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
#SPJ4
Answer:
3 gallons
Step-by-step explanation:
Let
x ----> the amount of pure acid (100% solution) in gallons
Remember that
we know that
solve for x
therefore
3 gallons of pure acid should be mixed with 3 gallons of a 20% acid solution in order to get a 60% acid solution
Given:
Total number of students = 27
Students who play basketball = 7
Student who play baseball = 18
Students who play neither sports = 7
To find:
The probability the student chosen at randomly from the class plays both basketball and base ball.
Solution:
Let the following events,
A : Student plays basketball
B : Student plays baseball
U : Union set or all students.
Then according to given information,
We know that,
Now,
It means, the number of students who play both sports is 5.
The probability the student chosen at randomly from the class plays both basketball and base ball is
Therefore, the required probability is .