The sum of two numbers is 70. the larger number is 4 more than twice the smaller number. what is the smaller number?
1 answer:
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To get the result we have to transform given formula into y=ax+b form.
Lets do this
5x+3y=6 /-5x (subtract 5x both sides)
3y=-5x+6 /:3 (divide both sides by 3)
y=
In form y=ax+b we know that a is slope and b is y intersect. We can read from our transformed equation that slope a=
and its the result
Lets do this
5x+3y=6 /-5x (subtract 5x both sides)
3y=-5x+6 /:3 (divide both sides by 3)
y=
In form y=ax+b we know that a is slope and b is y intersect. We can read from our transformed equation that slope a=
4.
known side: opposite (150m)
unknown sides: adjacent and hypotenuse
using Tan to find the distance from the tower's base to the key.
why do we use Tan to find the distance?
the tower creates an angle of 72 degrees with the ground, which will be called α, and it is 150m high from the ground which is opposite ∠α. (shown in picture). we can see that the distance from the base of the tower to the key is the adjacent of the ∠α.
Tan α = opposite / adjacent
=> Tan 72° = 150 / x
=> x = 150 / Tan 72°
=> x = 48.73795443 m = ~48.7m
5.
4.
known side: opposite (150m)
unknown sides: adjacent and hypotenuse
using Sin to find the distance that the ant travelled.
why do we use Sinn to find the distance?
the tower creates an angle of 72 degrees with the ground, which will be called α, and it is 150m high from the ground which is opposite ∠α. (shown in picture). the ant travelled along the tower's body, which is the hypotenuse of the triangle, from the top until reaching the ground.
Sin α = opposite / hypotenuse
=> Sin 72° = 150 / x
=> x = 150 / Sin 72°
=> x = 157.7193336 m = ~157.7m
6.
(using unrounded numbers to calculate because there is a small difference in results if using the rounded numbers)
c^2 = a^2 + b^2 (pythago)
157.7^2 = 150^2 + 48.7^2
24875.3882 = 24875.3882 (correct)
