7 the product of two positive numbers is 100 what

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7.The product of two positive numbers is 100. What numbers will produce the leastpossible sum? Confirm that the sum is in fact a minimum. (8 marks)2
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Chapter 11 / Exercise 02
Calculus: Early Transcendental Functions
Edwards/Larson
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x=100x=10y=10010y=10s=x+ys=10+10s=20d2dx2=x+100xf '(x)=1100x2f ' '(x)=200x3f' '(10)=200(10)3f' '(10)=15=0.20Therefore, the minimum value is 20.
8.ABCis a triangle whereAis(1,3),Bis(−2,1), and(−1,4). Determine whetherABCis a right-angle triangle.Cis
Task #3: Communication Questions9.Discuss how displacement, velocity, and acceleration are related to a function and itsderivatives. Create an equation for the displacement of an object and determine theequations for the velocity and acceleration of the object at any timet. (6 marks)
t=0.59sEquation for Velocity:v(t)=s '(t)v(t)=0.12(t)v(0.59)=0.12(0.59)v(0.59)=0.071m/sEquation for Acceleration:a(t)=v'(t)a(t)=0.24m/s210. What is the difference between a scalar and a vector quantity? Include an example ofeach. (4 marks)
Scalar Quantity Example: AreaVector Quantity Example: Acceleration11. List and describe the three properties of vector arithmetic. Give an example of eachproperty using vectors in Cartesian form. (12 marks: 4 marks for each property))
¿(−1,13)u+(v+w)=(2,3)+[(1,5)+(2,5)]12¿(5+5,(¿)]¿(2,3)+¿¿(2,3)+(3,10)¿(−1,13)Therefore,(u+v)+w=u+(v+w).2.Distributive Property of Scalar MultiplicationFor any scalar quantity a and vector quantitiesuv:a(u+v)=au+avoExample:a(u+v)= 5[(4, 3,7) + (-3, 0, 6)]= [(20, 15, 35) + (-15, 0, 30)]= (5, 15, 65)au+av= 5(4, 3, 7) + 5(-3, 0, 6)= (20, 15,35) + (-15, 0, 30)= (5, 15, 65)Therefore,a(u+v)=au+av.3.Associative Property of Vector Addition
For any three vectorsu,vw:(u+v)+w=u+(v+w)oExample:(u+v)+w=[(3,5)+(6,4)]+(2,0)¿[(36),(5+4

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Calculus: Early Transcendental Functions
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Chapter 11 / Exercise 02
Calculus: Early Transcendental Functions
Edwards/Larson
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