A road is inclined at an angle of 5°. After driving 5,328 feet along this road, find the
driver's increase in altitude Round to the
nearest foot

464 feet

Step-by-step explanation:

The Sine of the angle of inclination gives the increase in altitude.

This is because the Sine of an angle is equal to the Opposite side divided by the Hypotenuse side. i.e

Sin Ф = Opposite  ÷ Hypotenuse

Sin 5° = O ÷ 5328

0·08716 = O ÷ 5328

Make O the subject and multiply every fraction by 5328

(0·08716/1 × 5328)= (O/5328 × 5328)

464·388 = O

∴ The increase in altitude is 464·388 feet

This is supposed to be to the nearest foot so we round off

464·388 becomes 464 feet

(0,-3) see attached graph

step-by-step explanation:

a. to solve the system, graph the two equations.

x = y+3 becomes y=x-3 has m=1/1 and b=-3. start at (0,-3) on the y-axis and plot a point. then move up 1 unit and 1 unit to the right. plot a point and connect.

y=-4x+3 has m =-4/1 and b=-3. start at (0,-3) on the y-axis and plot a point. then move down four units and to the right 1 unit. plot a point and connect.

the solution is the point (x,y) where the two lines intersect. by the graph below it is (0,-3).

b. to solve by substitution, substitute y = -4x-3 into x= y+3

x= (-4x-3) +3

x=-4x

5x=0

x=0

now substitute x = 0 back in to find y.

y= -4(0)-3

y=0-3

y=-3

solution is (0,-3)

c. use elimination by adding the equations together.

x-y=3

4x+y=-3

5x=0

x=0

then substitute into one equation to find y.

y=-4(0)-3

y=-3