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April 17, 2014

Homework Help: math

Posted by ahh on Wednesday, November 8, 2006 at 7:10am.

16) AB = 3.2cm
BC = 8.4cm
The area of the triangle ABC is 10cm.
Calculate the perimeter and give the answer correct to 3 significant figures.


19) Bill said that the line y=6 cuts the curve x + y =25 at two points.
a) By eliminating y, show that Bill is incorrect.
b) By eliminating y, find the solutions to the simultaneous equations
x + y = 25
y = 2x - 2


26)
c) Factorise (p+q) + 5(p+q)
e) Simplify 2t * 3rt4


30) It is always possible to draw a circle which passes through all four vertices of a rectangle. Explain why.



(26) (c) factor out the (p+q) term and you get (p+q)(p+q+5)
(d) factor out the t term. I assume the last 4 is supposed to be an exponent.

(30) Draw the intersecting diagonals of the rectangle. Use geometry axioms and theorems to prove that the distance from the intersection of the diagonals to the corners are equal for all 4 corners. Therefore a circle centered on the intersection passes through all corners.

16) AB = 3.2cm
BC = 8.4cm
The area of the triangle ABC is 10cm.
Calculate the perimeter and give the answer correct to 3 significant figures

1--Triangle ABC has a base of BC = 8.4, a left side of AB = 3.2 and an unknown left side of AC.
2--Draw altitude AD perpendicular to BC
3--SInce the area A = 10, A = 8.4h/2 = 4.2h making h == 2.38095.
4--With AB = 3.2 and h == 2.38095, BD = sqrt(3.2^2 - 2.38095^2) = 2.138
5--CD therefore equals 8.4 - 2.138 = 6.262.
6--Thus, AC = sqrt(2.38095^2 + 6.262^2) = 6.699.
7--The perimeter is therefore 8.4 + 3.2 + 6.699 = 18.299.

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