The radius of the balloon given the information in the question is 8.98cm.
<h3>What is the radius of the balloon?</h3>
The first step is to determine the volum of the balloon.
Volume = 81π cm^3 x 12 = 972π cm^3
Now, determine the radius using this formula:
∛[Volume / (4/3π )]
∛[972π cm^3/ (4/3π )] = 8.98cm
Here is the complete question:
Andy is blowing up a spherically shaped balloon. If he is able to blow 81π cm^3 of air with every breath, it takes him 12 breaths to fully inflate the balloon. What is the radius of the balloon?
To learn more about the volume of a sphere, please check: brainly.com/question/13705125
Answer:
Infinitely many solutions
Step-by-step explanation:
Answer:
![x_1 =-14.43 in, x_2 = 2.426in](https://tex.z-dn.net/?f=x_1%20%3D-14.43%20in%2C%20x_2%20%3D%202.426in)
Since the measurement can't be negative the correct answer for this case would be ![x =2.426 in](https://tex.z-dn.net/?f=%20x%20%3D2.426%20in)
Step-by-step explanation:
Let's assume that the figure attached illustrate the situation.
For this case the we know that the original area given by:
![A_i = 7 in *5 in = 35in^2](https://tex.z-dn.net/?f=%20A_i%20%3D%207%20in%20%2A5%20in%20%3D%2035in%5E2)
And we know that the initial area is a half of the entire area in red
, so then:
![A_f = 2 A_ i =2*35 = 70](https://tex.z-dn.net/?f=%20A_f%20%3D%202%20A_%20i%20%3D2%2A35%20%3D%2070)
And we know that the area for a rectangular pieces is the length multiplied by the width so we have this:
![70 = (x+7) (x+5)](https://tex.z-dn.net/?f=%2070%20%3D%20%28x%2B7%29%20%28x%2B5%29%20)
We multiply both terms using algebra and the distributive property and we got:
![70 =x^2 +12 x +5](https://tex.z-dn.net/?f=%2070%20%3Dx%5E2%20%2B12%20x%20%2B5)
And we can rewrite the expression like this:
![x^2 +12 x -35 = 0](https://tex.z-dn.net/?f=%20x%5E2%20%2B12%20x%20-35%20%3D%200)
And we can solve this using the quadratic formula given by:
![x = \frac{-b \pm \sqrt{b^2 -4ac}}{2a}](https://tex.z-dn.net/?f=%20x%20%3D%20%5Cfrac%7B-b%20%5Cpm%20%5Csqrt%7Bb%5E2%20-4ac%7D%7D%7B2a%7D)
Where
if we replace we got:
![x = \frac{-12 \pm \sqrt{(12)^2 -4(1)(-35)}}{2*1}](https://tex.z-dn.net/?f=%20x%20%3D%20%5Cfrac%7B-12%20%5Cpm%20%5Csqrt%7B%2812%29%5E2%20-4%281%29%28-35%29%7D%7D%7B2%2A1%7D)
And the two possible solutions are then:
![x_1 =-14.43 in, x_2 = 2.426in](https://tex.z-dn.net/?f=x_1%20%3D-14.43%20in%2C%20x_2%20%3D%202.426in)
Since the measurement can't be negative the correct answer for this case would be ![x =2.426 in](https://tex.z-dn.net/?f=%20x%20%3D2.426%20in)
So its asking you to find the gravity on earth relative to the gravity on mars.
Set up an equation to figure out the difference between the two gravities
x=.38
I don't know what constant of proportionality is in this context but a ball on mars would weigh .38 the amount that it does on earth.
Answer:
team a and team c scored 74 points which is 48 points more than team b, scoring 26 points.
Step-by-step explanation: