According to the Pythagorean theorem, the square of the hypotenuse (the longest side) of a right-angled triangle equals to the sum of the squares of the other two sides. In this case, the ladder is the hypotenuse, which equals to the distance between the bottom of the ladder and the tree + the distance we want to find (x):
5² + x² = 13²
25 + x² = 169
x² = 144
x = √144 = 12.
The distance between the ground and the top of the ladder is 12 ft.
The formula for slope while using two points is
y2-y1
_____
x2-x1
given: (4,5) (x1,y1) and (7,3) (x2,y2)
Plug in
3-5/7-4
solve
-2/3 =slope
Answer:
18π ≈ 56.5 meters
Step-by-step explanation:
The length of the arc of a circle is given by the formula ...
s = rθ . . . . where r is the radius, and θ is the central angle in radians
<h3>Application</h3>
You are given the values of r and θ, so you only need to put them into the formula and simplify.
s = (27 m)(2π/3) = 18π m
The length of the arc is 18π meters, about 56.5 meters.
Answer:
7 minutes 48 seconds.
Step-by-step explanation:
Average speed for the whole journey is
distance / time, so
105 = (2*80)/ (t + t2)
where t is the time when it is moving and t2 is the time it stays at town Q.
Time for journey P to Q
= distance / speed
= 80 /120
= 2/3 hours,
Time for journey Q to P
= 80/110
= 8/11 hours
So t = 2/3 + 8/11
= 46/33 hours.
- and substituting in the equation for the whole journey:
160 / (46/33 + t2) = 105
105*46/33 + 105*t2 = 160
105 t2 = 160 - (105*46)/33
= 160 - 146.364
= 13.636
t2 = 13.636/105 = 0.1299 hours.
= 7 minutes 48 seconds.
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