Elena should put a point where the two circles intersect and draw line segments connecting that point to points A and B to finish her triangle.
Answer:
The shadow is decreasing at the rate of 3.55 inch/min
Step-by-step explanation:
The height of the building = 60ft
The shadow of the building on the level ground is 25ft long
Ѳ is increasing at the rate of 0.24°/min
Using SOHCAHTOA,
Tan Ѳ = opposite/ adjacent
= height of the building / length of the shadow
Tan Ѳ = h/x
X= h/tan Ѳ
Recall that tan Ѳ = sin Ѳ/cos Ѳ
X= h/x (sin Ѳ/cos Ѳ)
Differentiate with respect to t
dx/dt = (-h/sin²Ѳ)dѲ/dt
When x= 25ft
tanѲ = h/x
= 60/25
Ѳ= tan^-1(60/25)
= 67.38°
dѲ/dt= 0.24°/min
Convert the height in ft to inches
1 ft = 12 inches
Therefore, 60ft = 60*12
= 720 inches
Convert degree/min to radian/min
1°= 0.0175radian
Therefore, 0.24° = 0.24 * 0.0175
= 0.0042 radian/min
Recall that
dx/dt = (-h/sin²Ѳ)dѲ/dt
= (-720/sin²(67.38))*0.0042
= (-720/0.8521)*0.0042
-3.55 inch/min
Therefore, the rate at which the length of the shadow of the building decreases is 3.55 inches/min
This is the answer!! Also I use Photomath to help with my hw!
Question author, it's spelled pi not pie, and we use just use the Greek letter π. Students, demand better from your teachers.
1. Rectangular prism, aka a box. Volume is length times width times height.
V = 5×7×9 = 315 cubic feet
That's cubic feet of course, the product of three lengths. We didn't even need to do the problem, just look for the common answer and pick the one with the right units. I just saw that same pattern in a volume problem yesterday.
Answer: 315 cubic feet, first choice
2. Cylinder, volume is base area times height, πr²h. We have a radius of r=14/2=7 yd and h=8 yd. We're using π=3.14.
V = πr²h = 3.14(7²)(8) = 1230.88 cubic yds
Answer: 1230.9 cubic yards, last choice
Since the trapezoid can be inscribed in a circle, that means angle B + angle D = 180 degree. Since AB is parallel to CD, then angle B + angle C = 180 degree. Therefore, angle D = angle C.