Help please time limit...Amanda is choosing between two exercise routines.
1 answer:
Amanda must spend more than 8 minutes on Routine #1 to burn more calories than Routine #2.
Step-by-step explanation:
Routine # 1;
Calories burned in running = 15.5 per minute
Let,
t be the minutes spent running.
T = total calories burned
T = 15.5t
Routine # 2;
Calories burned while walking = 22 calories
Calories burned while running = 12.75 per minute
T = 12.75t + 22
For burning more calories in Routine 1;
Routine 1 > Routine 2
Dividing both sides by 2.75
Amanda must spend more than 8 minutes on Routine #1 to burn more calories than Routine #2.
Keywords: linear inequality, division
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c) Equating the two expressions for the shorter leg, we have
.. 60/(x -1) = √(2x -1)
.. 3600/(x -1)^2 = (2x -1)
.. (2x -1)(x^2 -2x +1) = 3600
.. 2x^3 -5x^2 +4x -3601 = 0
d) There is one positive real root, at x=13. A graphical solution works well.
The three sides of the triangle are 5 in, 12 in, 13 in.
_____
5-12-13 is a well-known Pythagorean triple. It is the next smallest one after 3-4-5.
b) Based on the area, the other leg is 2*30/(x -1). Based on the Pythagorean theorem, the other leg is √(x^2 -(x -1)^2).
c) Equating the two expressions for the shorter leg, we have
.. 60/(x -1) = √(2x -1)
.. 3600/(x -1)^2 = (2x -1)
.. (2x -1)(x^2 -2x +1) = 3600
.. 2x^3 -5x^2 +4x -3601 = 0
d) There is one positive real root, at x=13. A graphical solution works well.
The three sides of the triangle are 5 in, 12 in, 13 in.
_____
5-12-13 is a well-known Pythagorean triple. It is the next smallest one after 3-4-5.