Answer: 359 ft
<u>Step-by-step explanation:</u>
Whenever you have a problem like this, you must first make an assumption that the building (in this case the lighthouse) is perpendicular to the ground (or sea). This allows you to create a right triangle (see attached image).
The angle of depression is the angle from an imaginary perpendicular line passing through the top of the building. Since that imaginary line is parallel to the ground (or sea), you can use alternate interior angles to place that angle in the triangle.
NOTE: BOTH angle of elevation and angle of depression are placed in the lower corner of the triangle. Don't let the names confuse you!
Now you can use trigonometry to solve ....
In the given problem, we have the side OPPOSITE of the given angle (24°) and need the side ADJACENT to the angle, so we will use tan to solve for x.
1. Since each child kicks the same number of times, it is not important whether he or she kicks 1 time, 2, 3 or more times. So let all of them kick 1 time.
2. assume we start with a girl. We can start with either of the 77 girls, then second is a boy which can be either of the 76, the third is a girl which can be either of the 76 remaining, then the forth is one of the 76 boys...
3. So starting with a girl we have
77*(77)*76*(76)*75*(75)....*2*(2)*1*(1)=77!*77!
4. OR we could have started with a boy, where we would get again 77!*77!
5. Answer: 77!*77!+77!*77!=2
Correct! 12 is a multiple of 6 and 8 is a multiple of 4.
C = 82.8°
<span>b = 27.5 </span>
<span>Here's the working in case you need to see it. </span>
<span>Using Law of Cosines to first find b: </span>
<span>b² = a² + c² - 2acCOS(B) </span>
<span>b² = (41)² + (20)² - 2(41)(20)COS(36) </span>
<span>b = about 27.5 </span>
<span>Now using Law of Sines to find A </span>
<span>sin(36) / (27.5 = sin(A) / (41) </span>
<span>sin(A) = 41sin36 / 27.5 </span>
<span>sin(A) = 0.876334376145 </span>
<span>A = SinInverse(0.876334376145) </span>
<span>A = about 61.2° </span>
<span>Now using 180-61.2-36 to find B = 82.8° </span>
<span>Have a good day! </span>
Answer:
The number of bacteria at initial = 187
Step-by-step explanation:
Given that the population of bacteria in a culture grows at a rate proportional to the number of bacteria present at time t.
Integrating both side we get
㏑ N = k t + C ------- (1)
Now given that after 3 hours it is observed that 500 bacteria are present and after 10 hours 5000 bacteria are present.
⇒ ㏑ 500 = 3 k + C -------- (2)
⇒ ㏑ 5000 = 10 k + C ------ (3)
⇒ ㏑ 5000 - ㏑ 500 = 7 k
⇒ ㏑
= 7 k
⇒ ㏑ 10 = 7 k
⇒ k = 0.329
Put this value of k in equation (2),
⇒ ㏑ 500 = 3 × 0.329 + C
⇒ C = 5.23
Put this value of C in equation 1 we get,
⇒ ㏑ N = k t + 5.23
Initially when t = 0 , then
⇒ ㏑ N = 5.23
⇒ N = 187
Thus the number of bacteria at initial = 187
