25 ++ 5−3 700557-5 3

The Determinant Of A 3 X 3 Matrix General Shortcut Method Studypug

There are 2401 students in a school A PT teacher wants them to stand in rows and columns such that the number of rows is equal to the number of columnsX x x x x= − − 2 4 6 cos 1 2!

5 3

5 3-Example 5 Find the equation of the line passing through (−4, −2) and (1, 3) Solution When finding a linear equation using slopeintercept form y=mxb y = m x b , the goal is to find m and then b Step 1 Find the slope m In this case, given two points, use the slope formula Substitute m=1 m = 1D) −5sin(5x)5ex1 − 14 3 3 √ x−1;

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find three points by also plugging in t1 = 1 and t2 = 1 which gives Q(5,2,−2) and R(1,3,3) So we have three points Note also that PQ = h1,2,−3i and PR = h−3,3,2i (so I really didn't have to find Q and R I could have just grabbed the direction vectors from the lines)3, 8 3 1, 4 7 5, 2 3 2 − − − − x xy y x x xy x Like Terms Terms that are constants or terms that contain the same variables raised to the same exponents We can combine and simplify only like terms Like Terms as constant –4, 154, 374, –037, 𝜋, ⋯ Like Terms as variable term –5 t5 2 Given the following equation, which could be the value of x ?

Np(1− p) = 5, which says that, P{495− 50 5 ≤ X −50 5 ≤ 505− 50 5} = P({−1 ≤ Z ≤ 1} 5 Suppose that 15% of the student population at small colleges consists of Gary Johnson fans (Libertarian candidate for president in most states) If a college has 300 students, what is the probability that at least 35 of them are GarySolving Literal Equations A Literal Equation is an equation containing more than one variable We can solve a literal equation for any one variable in terms of the others For example, if we wish to solve x − y = b for x, we will need to add y to each side of the equation in order to isolate x x − y = b x − y y = b y x = b y Example Solve AC = V for ADivide both sides of the Davneet Singh is a graduate from Indian Institute of Technology, Kanpur He has been teaching from the past 10 years He provides courses for Maths and Science at Teachoo

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2 Simplified Dirac identities thatthe"deltafunction"—whichhepresumestosatisfytheconditions ∞ −∞ δ(x−a)dx =0 δ(x−a)=0 for x = a —is5 4 3 2 1 −5 −4 −3 −2 −1 −1 1 2 3 4 5 −2 −3 −4 −5

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