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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∠2 =∠1 which is 180° -65° =115<span>°
So </span>∠2=115<span>° </span>
Answer:
Step-by-step explanation:
small=s, s=3.99
large=l, l=19.20
10s+8l=192.20
20s+l=99
we can see that in the second equation, 20s+l=99
l=99-20s
lets replace l in the first equation
10s+8(99-20s)=192.20
10s+792-160s=192.20
-150s=-792+192.20
150s=599.80
s=3.99
l=99-20(3.99)=99-79.80=19.20
The image showing the dimensions is missing, so i have attached it.
Answer:
A = 156 square feet
Step-by-step explanation:
To find how much plywood Jesse will need to cover all the surface simply means we are to find the surface area.
The surface area of the triangular prism is given by;
A = (2 * (Area of the base)) + (Perimeter of base x height)
Now, area of the base=bh/2
b = 3 ft
h = 4 ft
area of the base = 3*4/2 = 6 ft²
perimeter of the base = L + b + h = 4 + 3 + 5 = 12 ft
height of the prism;h = 12 ft
Thus;
surface area of the triangular prism;
A = (2 * 6) + (12*12)
A = 12 + 144
A = 156 ft²
Answer:
the number of cookies that are oatmeal cookies is 24
Step-by-step explanation:
Given that
There are 64 cookies in a jar
And, the probability of randomly selecting the oatmeal cookies is 37.5%
We need to find out the number of cookies that are oatmeal cookies
So, the number of cookies that are oatmeal cookies are
= 64 cookies × 37.50%
= 24 cookies
hence, the number of cookies that are oatmeal cookies is 24
