Answer:
0.128rad/sec
Step-by-step explanation:
Let x represent the between the man and the point on the path
θ = the angle
dx/dt = 4 ft/s
dθ/dt = rate is the searchlight rotating when the man is 15 ft from the point on the path closest to the searchlight
tan θ = x/20 ft
Cross Multiply
20tan θ = x
dx/dt = 20sec² θ dθ/dt
dθ/dt = 1/20 × cos² θ dx/dt
dθ/dt= 1/20 × cos² θ × 4
dθ/dt = 1/5 × cos² θ
Note : cos θ = 4/5
dθ/dt = 1/5 × (4/5)²
dθ/dt = 16/125
dθ/dt = 0.128rad/sec
Answer:
red: 9/20, 0.45, 45%
White: 15%, 0.15, 3/20
Blue: 0.4, 2/5, 40%
Step-by-step explanation:
For red: you start with 9/20. It’s best to get to a denominator of 10. So divide each number by 2. You would get 4.5/10. Then change to a percent by moving the decimal of the numerator one to the right and changing it to percent. 4.5 -> 45. -> 45%. Then for the decimal, divide 45 by 100. 45/100 = 0.45.
For white: you start with 15%. Divide by 100. 15/100=0.15. Put into a fraction with a denominator of 100. It would be 15/100. Simplify. Each number can be divided by 5, so your fraction would be 3/20.
For blue: you start with 0.4. Turn this into a fraction. Since there is one decimal place, it can have a denominator of 10. The fraction is 4/10, simplified to 2/5. Using the fraction 4/10, the percent would be 40%.
I hope this helps!
Answer:
1. 392 in², 2. 94.99 cm², 3. 145.2 ft², 4. 161.5 m², 5. 17 ft and 81 cm
Step-by-step explanation:
1. A = 16 x 19
A = 304
A = 1/2(11x16)
A = 1/2(176)
A = 88
304 + 88 = 392 in²
2. A = πr²
A = 3.14*5.5²
A = 3.14*30.25
A = 94.985
A = 94.99 cm²
3. A = 1/2(bh)
A = 1/2(11x26.4)
A = 1/2(290.4)
A = 145.2 ft²
4. A = bh
A = 9.5*17
A = 161.5 m²
5. part 1
A = (1/2) · (p + q) · h
112 = (1/2)(11+q)(8)
112 = 4(11+q)
112 = 44 + 4q
68 = 4q
17 = q
17 ft
5. part 2
A = lw
364.5 = 27w
13.5 = w
P = 2l + 2w
P = 2(27) + 2(13.5)
P = 54 + 27
P = 81
81 cm
Hope this helps :)
