The perimeter of a retangular field is 294 yards. if the width of the field is 64 yards what is the length?

83 yards

Step-by-step explanation:

We are given;

We are required to determine the length;

That is;

P = 2 (L + W)

P = 2L + 2W

Rearranging the formula;

2L = P - 2W

Therefore;

2L = 294 yards - 2 (64 yards)

     = 294 - 128

     = 166

L = 166 ÷ 2

  = 83 yards

Thus, the length of the rectangle is 83 yards.

This is the quadratic function:

h(x)=ax²+bx+c

We have two points:

(1,58)

(2,112)

Now, we calculate this quadratic funtion.

we assume that h(0)=0

Therefore:

a(0)²+b(0)+c=0

c=0

(1,58)

a(1)²+b(1)=58

a+b=58  (1)

(2,112)

a(2)²+b(2)=112

4a+2b=112

2a+b=56  (1)

With the equations (1) and (2) we make a system of equations:

a+b=58

2a+b=56

we can solve this system of equations by reduction method.

-(a+b=58)

2a+b=56

a=-2

-2(a+b=58)

 2a+b=56

      -b=-60  ⇒  b=60

The function is:

h(x)=ax²+bx+c

h(x)=-2x²+60x

Now find the height, in feet, of the rock after 10 seconds in the air.

h(10)=-2(10)²+60(10)

h(10)=-200+600=400

400 ft.