How long will P2.5M amounts to P4.5M at 8% compounded quarterly?

Problem
By the conditions of a will, the sum of P2.5M is left to a girl to be held in a trust fund by her guardian until it amounts to P4.5M. When will the girl receive the money if the fund is invested at 8% compounded quarterly?

A.   7 years C.   7.42 years
B.   6.8 years D.   7.25 years

 

Length of hypotenuse of a right triangle of known area in the xy-plane

Problem
For triangle BOA, B is on the y-axis, O is the origin, and A is on the x-axis. Point C(5, 2) is on the line AB. Find the length of AB if the area of the triangle is 36 unit2.

A.   24.31 units C.   13.42 units
B.   18.30 units D.   10.80 units

 

The Straight Line

Definition
Straight line is the locus or path of a point that moves without changing its direction.
 

straight-line-01.jpg

 

General Equation
The general equation of the straight line is given by

$ax + by + c = 0$

 

Volume of regular tetrahedron of given length of edges

Problem
Determine the volume of a regular tetrahedron of edge 2 ft.

A.   1.54 ft3 C.   1.34 ft3
B.   1.01 ft3 D.   0.943 ft3

 

Problem 02 - Semi-Elliptical Arch in a Stone Bridge

Problem
A semi-elliptical arch in a stone bridge has a span of 6 meters and a central height of 2 meters. Find the height of the arch at a distance of 1.5 m from the center of the arch.
 

A.   1.41 m C.   1.56 m
B.   1.63 m D.   1.73 m

 

Curvature and Radius of Curvature

Curvature and Radius of Curvature in xy-Plane | Derivation of Formula | Differential Calculus

Curvature (symbol, $\kappa$) is the mathematical expression of how much a curve actually curved. It is the measure of the average change in direction of the curve per unit of arc. Imagine a particle to move along the circle from point 1 to point 2, the higher the number of $\kappa$, the more quickly the particle changes in direction. This quick change in direction is apparent in smaller circles.
 

Circle of Curvature

 

Problem 921 | Kern Area of a Wide Flange Section: W360 x 122

Problem 921
Calculate the sketch the kern of a W360 × 122 section.
 

921-wide-flange-section-properties.jpg

 

Problem
In the expansion of (2x - 1/x)10, find the coefficient of the 8th term.

A.   980 C.   960
B.   970 D.   990

 

Problem
The formula $v = \sqrt{2gh}$ give the velocity, in feet per second, of an object when it falls h feet accelerated by gravity g, in feet per second squared. If g is approximately 32 feet per second squared, find how far an object has fallen if its velocity is 80 feet per second.

A.   80 feet C.   70 feet
B.   100 feet D.   90 feet

 

Problem
Earth is approximately 93,000,000.00 miles from the sun, and the Jupiter is approximately 484,000,900.00 miles from the sun. How long would it take a spaceship traveling at 7,500.00 mph to fly from Earth to Jupiter?

A.   9.0 years C.   6.0 years
B.   5.0 years D.   3.0 years

 

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