Physics, 29.08.2019 16:30 alext8691

Physics
on the graph above, what is the total displacement during the time interval 0s-8s ?

Physics on the graph above, what is the total displacement during the time interval 0s-

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Answer from: Quest

This is actually a calculus question. so, basically, this is a related rates question where you are given 1 quantity and you have to find the other. we'll define some variables first.x = 9 ftdx/dt = 7 ft/secl = 15 ftsince you want to find the area, you have to find a formula for it. which is: $a = \frac{1}{2}x*h$ we know the base (x), but we don't know the height (h). we can figure it out by solving for it. we have to form an equation which we can figure out height from given the information we have. this equation is: $x^2+h^2=l^2$ plug in known values: $9^2+h^2=15^2$ solve for h: $h^2 = 15^2-9^2$ $h^2=144$ $h = \sqrt{144}=12$ now, let's solve for the rate at which h is changing. we can do so by differentiating the pythagorean theorem (above). let's do that: $x^2+h^2=15$ $2x \frac{dx}{dt}+2h \frac{dh}{dt}=0$ $\frac{dh}{dt} = \frac{-2x \frac{dx}{dt} }{2h}$ $\frac{dh}{dt} = \frac{-x \frac{dx}{dt} }{h}$ plug in values: $\frac{dh}{dt} = \frac{-9*7}{12} = \frac{-63}{12} = \frac{-21}{4}$ now we have all the given information to do this problem. so, to figure out the rate of change of area, we can differentiate (with respect to time) the earlier equation: $\frac{d}{dt}(a) = \frac{d}{dt} (\frac{1}{2}x*h)$ which is equal to: $\frac{da}{dt}= \frac{1}{2}( \frac{dx}{dt}h+x \frac{dh}{dt})$ plug in known values: $\frac{da}{dt} = \frac{1}{2}(7*12+9* \frac{-21}{4} ) = \frac{1}{2}(84- \frac{189}{4} )$ $\frac{1}{2}( \frac{147}{4}) = \frac{147}{8}$ so, the area of the triangle is changing at approximately 18.375ft²/sechope this all makes sense. if it doesn't, either contact me, or watch khan academy - he explains it real well. special credit to turtaniumx and quietself for letting me know of the error, and fix it!

Answer from: Quest

Hello there,your correct answer would be 4 joules.40/10=4as 1n/m=1 4n-m= 4 joules hope this .~jurgen

Answer from: Quest

From a chemical point of view, proteins are by far the most structurally complex and functionally sophisticated molecules known. this is perhaps not surprising, once one realizes that the structure and chemistry of each proteinhas been developed and fine-tuned over billions of years of evolutionary history. we start this chapter by considering how the location of each amino acid in the long string of amino acids that forms a protein determines its three-dimensional shape. we will then use this understanding of protein structure at the atomic level to describe how the precise shape of each protein molecule determines its function in a cell.

Answer from: Quest

The kind of energy involved in hearing and vision is wave energy.

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