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Home Question Bank Math Calculus Archive 2025 January 13

Calculus Questions from Jan 13,2025

Browse the Calculus Q&A Archive for Jan 13,2025, featuring a collection of homework questions and answers from this day. Find detailed solutions to enhance your understanding.

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A storage shed is to be built in the shape of a box with a square base. It is to have a volume of 729 cubic feet. The concrete for the base costs per square foot, the material for the roof costs per square foot, and the material for the sides costs per square foot. Find the dimensions of the most economical shed. Let x represent the length of one of the sides of the base and let represent the cost of the shed. What is the objective function? (Type an expression.) The interval of interest of the objective function is . (Simplify your answer. Type your answer in interval notation.) The length of one side of the shed's base is . The height of the shed is . Find the point on the line that is closest to the point . What is the least distance between and ? Let be the distance between the two points. What is the objective function in terms of one number, ? (Type an expression.) The interval of interest of the objective function is . (Simplify your answer. Type your answer in interval notation.) The point on the line that is closest to the point is (Type an ordered pair.) The least distance between and ( 52,0 is approximately (Round to the nearest tenth as needed.) A storage shed is to be built in the shape of a box with a square base. It is to have a volume of 539 cubic feet. The concrete for the base costs per square foot, the material for the roof costs per square foot, and the material for the sides costs per square foot. Find the dimensions of the most economical shed. Let x represent the length of one of the sides of the base and let C represent the cost of the shed. What is the objective function? (Type an expression.) The interval of interest of the objective function is . (Simplify your answer. Type your answer in interval notation.) The length of one side of the shed's base is The height of the shed is Find writing your answer in simplest form. L'objectir de T'exercice est de dêmontrer que, pour tout tos, Le cas a êté traité dans l'exercice D. Partie A icas On considere la fonction definie sur par: 1. Déterminer la dérivée de sur . What two positive real numbers whose product is 32 have the smallest possible sum? Let S be the sum of the two numbers. What is the objective function in terms of one number, x ? (Type an expression.) The interval of interest of the function is . (Simplify your answer. Type your answer in interval notation.) The numbers are and . (Type exact answers, using radicals as needed.) A curve cuts the -axis at and has gradient function (a) Find the equation of the curve. (a) (b) Sharks? Sormal to the curve at [ 6 marl Find the point P on the line that is closest to the point . What is the least distance between P and ? Let D be the distance between the two points. What is the objective function in terms of one number, x ? (Type an expression.) The interval of interest of the objective function is (Simplify your answer. Type your answer in interval notation.) The point P on the line that is closest to the point is (Type an ordered pair.) The least distance between P and is approximately (Round to the nearest tenth as needed.) Un solide a pour base la courbe décrite par la fonction de à . Si chaque section transversale perpendicular aux axes est un rectangle où la largeur est double de la hauteur, trouvez son volume. A curve cuts the -axis at and has gradient function (a) Find the equation of the curve. [4 marks (a (b) Show that the perpendicular bisector of the line joining to is the normal to the curve at [6 mark
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