math experts help needed? Thank you?

Question

Solve the formula for the given letter. Assume all variables represent non-negative numbers. E=nc^2, for c.


The width of a rectangle is 5 ft less than the length. The area is 6ft squared. Find the length and the width.


Astudent opens a mathematics book to two facing pages. The product of the page number is 2352. Find the page numbers.


Determine the nature of the solutions of the equation. x^2+16=0.


Solve by completing the square. x^2+(3/2)x=3

Answer 1

E = nc² for c
E/n = c²
√(E/n) = c : since you specified c is not negative. Otherwise the c could also be negative, since roots are both positive or negative.

x(x - 5) = 6
x² - 5x - 6 = 0
(x - 6)(x + 1) = 0
X = 6 or -1
Since a length can not be negative , the length is 6 and the width is 1: 6ft x 1 ft = 6 ft²

x(x + 1) = 2352
x² + x - 2352 = 0
(x - 48)(x + 49) = 0
The positive root is the smaller number, or x = 48
So the book is opened to pages 48 and (48 + 1 or) page 49

The solutions to x² = -16 are x = ±√-4 -- an imaginary number ±4i -- since no real number, when squared, can give a negative number

x² + (3/2)x = 3 : original equation
x² + (3/2)x + 9/16 = 3+ 9/16 : (1/2)(3/2) = 3/4 : (3/4)² = 9/16 : add this to both sides
(x + 3/4)² = 57/16 : factor on left
x + 3/4 = ±(√57) / √16 : root both sides
x + 3/4 = ± (√57) / 4 : simplify denominator on right
x = -3/4 ± (√57) / 4 : get x alone on left
x = (-3 ± √57) / 4 : put over common donominator

Answer 2

expensive, it is not had to be expert to remedy those problems. think the selection is N then: a million) 4N+3=15 4N=15-3=12 N=12/4=3 N=3 2) 2N+4=sixteen 2N=sixteen-4=12 N=12/2=6 3) 26=3N+5 26-5=3N 21=3N N=21/3=7 N=7 4) 4N+12=32 4N=32-12=20 N=20/4=5 N=5 5) 6N+33=35 6N=35-33=2 6N=2 N=2/6 N=a million/3

Answer 3

2) Since W = L - 5 and the area (L * W) is 6, you can say

L * (L-5) = 6

Solve for L

3) P * (P+1) = 2352

Solve for P

Answer 4

E=nc^2, for c.
divide by n
E/n = c^2
take square root
c = square root(E/n)