The total amount of material she needs is 4 3/8 yards
For this case we have the following equation:
r = 9 sin (θ)
In addition, we have the following change of variables:
y = r * sine (θ)
Rewriting the equation we have:
r = 9 sin (θ)
r = 9 (y / r)
r ^ 2 = 9y
On the other hand:
r ^ 2 = x ^ 2 + y ^ 2
Substituting values:
x ^ 2 + y ^ 2 = 9y
Rewriting:
x ^ 2 + y ^ 2 - 9y = 0
Completing squares:
x ^ 2 + y ^ 2 - 9y + (-9/2) ^ 2 = (-9/2) ^ 2
Rewriting:
x ^ 2 + 1/4 (2y-9) ^ 2 = 81/4
4x ^ 2 + (2y-9) ^ 2 = 81
Answer:
The Cartesian equation is:
4x ^ 2 + (2y-9) ^ 2 = 81
The answer is 7.66 repeating. I hope this helps
First we multiply the numbers ignoring the decimal and then place the decimal in the position
3.04 *7.091 = 2155664
Now the first number has two digits after the decimal and the second number has three digits after the decimal.
Therefore in the final result we have to move the decimal (2+3) =5 place from the left,
So the answer would be 21.55664
So, the correct answer is 21.55664
Jerry calculated the answer correctly , but made an error in the placement of the decimal point. The answer is not reasonable because 2.155664 and 21.55664 mean two completely different answer far apart from each other
