Answer:
Side 1=21 ft, Side 2=7, Side 3=24
Step-by-step explanation:
52 = (3x) + (x) + (x+17) -> 52 = 5x + 17 -> 5x = 35 -> x = 7
Plus 7 into the equation whenever you see an x.
A. -(a+5)
Because the negative sign is outside the parenthesis, multiplying by -1 just removes the negative sign:
-(a+5) * -1 = a+5
B. -(-x+31)
Apply the distributive property:
-(-x+31) becomes (- -x +31) which simplifies to (x+31)
multiply that by -1 to get -x+31
C. -(4x+12)
Because the negative sign is outside the parenthesis, multiplying by -1 just removes the negative sign:
-(4x+12) * -1 = 4x+12
Answer:
2 meters
Step-by-step explanation:
We need to use trigonometry for this. The appropriate one would be tangent, which is (opposite side) divided by (adjacent side).
In this case, the opposite side of angle A is BC, which is 6 meters. The adjacent side of angle A is AB, which is the ground. Since we don't know its length, we call it x.
Now, we write:
= 6/x
To solve, we just multiply both sides by tan(x) and x:
x = 6/[tan(72)] ≈ 1.95 meters ≈ 2 meters.
Thus, the answer is 2 meters.
Hope this helps!
Answer:
5a. -0.4 m/s²
5b. 290 m
6. 12.9 s
7. 100 s
8. 17.2 km/hr
Step-by-step explanation:
5. "While approaching a police officer parked in the median, you accelerate uniformly from 31 m/s to 27 m/s in a time of 10 s.
a. What is your acceleration?
b. How far do you travel in that time?"
Given:
v₀ = 31 m/s
v = 27 m/s
t = 10 s
Find: a and Δx
v = at + v₀
(27 m/s) = a (10 s) + (31 m/s)
a = -0.4 m/s²
Δx = ½ (v + v₀) t
Δx = ½ (27 m/s + 31 m/s) (10 s)
Δx = 290 m
6. "If a pronghorn antelope accelerates from rest in a straight line with a constant acceleration of 1.7 m/s², how long does it take for the antelope to reach a speed of 22 m/s?"
Given:
v₀ = 0 m/s
v = 22 m/s
a = 1.7 m/s²
Find: t
v = at + v₀
(22 m/s) = (1.7 m/s²) t + (0 m/s)
t = 12.9 s
7. "A 1200 kg airplane starts from rest and moves forward with a constant acceleration of 5 m/s² along a runway that is 250 m long. How long does it take the plane to travel the 250 m?"
Given:
v₀ = 0 m/s
a = 5 m/s²
Δx = 250 m
Find: t
Δx = v₀ t + ½ at²
(250 m) = (0 m/s) t + ½ (5 m/s²) t²
t = 100 s
8. "During a marathon, a runner runs the first 10 km in 0.58 hours, the next 10 km in 0.54 hours and the last 10 km in 0.62 hours. What is the average speed of the runner during that marathon?"
This isn't a constant acceleration problem, so there's no need for a chart.
Average speed = total distance / total time
v = (10 km + 10 km + 10 km) / (0.58 hr + 0.54 hr + 0.62 hr)
v = 30 km / 1.74 hr
v = 17.2 km/hr
