prob. solving?

Question

pls show me the solutions.. tnx
Pls. help me solve dis..

1. The sum of a number and its reciprocal is 10/3. find the number.

2. A rectangle 25cm by 50cm is increased on all sides by the same amount. Its area increases 400 sq. m. By how much is each dimension increased?

3. At a conclusion of a committee meeting, a total of 28 handshakes were exchanged. Assuming each person was equally polite toward all the others, how many people were present?

4. Two trains left the same station at the same time. One was travelling due north at a speed that was 10kph than faster the other train, which was travelling due east. After one hour, the trains were 71 km apart. How fast, to the nearest km per hour, was each train travelling?

5. The base of a triangle is 4cm shorter than the altitude, and the area of a triangle is 126cm^2. Find the length of the base and the altitude.

pls. show me the solutions... tnx and godbless

Answer 1

sHuna,
Just a hint, when you're posting your homework, just post them one at a time.
A lot of people will answer a single question, but it there's 5 they'll say "to hell with it".

Anyway, to question 1.
N + 1/N = 10/3
That's a quadratic.

Answer 2

>>pls. show me the solutions...

I'm not going to do your homework for you, let alone for free. But I'll at least show you how you might be able to solve them on your own.

1. If n is the number, then its reciprocal is 1/n. So n + 1/n = 10/3. Solve this for n (hint: multiply both sides by n first).

2. If it was increased by x, then the length was increased to 25+x and the width to 50+x. So the new area is (25+x)(50+x). Set this equal to 400 and solve for x (hint: expand the expression and get it into a quadratic equation).

3. If there are n people in the room, then each of them shakes hands with n-1 other people. So it would seem there are n(n-1). However, we're counting each handshake twice, since a single handshake is a handshake for two different people at the same time. So set n(n-1)/2 equal to 28 and solve for n.

4. One train's speed was s, and the other was s+10. After one hour, these would also be their distances from the station in kilometers. Use the Pythagorean theorem to find the distance between the two trains (draw a diagram to see why), set it equal to 71, and solve for s. Then write s and s+10.

5. Remember the area of a triangle is (1/2)bh, where b is the base and h is the height (or altitude). If the height is h, then the base here is h-4. Plug these into the formula, set it equal to the given area, and solve for h. Then use h to find the base length too.

>>tnx and godbless

I'm an atheist, but thanks for the thought.

Answer 3

n + 1/n = 10/3

n^2 + 1 = nx10/3

3n^2 + 3 = 10n

3n^2 - 10n + 3 = 0

Solving for n,

n1 = [10 + sqrt(100 - 36)] / 6

= (10 + 8) / 6 = 3

Similarly n2 = (10 - 8) / 6 = 1/3

The two numbers are 3 and 1/3 respectively. Pl. note that we could have done it by common sense and inspection but then we will not know how to solve equations and quadratic equation solutions.

2) Original area = 25 x 50 = 1250 sq.cm

New Area = 400 sq.m

If a is one side, 2a is the other side and area = 2a^2

2a^2 = 400

a^2 = 200

a = 14.14 m

2a = 28.28 m