The interior angles of any triangle always sum to 180°.
In the triangle, angles C and D are labeled congruent, so the missing angle has measure
180° - 2 (6x - 5)°
This angle is supplementary to the one labeled (11x + 1)°, which means
180° = (11x + 1)° + (180° - 2 (6x - 5)°)
Solve for x :
180° = (11x + 1)° + 180° - 2 (6x - 5)°
0 = (11x + 1)° - 2 (6x - 5)°
0 = (11x)° + 1° - (12x)° + 10°
(12x - 11x)° = 1° + 10°
x° = 11°
x = 11
6x - 6 - 7x = -13/2
Multiply both sides by 2:
12x - 12 - 14x = -13
Simplify:
-2x - 12 = -13
Add 12 to both sides:
-2x = -1
Divide both sides by 2:
-x = -1
Change to a positive value of x:
x = 1
Answer:
La respuesta es 7/8
Step-by-step explanation:
Answer:
A) 48/13 ft/sec
B) 22/13 ft/sec
Step-by-step explanation: Given that:
A light is on the top of a 12 ft tall pole and a 5ft 6in tall person is walking away from the pole at a rate of 2 ft/sec.
A) At what rate is the tip of the shadow moving away from the pole when the person is 25 ft from the pole?
Using similar triangles, we can say:
12/L = 55/(L - x)
Cross multiply to get:
12(l - x) = 5.5l
12l - 12x = 5.5l
6.5l = 12x
x = (6.5/12)l
Taking the derivative with respect to time we get:
dx/dt = (6.5/12)dl/dt or
dl/dt = (12/6.5)(dx/dt)
Since dx/dt = 2 so
dl/dt = (12/6.5)(2)
= 24/6.5
= 48/13 ft/sec
B) At what rate is the tip of the shadow moving away from the person when the person is 25 ft from the pole ?
Subtract the rate the shadow is going from the rate the man is going. Therefore
48/13 - 2 = 22/13 ft/sec.
