In ΔQRS, the measure of ∠S=90°, the measure of ∠Q=6°, and RS = 20 feet. Find the length of SQ to the nearest tenth of a foot.
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Answer:
Step-by-step explanation:
Taking equation (1)
Multiplying both sides by 2
Adding 6y to both sides
Putting this in (2)
5(18+6y) + y = 28
5(18+6y) + y = 28
90 + 30y+y = 28
31y+90-28 = 0
31 y + 62 = 0
31y = -62
Dividing both sides by 31
y = -2
Now,
x = 18 + 6y
x = 18+6(-2)
x = 18-12
x = 6
<h2>Answer:</h2>
cylinder
<h2>Step-by-step explanation:</h2>Archimedes was a brilliant mathematician. This man rose the formula of the volume of a sphere by comparing this shape to a cylinder. The volume of a sphere is hard to calculate by comparing this object to a cube. So Archimedes imagined cutting a sphere into two halves, called hemispheres. So an hemisphere gave him a flat surface, which is easier to work with. Therefore, if he'd find the volume of a hemisphere, then he'd multiply the result by 2 and would get the volume of a sphere. Then he imagined a hemisphere within a cylinder as the one shown below. Also, he imagined a cone within the same cylinder. <em>What did he find? </em>He found that the volume of the hemisphere should be equal to the volume of the cylinder minus the volume of the cone:
Then the volume of a sphere is twice this volume:
If HG and GF are both 3, then the whole length of the base is 6. The tan ratio is the side opposite the reference angle (length 4) over the side adjacent to the angle (length 6), which for us looks like this:
Now use the inverse tan button (2nd-->tan) to get
As far as the sin y goes, you have to use the Law of Sines because you are not working with a right triangle in that case. I mean you are as far as having to find out what the hypotenuses are triangle EFH and triangle EFG. The hypotenuse in triangle EFH is 7.211, and the hypotenuse in triangle EFG is 5. Using the Law of Sines to solve for y, you get this:
Solving for y and using the inverse sin gives you that y = 53.12
If you are not familiar with setting up the Law of Sines, nothing I could tell you here would help. If you are familiar, then you get the idea of where the numbers came from and why they are set up that way. Hope that helps. That second part was quite hard.
Now use the inverse tan button (2nd-->tan) to get
As far as the sin y goes, you have to use the Law of Sines because you are not working with a right triangle in that case. I mean you are as far as having to find out what the hypotenuses are triangle EFH and triangle EFG. The hypotenuse in triangle EFH is 7.211, and the hypotenuse in triangle EFG is 5. Using the Law of Sines to solve for y, you get this:
Solving for y and using the inverse sin gives you that y = 53.12
If you are not familiar with setting up the Law of Sines, nothing I could tell you here would help. If you are familiar, then you get the idea of where the numbers came from and why they are set up that way. Hope that helps. That second part was quite hard.