Vishal C.

Tutor for 3 years

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Pre-Algebra

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Question:

Ravi has a board that is 3 feet long. He plans to use it to make 4 shelves whose lengths are to be a series of consecutive even numbers. How long should each shelf be in inches?

Vishal C.

Answer:

Being consecutive even numbers, we need to add 2 to the previous number. Assign variables: Let x= length of the first shelf x+2= length of the second shelf x+4= length of the third shelf x+6= length of the fourth shelf Convert three feet to inches $$3*{12} = 36$$ Sum of four shelves is 36 x + x + 2 + x + 4 + x + 6 = 36 Combine like terms 4x + 12 = 36 Isolate variable x 4x = 36 - 12 4x = 24 x = 6 So, the lengths of the shelves in inches should be 6, 8, 10 and 12.

Calculus

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Question:

If the hypotenuse of the right triangle is given, show that the area is maximum when the triangle is isosceles?

Vishal C.

Answer:

Let the two sides and hypotenuse be x, y and c respectively. now, according to Pythagoras, $$x^{2} +y^{2}=c^{2}$$ Now, differentiating with respect to x, we have, 2x+2yy'=0 y'= -x/y Area of the triangle: $$A= (x*y)/2$$ Now, differentiating the area, we have, dA/dx= [xy'+y]/2 =0 xy'+y = 0 Substituting the value ofy', we have, x(-x/y) + y = 0 $$y= x^{2}/y$$ $$y^{2} = x{2}$$ y=x so, the triangle should be isosceles.

Algebra

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Question:

Evaluate f(2)-f(1) f(x)= 6x+1

Vishal C.

Answer:

Given the function f(x)= 6x+1 f(2)-f(1) is given by... f(2)-f(1)= (6*2+1)-(6*1+1) = 6

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