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Alex787 [66]
2 years ago
8

A semi-ellipse-shaped gate has a maximum height of 20 feet and a width of 15 feet, both measured along the center. Can a truck w

ith a height of 12 feet and a width of 16 feet with a load and 10 feet without a load pass through the gate?
Mathematics
1 answer:
Free_Kalibri [48]2 years ago
6 0
<h2>Answer with explanation:</h2>

We are given a semi-ellipse gate whose dimensions are as follows:

  Height of 20 feet and a width of 15 feet.

Now, if a truck is loaded then:

Height of truck is: 12 feet and a width of truck is: 16 feet

The truck won't pass through the gate since the width of truck is more than that of the gate.

When the truck is not loaded then:

 Height of truck is: 12 feet and a width of truck is: 10 feet

The truck would easily pass through  the gate since, the dimensions of truck are less than that of the gate.

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15 Points!
goblinko [34]

Answer:

coordinate of point A is (a,b)

coordinate of point C is (2c,d)

slope of AD and BC =\frac{b}{a-c}

Step-by-step explanation:

According to midpoint formula

If we have points P (x_{1} ,y_{1} ) and Q (x_{2} ,y_{2} )

then the coordinate (x,y) of mid point of line PQ is given by

x=\frac{x_{1} +x_{2} }{2} and y=\frac{y_{1} +y_{2} }{2}

now from the given diagram A is the mid point of line joining  R(0,0) and S(2a,2b)

Using midpoint formula, coordinates of point A is given by

x=\frac{0+2a}{2}= a and y=\frac{0+2b}{2} =b

so we have

coordinate of point A is (a,b)

Also C is the midpoint of line joining T (2c,2d) and V(2c,0)

coordinate of point C is given by

x= \frac{2c+2c}{2} =2c and y=\frac{2d+0}{2} =d

so we have

coordinate of point C is (2c,d)

it is given that coordinate of point B is (a+c, b+d) and coordinate of D is (c,0)

If we have points P (x_{1} ,y_{1} ) and Q (x_{2} ,y_{2} )

then the slope of PQ =\frac{y_{2} -y_{1} }{x_{2}-x_{1}  }

hence slope of AD= \frac{0-b }{c-a}

                                 =\frac{-b}{c-a}

                                  =\frac{-b}{-(a-c)}

                                  =\frac{b}{a-c}

and slope of BC  =\frac{d-(b+d)}{2c-(a+c)}

                            =\frac{d-b-d}{2c-a-c}

                             =\frac{-b}{c-a}

                              =\frac{b}{a-c}

so we have

slope of AD and BC =\frac{b}{a-c}

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