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Evaluate \(\int_{3}^{2} \int_{0}^{\frac{\pi}{2}} \enspace (y + y^{2}cosx ) \enspace dx dy\)
Answered
Mathematics I
A particle moves in a straight line and has acceleration given by
a(t) = 6t
2
+ 1
. Its initial velocity is
4m/sec
and its initial displacement is
s(0) = 5cm
. Find its position function
s(t).
Answered
Mathematics I
If \(f(x,y) = \frac{xy}{x^2 + y^2}\), does f(x, y) exist, as (x, y) → (0, 0)?
Answered
No Subject
A farmer has 2000 ft of fencing and wants to fence off a rectangular field that borders a straight river. He needs no fence along the river. What are the dimensions of the field that has the largest area?
Answered
Mathematics I
Sketch the curve \(y = \frac{1}{x – 3}\)
Answered
Mathematics I
Find the equation of the tangent to the parabola y = x
2
+ x + 1 at (0, 1)
Answered
Mathematics I
Dry air is moving upward. If the ground temperature is 20
0
and the temperature at a height of 1km is 10
0
C, express the temperature T in
0
C as a function of the height h (in kilometers), assuming that a linear model is appropriate. (b)Draw the graph of the function in part (a). What does the slope represent? (c) What is the temperature at a height of 2km?
Answered
Mathematics I
If f(x) = x
2
then find \(\frac{f(2+h) – f(2)}{h}\)
Answered
Mathematics I
Asked on 2077 Exam
The output of a digital circuit (y) is given by this expression: \( y=(CB + \overline{C}A)(\overline{BA})\) where A,B and C represent inputs. Draw a circuit of the above equation using OR, AND and NOT gate and hence find its truth table.
Answered
First Semester
Assuming that atoms are in a crystal structure and arranged as close-packed spheres, what is the ratio of the volume of the atoms to the volume available for the simple cubic structure? Assume a one-atom basis.
Answered
First Semester
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