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
Answer:
here you go
Step-by-step explanation:
18 is 24c/d^5
19 is 48a^/b^3
/ indicates a fraction
^ indicates an exponent
true
Typically, the price charged must cover more than labor costs figured at an hourly rate. There may be costs related to rent, utilities, administration, equipment use and/or depreciation. These costs are often called overhead<span>.</span>
Answer:
The requirements for the hypothesis test does satisfied the method for testing the claim that from two population proportions the rate of polio is less for children given the salk vaccine.
Step-by-step explanation:
The percentage of children in the treatment group was:
(201229/401974)*100 = 49.9%
The percentage of children given placebo was:
(200745/401974)*100 = 50.1%
The percentage of children that developed polio in the treatment group:
(33/200745)*100 = 0.0164%
The percentage of children that developed polio in the placebo group:
(115/201229)*100 = 0.0571%
The percentage difference between the two group:
((0.0571-0.0164)/0.0571) = 61.62%
Therefore:
The amount of children used for each group was almost divided into half of the total amount of children. The test revealed although very small percentages of the both group developed polio, 68.62% more children given placebo than the children that was given the salk vaccine. Therefore, the study shows that the rate of polio is less for children given the salk vaccine and the the hypthesis test is satisfied.
