Dragan

An eight-sided game piece is shaped like two identical square pyramids attached at their bases. The perimeters of the square bases are 80 millimeters, and the slant height of each pyramid is 17 millimeters. What is the length of the game piece?

Square side is        a = 80/4 = 20 mm      a/2 = 10 mm

Slant height is         S = 17 mm

Pyramid height        h = sqrt [S² - ( a/2 )²]     h = 13.74772708 mm

The length of the game piece is      L = 2h = 27.49545417 mm   

Can you solve it now?  

If I put $500 into an account and left it alone for three years earning simple interest, and at the end of three years I withdrew $650, what interest rate was I earning? Can you explain how you got your answer so i can understand what to do.

Simple interest formula is:          A = P ( 1 + rt )

A - final amount                            650 = 500 ( 1 + r * 3 )  /500

P - principal                                   650/500 = 1 + 3r 

r - interest rate                                1.3 = 1 + 3r

t - time ( in years)                               3r = 0.3

                                                             r = 0.1    ( 10% )  

A water tank in the form of an inverted frustum of a right cone has an altitude of 38 ft., and a slant height of 46 ft. The ratio of the upper and lower radii is 5:4. Compute for the measurement of the shorter radius.

Height =>      h = 38 ft

Slant height => H = 46 ft

Upper radius  R = ?                         R = D * 5 

Lower radius   r = ?                          r = D * 4     

Ratio    R : r = 5 : 4

Let the defference of R - r be  D

D = sqrt(H² - h²)  = sqrt (672)

I wish I could delete my "answer". I made a boo-boo. 

Thanks for GeoGebra!  

Quadrilateral PQRS is a square whos side length is 10. Let X and Y be points outside the square so that XQ = YS = 6 and XP = YR = 8. Find XY^2.

SR = 10

YR = 8

YS = 6

Angle SYR = 90°

Angle RSY = ?         tan(RSY) = YR / YS   ∠ RSY = 53.13° 

LY = cos(53.13°) * YS = 3.6

LS = sqrt [(YS)² - (LY)²] = 4.8

YN = SP + 2 * LS = 19.6

NX = SR - 2 * LY = 2.8

XY² = YN² + NX² = 392    

The corner of a unit cube is chopped off such that the cut runs through the three vertices adjacent to the vertex of the chosen corner. What is the height of the remaining cube when the freshly-cut face is placed on a table?

Let the area of a single side of the cube be A = 25 cm².

The length of the edge is  E = 5 cm

Let D be diagonal of a side of the cube.    D = 5 / sin(45°) = 7.071067812              

Angle after cutting the corner is: tan(β) = E / (D/2)       β = 54.7356°

The height of the remaining cube is   H = D * sin(β)  = 5.7735 cm  

Square MATH has sides of length 4, and N is the midpoint of TH. A circle with radius 2 and center N intersects a circle with radius 4 and center M at points P and H. What is the distance from P to MH.

MH = 4

HN = 2

Angles HMN and PMN are equal.

tan(∠ HMN) = HN / MH = 26.565°

Angle HMP = (∠ HMN) * 2 = 53.13°

LP => the distance from P to MH

LP = sin(∠ HMN) * MP          LP = 3.2