Answer: 111.4m
Explanation:
1) Trigonometric ratios
You only need to use tangent ratio.
tangent ratio = opposite-leg / adjacent-leg = balloon height / horizontal distance
2) First, find the height of the ballon when he is watching at an angle of elevation of 28°
tangent ratio = opposite-leg / adjacent-leg = balloon height / horizontal distance
tan(28°) = balloon height/65m ⇒balloon height = tan(28°)×65m
balloon height = 34.56m
3) Second, find the height of the balloon,when he is watching at an angle of elevation of 66°
tan(66°) = height of the balloon / 65m ⇒ height of the balloon = tan(66°)×65m
height of the balloon = 145.99m
4) Vertical distance the balloon ascended while Charlie watched.
Subtract the final initial height from the final height:
145.99m - 34.56m = 111.43m
4) Round to the nearest tenth: 111.4 m
<span>a= 2 ft/s^2
t=3 s
vi=4 ft/s
vf=?
One can use the kinematic equation: vf=vi+at
vf=(4 ft/s)+(2 ft/s^2)(3 s)= (4 ft/s)+(6 ft/s)=10 ft/s</span>
Answer:
117 students
Step-by-step explanation:
13/100 = X/900
(13 * 900)/100 = 117
Answer:
225
Step-by-step explanation:
The sum of this series is given by the formula:
![S_n=\frac{n}{2}[2a+(n-1)d]](https://tex.z-dn.net/?f=S_n%3D%5Cfrac%7Bn%7D%7B2%7D%5B2a%2B%28n-1%29d%5D)
Where
S_n is the sum
a is the first term (we get this by plugging in n = 1 into "2n-1", we have 2(1) - 1 = 1)
n is the number of terms (the sum is defined for n = 1 to n = 15, so 15 terms)
d is the common different (the difference is successive terms. Here, 2nd term would be 2(2) - 1 = 3, and first term was 1, so d = 3 -1 = 2)
<em>plugging in the info, we will get the sum:</em>
<em>![S_n=\frac{n}{2}[2a+(n-1)d]\\S_{15}=\frac{15}{2}[2(1)+(15-1)(2)]\\=225](https://tex.z-dn.net/?f=S_n%3D%5Cfrac%7Bn%7D%7B2%7D%5B2a%2B%28n-1%29d%5D%5C%5CS_%7B15%7D%3D%5Cfrac%7B15%7D%7B2%7D%5B2%281%29%2B%2815-1%29%282%29%5D%5C%5C%3D225)
</em>
<em>The sum is 225</em>
The answer is the second choice.
(4,4) is a solution to both line A and B
