Answer: 46.90mins
Step-by-step explanation:
The given data:
The diameter of the balloon = 55 feet
The rate of increase of the radius of the balloon when inflated = 1.5 feet/min.
Solution:
dr/dt = 1.5 feet per minute = 1.5 ft/min
V = 4/3·π·r³
The maximum volume of the balloon
= 4/3 × 3.14 × 55³
= 696556.67 ft³
When the volume 2/3 the maximum volume
= 2/3 × 696556.67 ft³
= 464371.11 ft³
The radius, r₂ at the point is
= 4/3·π·r₂³
= 464371.11 ft³
r₂³ = 464371.11 ft³ × 3/4
= 348278.33 ft³
348278.333333
r₂ = ∛(348278.33 ft³) ≈ 70.36 ft
The time for the radius to increase to the above length = Length/(Rate of increase of length of the radius)
The time for the radius to increase to the
above length
Time taken for the radius to increase the length.
= is 70.369 ft/(1.5 ft/min)
= 46.90 minutes
46.90mins is the time taken to inflate the balloon.
Answer: ![m\angle EYL=96\°](https://tex.z-dn.net/?f=m%5Cangle%20EYL%3D96%5C%C2%B0)
Step-by-step explanation:
For this exercise you need to use the formula for calculate the measure of the angle formed by two tangents intersecting outside of a circle. This is:
![Angle\ formed \ by\ two\ tangents = \frac{1}{2}(Difference\ of\ Intercepted\ Arcs)](https://tex.z-dn.net/?f=Angle%5C%20formed%20%5C%20by%5C%20two%5C%20tangents%20%3D%20%5Cfrac%7B1%7D%7B2%7D%28Difference%5C%20of%5C%20Intercepted%5C%20Arcs%29)
According to the information given in the exercise, you know that:
![Angle\ formed \ by\ two\ tangents = m\angle EYL\\\\Difference\ of\ Intercepted\ Arcs=m LVE-mLHE](https://tex.z-dn.net/?f=Angle%5C%20formed%20%5C%20by%5C%20two%5C%20tangents%20%3D%20%20m%5Cangle%20EYL%5C%5C%5C%5CDifference%5C%20of%5C%20Intercepted%5C%20Arcs%3Dm%20LVE-mLHE)
Since there are 360 degrees in a circle, you can determine that:
![mLVE=360\°-mLHE\\\\mLVE=360\°-84\°\\\\mLVE=276\°](https://tex.z-dn.net/?f=mLVE%3D360%5C%C2%B0-mLHE%5C%5C%5C%5CmLVE%3D360%5C%C2%B0-84%5C%C2%B0%5C%5C%5C%5CmLVE%3D276%5C%C2%B0)
Therefore, knowing these values, you can substitute them into the formula given above and the evaluate, in order to find the measure of the angle EYL. This is:
![m\angle EYL=\frac{1}{2}(276\°-84\°) \\\\m\angle EYL=96\°](https://tex.z-dn.net/?f=m%5Cangle%20EYL%3D%5Cfrac%7B1%7D%7B2%7D%28276%5C%C2%B0-84%5C%C2%B0%29%20%5C%5C%5C%5Cm%5Cangle%20EYL%3D96%5C%C2%B0)
If Lines AC and ED intersect at point B, then ∠ABD and ∠EBC are vertically opposite angles
The point where two lines meet is known as an angle.
If line Lines AC and ED intersect at point B, then ∠ABD and ∠EBC will be vertically opposite to each other (They will be equal).
To show that the are equal
Given the angles
m∠ABD = 5x - 5
m∠EBC = 3x + 15
m∠ABD = m∠EBC (vertical angles)
5x - 5 = 3x + 15
5x - 3x = 15 + 5
2x = 20
x = 10
Substitute x = 10 into m∠ABD and m∠EBC
m∠ABD = 5x - 5
m∠ABD = 5(10)-5
m∠ABD = 50 - 5
m∠ABD = 45
Get m∠EBC
m∠EBC = 3x+15
m∠EBC = 3(10)+15
m∠EBC = 30+15
m∠EBC = 45 degrees
We can see that both angles are equal. Hence we can also conclude that they are vertically opposite angles
Learn more here: brainly.com/question/23466343