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Properties of Dot Product
u→ • (v→ + w→) = u→ • v→ + u→ • w→ (cv→) • w→ = v→ •(cw→) = c (v→•w→)
v→ • w→ = w→ • v→ v→ • 0→ = 0
v→ • v→ = ||v→||2 if v→•v→ = 0 then v→ = 0→
The augmented matrix from a system of linear equations has the following reduced row-echelon form (a) How many equations are there in the system? (b) How many variab
Explain Adding Negative Fraction? To add negative fractions: 1. Find a common denominator. 2. Change the fractions to their equivalents, so that they have common denominators
1/a+b+x =1/a+1/b+1/x a+b ≠ 0 Ans: 1/a+b+x =1/a+1/b+1/x => 1/a+b+x -1/x = +1/a +1/b ⇒ x - ( a + b + x )/ x ( a + b + x ) = + a + b/ ab ⇒
the automatic hopper loader is set to put 36 tons of coal in each car. the actual weights of coal loaded into each car arw normally distributed with a mean of 36 tons and a standar
Find the Quadratic polynomial whose sum and product of zeros are √2 + 1, 1/ √2 + 1 Ans: sum = 2 √2 Product = 1 Q.P = X 2 - (sum) x + Product ∴ x 2 - (2 √2 )
A man travels 600km partly by train and partly by truck. If he covers 120km by train and the rest by truck, it takes him eight hours. But, if he travels 200km by train and the res
Players and spectators enter a ballpark according to independent Poisson processes having respective rates 5 and 20 per hour. Starting at an arbitrary time, compute the probability
a pizza driver delivered 27 pizzas in one night he delivered more then one pizza to only one house . every other house he only delivered pizza to 18 houses . how many pizzas did he
1. A rectangular piece of cardboard measuring 26 inches by 42 inches is to be made into a box with an open top by cutting equal size squares from each comer and folding up the side
y=x4/4lnx-x4/16 then dy/dx=? Solution) dy/dx=-x^3/4(2/lnx-1)^2. ^ means power
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