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vazorg [7]
3 years ago
5

Find the equation of the line passing through (2,3) and (1,5)

Mathematics
1 answer:
gavmur [86]3 years ago
5 0

Answer:

y =-2x+7

Step-by-step explanation:

Hello : let  A(2,3)    B(1,5)

the slope is :   (YB - YA)/(XB -XA)

(5-3)/(1-2)  = 2/-1 =-2

an equation is : y=ax+b     a is a slope

y = -2x +b

 

the line through point  (2,3) :  3 = (-2)(2)+b    

b = 7

the equation is : y =-2x+7    

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3 years ago
a) Estimate the volume of the solid that lies below the surface z = 7x + 5y2 and above the rectangle R = [0, 2]⨯[0, 4]. Use a Ri
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In the x direction we consider the m=2 subintervals [0, 1] and [1, 2] (each with length 1), while in the y direction we consider the n=2 subintervals [0, 2] and [2, 4] (with length 2). Then the lower right corners of the cells in the partition of R are (1, 0), (2, 0), (1, 2), (2, 2).

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\displaystyle\iint_Rf(x,y)\,\mathrm dx\,\mathrm dy\approx f(1,0)\cdot1\cdot2+f(2,0)\cdot1\cdot2+f(1,2)\cdot1\cdot2+f(2,2)\cdot1\cdot2=\boxed{164}

###

More generally, the lower-right-corner Riemann sum over m=\mu and n=\nu subintervals would be

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