Positive Slopes: Satisfying the Logic

Thread starter ktpr2
Start date Feb 15, 2005
Tags

Logic Positive

AI Thread Summary

Positive slopes can arise from points (x1, y1) and (x2, y2) under two conditions: both x1 must be less than x2 and y1 must be less than y2, or both x1 and x2 can be greater than their respective counterparts, resulting in a negative slope. The discussion highlights that positive slopes do not exclusively require x1 < x2 and y1 < y2, as the negative-negative case also produces a positive slope. Clarification on the conditions for positive slopes is essential for understanding slope behavior in coordinate geometry. The conversation emphasizes the importance of considering all possible scenarios when evaluating slopes. Understanding these conditions is crucial for accurate mathematical analysis.

Feb 15, 2005

ktpr2

Do all positive slopes taken from points (x1, y1) and (x2, y2) satisfy the following logic, x1 < x2 and y1 < y2?

Physics news on Phys.org

Feb 15, 2005

xanthym

Science Advisor

ktpr2 said:

Do all positive slopes taken from points (x1, y1) and (x2, y2) satisfy the following logic, x1 < x2 and y1 < y2?

Either of the following would have a POSITIVE slope:
Condition #1 -----> {x1 < x2} AND {y1 < y2}
Condition #2 -----> {x1 > x2} AND {y1 > y2}

~~

Last edited: Feb 15, 2005

Feb 15, 2005

ktpr2

whoops forgot about the negative/negative case; thanks

Thread 'I've come across another fluid pressure problem I don't understand'

Neglect gravity other than that of water; neglect friction. F1=ρgsh=1000*10*1*(1+4)=50000 N; F1=ρgsh=1000*10*0.1*4=4000 N; F3=50000-4000=46000 N?

View full post »

Thread 'Struggling to understand the concept of this question (ice cube in water optics question)'

TL;DR Summary: I came across this question from a Sri Lankan A-level textbook. Question - An ice cube with a length of 10 cm is immersed in water at 0 °C. An observer observes the ice cube from the water, and it seems to be 7.75 cm long. If the refractive index of water is 4/3, find the height of the ice cube immersed in the water. I could not understand how the apparent height of the ice cube in the water depends on the height of the ice cube immersed in the water. Does anyone have an...

View full post »

Thread 'Variable mass system : water sprayed into a moving container'

Starting with the mass considerations #m(t)# is mass of water #M_{c}# mass of container and #M(t)# mass of total system $$M(t) = M_{C} + m(t)$$ $$\Rightarrow \frac{dM(t)}{dt} = \frac{dm(t)}{dt}$$ $$P_i = Mv + u \, dm$$ $$P_f = (M + dm)(v + dv)$$ $$\Delta P = M \, dv + (v - u) \, dm$$ $$F = \frac{dP}{dt} = M \frac{dv}{dt} + (v - u) \frac{dm}{dt}$$ $$F = u \frac{dm}{dt} = \rho A u^2$$ from conservation of momentum , the cannon recoils with the same force which it applies. $$\quad \frac{dm}{dt}...

View full post »