Engineering Mathematics

Question 1

An elliptical plot of garden has a semi-major axis of 6 m and a semi-minor axis of 4.8 meters. If these are increased by 0.15 m each, find by differential equations the increase in area of the garden in sq. m.

Answer 1

1.62π

Question 2

The diameter of a circle is to be measured and its area computed. If the diameter can be measured with a maximum error of 0.001 cm and the area must be accurate to within 0.10 sq.cm. Find the largest diameter for which the process can be used.

Answer 2

64

Question 3

The altitude of a right circular cylinder is twice the radius of the base. The altitude is measured as 12 cm. With a possible error of 0.005 cm, find the approximately error in the calculated volume of the cylinder.

Answer 3

0.188 cu cm

Question 4

What is the allowable error in measuring the edge of a cube that is intended to hold a cu m, if the error in the computed volume is not to exceed 0.03 cu m?

Answer 4

0.0025

Question 5

The expression for the horsepower of an engine is P = 0.4 n x2 where n is the number of cylinders and x is the bore of cylinders. Determine the power differential added when four cylinder car has the cylinders rebored from 3.25 cm to 3.265 cm.

Answer 5

0.156 hp

Question 6

A surveying instrument is placed at a point 180 m from the base of a bldg on a level ground. The angle of elevation of the top of a bldg is 30 degrees as measured by the instrument. What would be error in the height of the bldg due to an error of 15 minutes in this measured angle by differential equation?

Answer 6

1.05

Question 7

Find the approximate increase by the use of differentials, in the volume of the sphere if the radius increases from 2 to 2.05.

Answer 7

2.51

Question 8

If the area of a circle is 64π sq mm, compute the allowable error in the area of a circle if the allowable error in the radius is 0.02 mm.

Answer 8

1.01 sq mm

Question 9

If the volume of a sphere is 1000π/6 cu mm and the allowable error in the diameter of the sphere is 0.03 mm, compute the allowable error in the volume of a sphere

Answer 9

4.71 cu mm

Question 10

A cube has a volume of 1728 cu mm. If the allowable error in the edge of a cube is 0.04 mm, compute the allowable error in the volume of the cube.

Answer 10

17.28 cu mm

Question 11

Find the coordinate of the vertex of the parabola y = x2 – 4x + 1 by making use of the fact that at the vertex, the slope of the tangent is zero.

Answer 11

(2,-3)