In sunlight, a vertical yardstick casts a 1 ft shadow at the same time that a nearby tree casts a 15 ft shadow. How tall is the
2 answers:
Answer:
Tree is 45 ft tall.
Step-by-step explanation:
In the figure attached AB is the tree and CD is the yardstick.
Shadow of tree AB is BO = 15 ft and shadow of yardstick is CO.
since length of a yardstick is = 1 yard or 3 ft.
Now we know that ΔABO and ΔDCO are similar.(since ∠A = ∠D and ∠B = ∠C = 90° so AA property proving triangles similar)
Therefore
By putting the values of AB and CD
x = 3×15 = 45 ft.
Therefore the height of the tree is 45 ft.
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Answer:
The prevalence of flu for the past year, as indicated from the survey participants, was of 17%.
Step-by-step explanation:
Given the survey, the prevalence of the flu, as a percentage, is given by:
Number of individuals diagnosed with flu, multiplied by 100, and divided by the size of the sample.
In this question, we have that:
Sample of 25,000, and 4,250 of those had been diagnosed with the flu at some point in the past year. So, the prevalence of the flu is given by:
The prevalence of flu for the past year, as indicated from the survey participants, was of 17%.
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
