Astudent visiting the sears tower skydeck is 1353 feet above the ground. find the distance the student can see to the horizon. use the formula to approximate the distance d in miles to the horizon when h is the height of the viewer’s eyes above the ground in feet. round to the nearest mile. a. 45 miles b. 601 miles c. 36 miles d. 1010 miles

Option A. 45 miles

Step-by-step explanation:

A student visiting the Sears Tower Skydeck is 1353 feet or 0.25625 miles above the ground.

We have to find the distance the student can see to the horizon.

We can see in the figure attached r is the radius of the earth.

h is the height of the tower and x is the distance to the horizon.

Now we can calculate the distance x by applying Pythagoras theorem in right angle ΔTOH. (Radius of the earth OH ⊥ tangent distance to the horizon TH)

(h + r)² = r² + x²

By putting the values in the formula

h = height of the tower = 0.25625 miles

r = radius of the earth = 3958.8 miles

(3958.8 + 0.25625)²= x² + (3958.8)²

x² = (3959.05)² - (3958.80)²

x² = 15674126.40 - 15672097.40

x² = 2029

x = √2029

x = 45.04 ≈ miles.

Therefore Option A. 45 miles is the answer.

the system of inequity is

step-by-step explanation:

from the given graph it is noticed that we have two related lines. one is solid and another is dashed.

if a line passing through two points, then the equation of line is

the solid line passing through the points (0,4) and (4,0).

the related equation of solid line is .

similarly, find the related equation of dashed line. the dashed liune passing through the points (0,0) and (3,1).

the related equation of dashed line is

from the given graph it is noticed that the point (0,1) lies on the shaded region, therefore the point (0,1) must be satisfied by the related equations.

check the related equations by the point (0,1).

this statement is true if the sign of inequality is < instead of equality. since it is an solid line therefore the sign of inequality will be . the required inequality is

similarly, check the second related equation.

it is a dashed line, so this statement is true if the sign of inequality is > . the required inequality is