suppose that receiving OP Do HomeworkLindsey Heckmann Google

OP Do Homework-Lindsey Heckmann Google Chrome Secure l https://www.mathxl.com/Student/PlayerHomework.aspx?homeworkld questionid 5&flushed; false&clda4498783;&centenwin; MATH 1023-College Algebra Summer I 2017 online Lindsey Heckmann 4 6/4/17 11:02 PM Homework: Homework Section 2.2 Circles Score 0 of 1 pt 5 of 8 (8 complete) v HW Score: 75%, 6 of 8 pts (x 2.2.41 Question Help Suppose that receiving stations x, Y and z are located on a coordinate plane at the points (-4-2) and (-69) respectively The epicenter of an earthquake determined to be 13 from X 5 units from 10 units from Z Where on the coordinate plane is the epicenter located? Find the coordinates of the epicenter. Type an ordered pair your answer in the answer bo and then chec Answer parts showing MATH 023 College

Solution

1. The coordinates of the receiving stations X, Y, Z are ( 12,6), (-4,-2) and (-6,9) respectively. Let the coordinates of the epicenter of the earthquake be (x,y). Then, we have [(x-12)²+ (y-6)²] = 13² or,               (x²+y² -24x-12y)+144+36 = 169 or,(x²+y²-24x-12y)= 169 -180 or,(x²+y²-24x-12y)= -11…(1), [(x+4)²+(y+2)²] = 5² or, (x²+y²+8x+4y)+16+4 = 25 or, (x²+y²+8x+4y) = 25-20 or, (x²+y²+8x+4y) = 5…(2) and [(x+6)²+(y-9)²] = 10² or, (x²+y²+12x-18y)+36+81= 100 or, (x²+y²+12x-18y)= 100-117 or, (x²+y²+12x-18y) = -17…(3). Now, on subtracting the 1^st and the 3^rd equations from the 2^nd equation, we get (8x+4y +24x+12y) = 5+11 or, 32x+16y = 16 or, 2x+y = 1…(4) and (8x+4y -12x+18y) = 5+17 or, -4x +22y =22 or, -2x+11y = 11…(5). Then, on adding the 4^th and the 5^th equations, we get 2x+y-2x+11y=1+11or,12y =12 so that y = 12/12 or, y = 1. On substituting y = 1 in the 4^th equation, we get 2x+1 = 1 or, 2x = 1-1 = 0 so that x = 0.Thus, the coordinates of the epicenter of the earthquake are (0,1).

2. Let the coordinates of the points whose distance from the point (-5,0) is 13 and whose distance from the point (0,-1) is also 13 be (x,y). Then, we have (x+5)²+ y²=13 or, x²+10x+25+y² =13 or, x²+10x+y² =-12   …(1) and x²+(y+1)² = 13 or, x²+y²+2y+1=13 or, x²+y²+2y= 12…(2). Now, on subtracting the 1^st equation from the 32^nd equation, we get x²+y²+2y-( x²+10x+y²) = 12+12 or, 2y-10x = 24 or, y -5x = 12 or, y = 12 +5x. Thus, the required points are ( x, 12+5x), where x is an arbitrary real number.

3 (a). The cost of the wooden board is $ 0.60 per 2 ft. Let x = 2p +q , where p,q are real numbers such that 10 x 16 . Then the cost of the wooden board which is x ft. long is c = $ 0.60p.Further, The only possible values of p are 5, 6,7,8. Since the extra length of the wooden board, beyond a multiple of 2 ft. is not charged, the cost of the wooden board is c = $ 0.60p such that 5 p 8 and 3.00 c 4.80.None of the given answers is correct.

(b). If the wooden board is 8.6 ft. = 2*4 + 0.6 ft. long its cost is $ 4*0.60 = $2.40, and if the wooden board is 15.1 ft. = 2*7 + 1.1 ft. long its cost is $ 7*0.60 = $ 4.20.

3. The equation of a line with slope m and y-intercept c is y = mx +c. Here, the given line passes through the points (-1,3) and (5,4) so that m = (4-3)/[5-(-1)] = 1/6 so that its equation becomes y = x/6 +c. Further, on substituting x = -1 and y = 3 in its equation, we get 3 = -1/6 +c so that c = 3+1/6 = 19/6. Then, the the equation of the required line is y = x/6 + 19/6 or, 6y = x +19 or, x-6y = -19.

4. The equation of a line with slope m and y-intercept c is y = mx +c. Here, the slope of the given line is 14/5. Let its equation be y = 14x/5 +c. Since this line passes through the point (-1,-1), on substituting x = -1 and y = -1 in its equation, we get -1 = (-14/5)+c so that c = (14/5)-1 = 9/5. Then the equation of the required line is y = 14x/5 + 9/5 or, 5y = 14x +9 or, 14x-5y = -9.