If the equation is r = 3 +4cos(θ) then because b/a>1 the curve is a limacon with an inner loop.
Given limacon with equation r=3+4cos(θ) and we have to answer how the quotient of a and b relate to the existence of an inner loop.
Equation is like a relationship between two or more variables expressed in equal to form and it is solved to find the value of variables.
formula of polar graph is similar to r= a+ b cos (θ).
Case 1. If a<b or b/a>1
then the curve is a limacon with inner loop.
Case 2. If a>b or b/a<1
Then the limacon does not have an inner loop.
Here given that
(θ)
It is observed that , a<b or b/a>1
Therefore the curve is limacon with an inner loop.
Hence because b/a>1 the curve is a limacon with an inner loop.
Learn more about limacon at brainly.com/question/14322218
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Answer:
Step-by-step explanation:
d is the answeru got it right
Given expression is
![\sqrt[4]{\frac{16x^{11}y^8}{81x^7y^6}}](https://tex.z-dn.net/?f=%20%5Csqrt%5B4%5D%7B%5Cfrac%7B16x%5E%7B11%7Dy%5E8%7D%7B81x%5E7y%5E6%7D%7D)
Radical is fourth root
first we simplify the terms inside the radical


So the expression becomes
![\sqrt[4]{\frac{16x^4y^2}{81}}](https://tex.z-dn.net/?f=%20%5Csqrt%5B4%5D%7B%5Cfrac%7B16x%5E4y%5E2%7D%7B81%7D%7D)
Now we take fourth root
![\sqrt[4]{16} = 2](https://tex.z-dn.net/?f=%5Csqrt%5B4%5D%7B16%7D%20%3D%202)
![\sqrt[4]{81} = 3](https://tex.z-dn.net/?f=%5Csqrt%5B4%5D%7B81%7D%20%3D%203)
![\sqrt[4]{x^4} = x](https://tex.z-dn.net/?f=%5Csqrt%5B4%5D%7Bx%5E4%7D%20%3D%20x)
We cannot simplify fourth root (y^2)
After simplification , expression becomes
![\frac{2x\sqrt[4]{y^2}}{3}](https://tex.z-dn.net/?f=%5Cfrac%7B2x%5Csqrt%5B4%5D%7By%5E2%7D%7D%7B3%7D)
Answer is option B
Answer: I would say b and c because 11 pounds is 176 ounces but i don't really know what the question wants but i hope this helped.
Answer:
the last one
Step-by-step explanation:
follow the lines in the order of the letters. look at each corner showering that the angle = 90°. the last option is the only one that proves that it is a right angle.
hope this helps