Explanation Given: The stopping distance of a certain vehicle can be calculated approximately by formula d = 0.0611 v 2 + 0.796 v + 5.72 and it has stopped before 140 feet. Definition used: Standard quadratic equation : “An equation in which the variable appears to the second power, but to no higher power, is called a quadratic equation. A standard quadratic equation can be expresses as, a x 2 ︸ + b x ︸ + c ︸ = 0 ↓ ↓ ↓ [ x 2 -term ] [ x -term ] [ Constant term ] That is every quadratic equation must have x 2 -term, but the x -term or constant tem may be missing.” Procedure used: 1. Identify the values of a , b and c by comparing the given equation with the standard quadratic equation a x 2 + b x + c = 0 . 2. Substitute the values of a , b and c into the quadratic equation formula x = − b ± b 2 − 4 a c 2 a . 3. Simplify the equation for x . 4. Check the solution by back substituting the values of x in the original equation. Calculation: The given stopping distance of a certain vehicle can be calculated approximately by formula d = 0.0611 v 2 + 0.796 v + 5.72 . Where v is the speed of the vehicle. Here a vehicle has stopped before 140 feet. Substitute d = 140 in the above formula as follows. d = 0.0611 v 2 + 0.796 v + 5.72 140 = − 0.0611 v 2 + 0.796 v + 5.72 0.0611 v 2 + 0.796 v + 5.72 − 140 = 0 0.0611 v 2 + 0.796 v − 134.28 = 0 Here the quadratic equation is 0.0611 v 2 + 0.796 v − 134.28 = 0 . Step 1: Identify the values of a , b and c by comparing the given equation with the standard quadratic equation a v 2 + b v + c = 0 . 0

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Chapter 11, Problem 19CPS

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To find: The maximum speed of a vehicle of before applying brakes.

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Exercice 2: Soit & l'ensemble des nombres réels. Partie A Soit g la fonction définie et dérivable sur R telle que, pour tout réel x. g(x) = - 2x ^ 3 + x ^ 2 - 1 1. a) Étudier les variations de la fonction g b) Déterminer les limites de la fonction gen -oo et en +00. 2. Démontrer que l'équation g(x) = 0 admet une unique solution dans R, notée a, et que a appartient à | - 1 ;0|. 3. En déduire le signe de g sur R. Partie B Soit ƒ la fonction définie et dérivable sur R telle que, pour tout réel s. f(x) = (1 + x + x ^ 2 + x ^ 3) * e ^ (- 2x + 1) On note f la fonction dérivée de la fonction ƒ sur R. 1. Démontrer que lim x -> ∞ f(x) = - ∞ 2. a) Démontrer que, pour tout x > 1 1 < x < x ^ 2 < x ^ 3 b) En déduire que, pour x > 1 0 < f(x) < 4x ^ 3 * e ^ (- 2x + 1) c) On admet que, pour tout entier naturel n. lim x -> ∞ x ^ n * e ^ (- x) = 0 Vérifier que, pour tout réel x, 4x ^ 3 * e ^ (- 2x + 1) = e/2 * (2x) ^ 3 * e ^ (-2x) puis montrer que: lim x -> ∞ 4x ^ 3 * e…

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Chapter 11 Solutions

EBK MATHEMATICS FOR THE TRADES

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The maximum speed of a vehicle of before applying brakes.

Solution Summary: The author calculates the maximum speed of a vehicle before applying brakes by formula d=0.0611v2+0.796v+5.72.

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