The gateway arc in st. louis was built in 1965. it is the talles monument in the united states. the arch can be modeled with the function y=0.00635x^2+4x where x and y are in feet.
a. how high above the grounf is the tallest point of the arch?
b. how far apart are the legs of the arch at thier bases?
c. what are the domain and range of this function?

A)  630 feet

B)  630 feet

C)  Domain: [0,630] and Range: [0,630]

Step-by-step explanation:

The gateway arc in St. Louis was built in 1965. It is the tallest monument in the united states.

The modeled of arc,

where x and y are in feet

Part A) The given model is parabolic curve. The highest point at vertex of parabolic curve.

The x-coordinate of maximum height,

where, a is coefficient of x² and b is coefficient of x

a = -0.00635

b = 4

Put x = 314.96 into model to get the value of y

Hence, the tallest point of the arch at 630 feet above ground.

Part B) The distance between the legs of arch is difference of zeros of equation.

Hence, the legs of the arch 630 feet apart to each other.

Part C)

Domain: It is input value of x where function is defined.

Range: It is output value of function for all defined value of x.

For this model, It is a function of arch. So, y value can't be negative.

Therefore,

Domain: [0,630]

Range: [0,630]

-2/

a.   we have two

lines:   y = 4-x   and  

y = 8-x^-1

given two simultaneous equations that are both to be

true, then the solution is the points where the lines cross. the intersection is

where the two equations are equal. therefore the solution that works for both

equations is when

4-x = 8-x^-1

this is where the two lines will cross and that is the

common point that satisfies both equations.

b.   4-x = 8-x^-1

  x           4-x       8-x^-1

-3           7        

8.33

-2           6         8.5

-1           5         9

  0           4        

-

  1           3        

7

  2           2        

7.5

  3           1         7.67

the table shows that none of the x values from -3 to 3 is

the solution because in no case does

4-x = 8-x^-1

to find the solution we need to rearrange the equation to

find for x:

4-x = 8-x^-1

multiply both sides with x:

4x-x^2 = 8x-1

x^2+4x-1=0

x= -4.236, 0.236

therefore there are two points that satisfies the

equation.

find y:  

x=-4.236

y = 4-x   = 4 – (-4.236)

= 8.236

y = 8-x^-1 =   .236)^-1

= 8.236

x=0.236

  y = 4-x   = 4 – (0.236) = 3.764

y = 8-x^-1 =   8-(0.236)^-1

= 3.764

thus the two lines cross at 2 points:

(-4.236, 8.236) & (0.236, 3.764)

c.   to solve

graphically the equation 4-x = 8-x^-1

we would graph both lines: y = 4-x   and   y

= 8-x^-1

the point on the graph where the lines cross is the

solution to the system of equations.

just graph the points on part b on a cartesian coordinate

system and extend the two lines.   the

solution is, as stated, the point where the two lines cross on the graph.

step-by-step explanation:

mark brainliest!