???? for all you math experts????

Question

Someone please help me w/ this question.. I'm just really confused w/ step B. And I dont know if I did step A correctly, please help...

Show and explain EACH step in solving the following application problems:
a. The length of a rectangle is 1 cm longer than its width. If the diagonal of the rectangle is 5cm, what are the dimensions (the length and width) of the rectangle?
b. Supposed that the cost C, in dollars, of producing x chairs is given by C = 2x^2 - 40x + 2400. How many chairs can be produced for $4650?

Answer 1

A) the answer is that it is a 3 X 4 cm rectangle. You could solve this using trig or properties of triangles or pythagorean theorem (it is a triangle with a right angle, its diagnal has a length of 5, it's diagnal is opposite the 90 degree, etc). I just used pythagorean with simple guess and check, my first guess got it: a squared plus be squared equals c squared....c squared is 5 squared which equals 25, 4 squared plus 3 squared equals 25 voila!

B) 2xsquared-40x +2400 = 4650
just work of this equation and solve.

Answer 2

a) The diagonal and the side and bottom form a right-angled triangle, for which you can use Pythagoras. If width is x, then length is x+1, therefore x^2 + (x+1)^2 = 5. Solve for x.
b) Set the equation equal to $4650.
2x^2 - 40x + 2400 = 4650
subtract 2400 from each side
divide through by 2
solve for x (which is obviously # of chairs)

Answer 3

A) The Rectangle is 3 cm by 4 cm. This would make the diagonal (or hypotenuse) 5 cm using the Pythagorean theorem.

B) The answer is 45.

Answer 4

The a is easy. For any triange with a right angle and the hypotenuse is 5 the two sides are 3 & 4.

If you need to work it out the equasion goes
5 squared = S squared + ( S + 1) squared
25= S^ + S^ + 2S +1
25-1 = 2S^ + 2S
24= 2S^ + 2S
24/2 =( 2S^ + 2S ) /2
12= S^ + S
12= S ( S + 1 )
Trial and error then shows S=3 S + 1= 4

As for B, sorry, I don't have time to work it.

Answer 5

Here is how you get part b.

This is a quadratic equation so

y= -b + Sqrt (b^2-4ac) / 2a

C= 2X^2 - 40x + 2400

4650 = 2x^2 - 40x + 2400
2x^2 - 40x -2250 = 0

plug into quadratic formula

y= 40 + Sqrt (40^2 - 4(2)(-2250) ) / 2
This yields the answer of 45

Answer 6

Aristotle Winger Dr. Aristotle Winger gained his Ph. D on the age of 26 from Carnegie Mellon college interior the area of Mathematical Sciences. A graduate of the Howard college type of 1998, he's a lot extra suitable than in straightforward terms a mathematician. He has been Professor of arithmetic at Emory and Henry college in Southwestern Virginia because of the fact the fall of 2004.

Answer 7

a) 4x3 I used the pythagoreum method.

b) 45 I used the quadratic formula

Answer 8

A~

got me stumped too!____________________________________________________

B~

C= 2x ^ 2-40x +2400
C= 2^ 4650^ 2-40^ 4650 +2400
C= 9300^ 2- 186000+ 2400
C= 18600- 186000+2400
C= -167400+ 2400
C= (-165,000)