Find the missing angle.
1 answer:
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The cone equation gives
which means that the intersection of the cone and sphere occurs at
i.e. along the vertical cylinder of radius
when 
.
We can parameterize the spherical cap in spherical coordinates by
where
and 
, which follows from the fact that the radius of the sphere is 3 and the height at which the sphere and cone intersect is . So the angle between the vertical line through the origin and any line through the origin normal to the sphere along the cone's surface is
Now the surface area of the cap is given by the surface integral,
which means that the intersection of the cone and sphere occurs at
i.e. along the vertical cylinder of radius
We can parameterize the spherical cap in spherical coordinates by
where
Now the surface area of the cap is given by the surface integral,
If something isn't clear or you're still confused about, let me know in the comments.
Step-by-step explanation:
Okay, here's my best try.
Suppose you have a bill for $8.45
If you are asked to add, say, 8% tax, you must calculate 8 percent of 8.45 and then add it to 8.45.
Begin by converting 8% to decimals by dividing by 100.
8% is 0.08 in decimal form.
To calculate a percentage of a number, you multiply the decimal percent by the number; example:
8.45 is being multiplied by 0.08. The result is: 0.676. (this is the tax; however you have to round up to two decimal places: $0.68)
After finding the tax amount, if you are asked to add it to the bill, you have to add it to the original bill; in this case, $8.45
This would be: 0.68+8.45=9.13.
Therefore, the total bill after tax is for $9.13
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With tips is the same thing, however, you can have 2 situations.
Situation 1: You are asked to calculate 15% tip of total bill.
In this situation, you can do the same we do to calculate tax.
Convert the percentage to decimal by dividing by 100.
and multiply it by the original bill.
. Rounding up, this would be $1.27 for tip.
If you were to add it to the original bill, simply sum.
The total bill after tips is for $9.72
Situation 2: You are asked to calculate 15% tip of the total bill with a tax of 8% included.
In this situation, you must first calculate the total bill with the tax added, like we did above; we got a bill for $9.13 (Tax included)
Then you can calculate 15% tip of this new bill that has tax included.
Convert
Multiply by the new bill (because this is the one that includes tax)
Round up.... $1.37 for tips.
If you are asked to give a total amount of money including tax and tips, add this to the bill.
9.13+1.37=10.50
This bill would be for $10.50