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iVinArrow [24]
3 years ago
9

The line passing through the points (-2, 10) and (5, -11)

Mathematics
1 answer:
aliya0001 [1]3 years ago
5 0
<h3>Answer:</h3>

y-intercept = (0, 4)

x-intercept = (3/4, 0)

<h3>Step-by-step explanation:</h3>

1 - Find the slope

slope = m = \frac{rise}{run} = \frac{y_2~-~y_1}{x_2~-~x_1} = \frac {-11-10}{5-(-2)} = \frac {-21}{7} = -3

2 - Plug the slope into y = mx + b and substitute a point into x and y to find the y-intercept, b, by isolating it.

y = mx + b

y = -3x + b

10 = (-3)(-2) + b

10 = 6 + b

-6   -6

4 = b

y-intercept = (0, 4)

3 - Rewrite the completed formula

y = -3x + 4

4 - Substitute 0 in for y to find the x-intercept

0 = -3x + 4

-4          - 4

-4 = -3x

-4/-3 = -3x/-3

 4/3 = x

x-intercept = (4/3, 0)

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An oil tank has to be drained for maintenance. The tank is shaped like a cylinder that is 3ft long with a diameter of 2.2 ft . S
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4 minutes 34 seconds will takes to empty the tank, if the starts completely full and oil drained at a rate of 2.5 ft^{3} per minute.

Step-by-step explanation:

              The given is,

                         Tank is shaped like a cylinder that is 3 ft long with a diameter of 2.2 ft.

                          Oil drained at a rate of 2.5 ft^{3} per minute.

Step:1

       Time taken to dry the oil tank is,

                           T   = \frac{Volume of oil}{Oil drain rate}  ....................................(1)

Step:2

      Volume of the oil is,

                           V = \pi  r^{2} h.................................................(2)

      Where, r - Radius of Cylinder

                             r = \frac{d}{2}

                             r = \frac{2.2}{2}

                             r = 1.1 ft

      From eqn (1),

                        V =  \pi × 1.1^{2} × 3

                           = 11.40398 ft^{3}

Step:3

     From equation (1)

                           = \frac{11.40398}{2.5}

                           = 4.56

                           = 4.56 minutes

                      T  = 4 minutes 34 seconds

Result:

      Time taken to dry the oil tank is 4 minutes 34 seconds, if a cylinder is 3 ft long with a diameter of 2.2 ft and oil is drained at a rate of 2.5ft^3 per minute.

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