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wolverine [178]
3 years ago
7

I need help with these questions

Mathematics
1 answer:
inysia [295]3 years ago
6 0

Answer:

28. m<A=20°, m<B=70°

32. m<A=103°, m<B=77°

Step-by-step explanation:

complementary angle=a+b=90°

supplementary angle=a+b=180°

28. A+B=90°

      5x+17x+2=90°

      22x+2=90°

      22x=90-2

      22x=88

        22x/22=88/22

      x=88/22=<u>4</u>

m<A=5x=5*4=<u>20°</u>

m<B=17x+2=17*4+2=68+2=<u>70°</u>

         <u>Check</u>

A+B=90°

20+70=90°

<u>90°=90°</u>

32. A+B=180°

     x+11+x-15=180°

     2x-4=180°

     2x=180+4

     2x=184

     2x/2=184/2

     x=184/2

     x=<u>92</u>

m<A=x+11=92+11=<u>103°</u>

m<B=x-15=92-15=<u>77°</u>

     <u>Check</u>

A+B=180°

103+77=180°

<u>180°=180°</u>

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Step-by-step explanation:

The area of a disk of revolution at any x about the x- axis is πy² where y=2x. If we integrate this area on the given range of values of x from x=0 to x=1 , we will get the volume of revolution about the x-axis, which here equals,

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Now we have to calculate the volume of revolution about the y-axis. For that we have to first see by drawing the diagram that the area of the CD like disk centered about the y-axis for any y, as we rotate the triangular area given in the question would be pi - pi*x². if we integrate this area over the range of value of y that is from y=0 to y=2 , we will obtain the volume of revolution about the y-axis, which is given by,

\int\limits^2_0 {pi - pix^{2} } \, dy = \int\limits^2_0 {1 - y^{2}/4 } \, dy

If we just evaluate the integral as usual we will get 4pi/3 again(In the second step i have just replaced x with y/2 as given by the equation of the line), which is the same answer we got for the volume of revolution about the x-axis. Which means that the answer B) is correct.

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