Question

A woman works out by running and swimming. When she runs, she burns 7 calories per minute. When she swims, she burns 8 calories per minute. She wants to burn at least 336 calories in her workout. Write an inequality that describes the situation. Let x represent the number of minutes running and y the number of minutes swimming. Because x and y must be positive, limit the boarders to quadrant I only.
8x+7y>=336

Sn: 1^2+...+(3n-2)^2 = n(6n^2-3n-1)/2

 
S1: 1^2 = 1(6*1^2-3(1)-1)/2

S2: 1^2+4^2 = 2(6*2^2-3*2-1)/2

S3: 1^2+4^2+7^2 = 3(6*3^2-3*3-1)/2

There all true but I don't know the induction for this

Answer 1

I do not have time
NOTE
in your previous question, the determinant of the 3 by 3 coef matric is zero, can not solve.

Answer 2

Oh okay thank you so much

Answer 3

Your inequality is correct. I have no idea what meaning of the rest is.

Think on a graph x,y, quadrant 1.

all the area inside the triangle boardered by x axis, y axis, and the line 8x+7y=335, the region inside is not an allowable solution. On the line, and outside the triangle, any point is allowed and is a solution. Thus, 2000,4000 is an allowable solution, whereas 2,5 is not.

Answer 4

Thank you!