The statement gives you the function that models the Area as a function of angle theta, and is telling the value of this angle.
Then, you only need to replace the value of the angle in the function, to obtain the requested area.
<span>A(Θ) = 16 sin Θ • (cos Θ + 1).
Θ = 60°
A(</span>60°<span>) = 16 sin(</span><span>60°) * [cos(</span><span>60°) + 1 ] = 16 * (√3) / 2 * [1/2 + 1] = 8(√3) * 3/2 = 12√3 ≈ 20.79
Answer: 20.8 in^2 </span>
Answer:
45 mph
Step-by-step explanation:
This is a really good question to know the answer to. It is tricky and a bit indirect (which means you have to find something else before you can find the speed of the car.)
Let's keep track of what he does in the time allotted.
How far does Joe go in 5 minutes? That's the amount of time he's on the road before she is.
convert 5 minutes into hours. 5 minutes * 1 hour / 60 minutes = 1/12 of an hour
d = r*t
r = 30 km/hour
t = 1/12 hour
d = 30 km/hr * 1/12 hour = 2.5 km
Now she's about to start. She wants to catch him in 10 minutes
d = r*t
r = x mph
t = 10 minutes = 10 minutes * 1 hour * 60 minutes = 1/6 of an hour.
How far does he go in the 10 minute time?
d = 30 * 1/6 = 5 km
What is his total distance
5 km + 2.5 km = 7.5 km
Finally how fast does she need to go to catch him
d = 7.5 km
r = ? This is what you are trying to find
t = 1/6 of an hour
d = r*t
7.5 km = r * (1/6)hour divide by 1/6 hour
7.5 km // 1/6 hour = r
r = 7.5 * 6 = 45 mph
It's evident that the first four terms are 4, 4/3, 4/9, and 4/27. So the fourth partial sum of the series is
It's as easy as adding up the fractions, but I bet this is supposed to be an exercise in taking advantage of the fact that the series is geometric and use the well-known formula for computing such a sum.
Multiply the sum by 1/3 and you have
Now subtracting this from
gives
That is, all the matching terms will cancel. Now solving for
, you
have
60,120,180,240,300,360,420,480,540,600,660,720,780,840,900,960,1020,1080,1140,1200,1260,1320,1380,1440,1500,1560,1620,1680,1740,1800,1860,1920,1980,2040,2100,2160,2220,2280,2340,2400,2460,2520,2580,2640,2700,2760,2820,2880,2940
