sin?) 2 = 2Cos 2 ? ⇒ Cos 2 ? + Sin 2 ?+2Cos? Sin? = 2Cos 2 ? ⇒
Differentiate following functions. (a) R ( w) = 4 w - 5 log 9 w (b) f ( x ) = 3e x + 10x 3 ln x Solution : (a) It will be the only example which doesn't includ
Two events A and B are independent events if the occurrence of event A is in no way related to the occurrence or non-occurrence of event B. Likewise for independent
Symmetry Definition : A line of symmetry divides a set of points into two halves, each being a reflection of the other. Each image point is also a point of the set. Defin
Geometric Applications to the Cross Product There are a so many geometric applications to the cross product also. Assume we have three vectors a → , b → and c → and we make
A Class 4 teacher was going to teach her class fractions. At the beginning of the term she asked the children, "If you had three chocolates, and wanted to divide them equally among
Katie's school has a rectangular courtyard whose area can be expressed as 3x 2 - 7x + 2. Which of the following could be the dimensions of the courtyard in terms of x? Since t
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