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Evgesh-ka [11]
3 years ago
15

A hot air balloon descends from an altitude of 2,000 feet at a constant rate of 90 feet per minute. The graph shows the altitude

of the balloon over time. Write a linear function in the form y = mx + b to represent the situation.
Mathematics
2 answers:
liberstina [14]3 years ago
6 0

Answer:

y=90x+2,000

Step-by-step explanation:

90 is the rate of change because the hot air balloon descends 90 feet per minute.

And 2,000 is the starting point because the hot air balloon started the descent at 2,000 feet.

ohaa [14]3 years ago
3 0

Answer:

y(t)=(-90\frac{feet}{minute})t+2000feet

Step-by-step explanation:

Given the linear function in the form

y=mx+b

We are going to represent the situation using the linear function.

We are going to call the variable ''x'' time. We can write x = t ⇒

y=mt+b

y(t) will be the altitude function that depends on the variable ''t'' that is time in minutes.

In the instant t=0minutes the hot air balloon has an altitude of 2000 feet ⇒

y(0)=2000feet=m(0)+b=b ⇒ b=2000feet

We can think that the slope ''m'' is the constant rate of the function.

Given that the hot air balloon descends, m ⇒m=-90\frac{feet}{minute}

Now we write the function :

y=mt+b\\

y(t)=(-90\frac{feet}{minute})t+2000feet

For example, when t = 0 ⇒

y(0)=(-90\frac{feet}{minute}).0+2000feet=2000feet

Or if we want to find the time when the hot air balloon finally descends :

0=(-90\frac{feet}{minute})t+2000feet

t=\frac{-2000feet}{-90\frac{feet}{minute}}=22.222minutes

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A square in a rectangle have the same perimeter. The length of a side of the square is 4x-1. The length of the rectangle is 2x+2
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The value x is 1, if the perimeter of square and rectangle are same. The perimeter of square and rectangle is 12 units.

Step-by-step explanation:

The given is,

                A square in a rectangle have the same perimeter

                The length of a side of the square is 4x-1

                The length of the rectangle is 2x+2 and width is 2x

Step:1

                Let, a - Side of square

                        l - Length of the rectangle

                       w - Width of the rectangle

Step:2

                Formula for perimeter of square is,

                                    p=4a.............................(1)

                Formula for perimeter of rectangle is,

                                   p=2(l+w)....................(2)

Step:3

                From given,

                            Equation (1) = Equation (2)

                                 4a = 2 (l+w)

               where,

                         a = 4x-1

                          l = 2x+2

                         w = 2x

               Substitute the values,

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

                            16x - 4 = 2 (4x + 2)

                            16x - 4 = 8x + 4

                          16x - 8x = 8                      

                                   8x = 8

                                     x = 1

Step:4

         Substitute the values of x,

                   a = 4(1)-1 = 3

                     l = 2(1)+2) = 4

                   w = 2(1) = 2

          Perimeter of square and rectangle is 12 units

Result:

           The value x is 1, if the perimeter of square and rectangle are same. The perimeter of square and rectangle is 12 units.

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