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AnnyKZ [126]
3 years ago
15

the line passing through point (4, -1) and perpendicular to the line whose equation is 2x - y - 7 = 0

Mathematics
1 answer:
ch4aika [34]3 years ago
7 0

Answer:

y = -x/2 + 1

Step-by-step explanation:

Step 1: find the slope

2x - y - 7 = 0

2x - 7 = y

y = 2x - 7

Equation of a line is y = mx + c

m = slope

m = 2

Note: if two lines are perpendicular to the other, both lines are negative reciprocal of each other

Therefore m = -1/2

Step 2: using a point slope form

y - y1 = m( x - x1)

( 4 , -1)

x = 4

y = -1

y - (-1) = -1/2(x - 4)

y + 1 = -1/2(x - 4)

Open the bracket

y + 1 = -x + 4 / 2

y = (-x + 4) / 2 - 1

LCM = 2

y = -x + 4 - 2 / 2

y = (-x + 2)/2

Separate the two, so as to get the slope and the intercept

y = -x/2 + 2/2

y = -x/2 + 1

The equation of the line is

y = -x/2 + 1

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This cuboid is made from cm squares
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the dimensions of the large cube is 4 by 6 by 3      width height and depth

a) volume of the cube   Vol = area of the base times height  

              area of the base = the width times the depth  

              Volume = Base Depth

                            =  Width x Depth x Height

                            =      4 x 3 x 6

                            =       12 x 6

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b )  the volume of the smaller cuboid has different dimensions    

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          Volume = Base Depth

                            =  Width x Depth x Heigh

                            =    2 x 2 x 1  

 Vol smaller cuboid    =   4

      How many smaller cubes can be made?

            The obvious answer might be to straight up divide the large cube volume by the smaler cuboid volume. That might work IF all of the cuboid dimensions divide evenly into the cube dimensions.

  Number of cuboid  =   Volume of the cube  /  Volume of the cuboid

                                  =             72 / 4

                                  =        18

Check this answer by dividing the dimension of the cube by the cuboid

         4 by 6 by 3

         2 by 2 by 1

      (4/2) by (6/2) by (3/1)

        2    by    3   by     3       = 2 x 3 x 3     =    18

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