X² + y² - 8x - 12y + 52 = 36
x² - 8x + y² - 12y + 52 = 36
x² - 8x + y² - 12y = 88
(x² - 8x + 16) + (y² - 12y + 36) = 88 + 16 + 36
(x - 4)² + (y - 6)² = 138
(h, k) = (x, y) = (4, 6)
Comment
This is an area problem. The key words are 120 square feet and 12 feet longer.
And of course width is a key word when you are reading this.
Formula
Area = L * W
Givens
W = W
L = W + 12
Substitute and Solve
Area = L* W
120 = W*(W + 12)
W^2 + 12W = 120 square feet
w^2 + 12w - 120 = 0
This does not factor easily. I would have thought that a graph might help but not if the dimension has to be to the nearest 1/100 of a foot. The only thing we can do is use the quadratic formula.
a = 1
b = 12
c = - 120
w = [ -b +/- sqrt(b^2 - 4ac) ]/(2a)
w = [-12 +/- sqrt(12^2 - 4*(1)(-120)] / 2*1
w = [-12 +/- sqrt(144 - (-480)]/2
w = [-12 +/- sqrt(624)] / 2
w = [- 12 +/- 24.979992] / 2 The minus root has no meaning whatever.
w = (12.979992) / 2
w = 6.489995 I'll round all this when I get done
L = w + 12
L = 6.489995 + 12
L = 18.489995
check
Area = L * W
Area = 6.489995*18.489995
Area = 119.999935 The difference is a rounding error
Answer
L = 18.489995 = 18.49 feet
W = 6.489995 = 6.49 feet
Note: in the check if you round first to the answer, LW = 120.0001 when you find the area for the check. Kind of strange how that nearest 1/100th makes a difference.
The radius is always half of the diameter so it would be 20 inches
Step-by-step explanation:
since packages are similarsimilar packages. The ratio of the volumes is 8:125. Determine the dimensions of the bigger package. The dimensions of the smaller package are... Height= 45cm, Length= 80cm, and Width= 25cm.
Length of bigger package = <em><u>8</u></em><em><u>0</u></em><em><u>×</u></em><em><u>1</u></em><em><u>2</u></em><em><u>5</u></em><em><u>/</u></em><em><u>8</u></em><em><u>=</u></em><em><u>1</u></em><em><u>2</u></em><em><u>5</u></em><em><u>0</u></em><em><u>c</u></em><em><u>m</u></em>
Width of bigger package =<em><u>2</u></em><em><u>5</u></em><em><u>×</u></em><em><u>1</u></em><em><u>2</u></em><em><u>5</u></em><em><u>/</u></em><em><u>8</u></em><em><u>=</u></em><em><u>3</u></em><em><u>9</u></em><em><u>0</u></em><em><u>.</u></em><em><u>6</u></em><em><u>2</u></em><em><u>5</u></em><em><u>c</u></em><em><u>m</u></em>
Height of bigger package =<em><u>4</u></em><em><u>5</u></em><em><u>×</u></em><em><u>1</u></em><em><u>2</u></em><em><u>5</u></em><em><u>/</u></em><em><u>8</u></em><em><u>=</u></em><em><u>7</u></em><em><u>0</u></em><em><u>3</u></em><em><u>.</u></em><em><u>1</u></em><em><u>2</u></em><em><u>5</u></em><em><u>cm</u></em>