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2 years ago

What type of limacon is graphed by the polar equation r=4+2sinttheta?

Mathematics

2 answers:

sergiy2304 [10]2 years ago

8 0

The type of limacon graphed is a convex.

nydimaria [60]2 years ago

6 0

Answer:

The graph is a convex limacon.

Step-by-step explanation:

Polar equation is defined as

$r=b+a\sin \theta$ and $r=b+a\cos \theta$

Types of limacon:

1. If b < a, then graph is a limacon with and inner loop.

2. If a < b < 2a, then graph is a dimpled limacon.

3. If 2a ≤ b, then graph is a convex limacon.

The given equation is

$r=4+2\sin \theta$

Here b=4 and a=2.

$2a=2(2)=4=b$

$2a=4$

$2a=b$ $[\because b=4]$

Since 2a ≤ b, therefore the graph is a convex limacon.

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What is the volume of the prism?

jolli1 [7]

V=a*b*c, a=(2+1/2), b=(2+1/2), c=(6+1/2)
V=(2+1/2)*(2+1/2)*(6+1/2) = 15/2 = 7+1/2
(seven whole and one second)

7 0

1 year ago

Read 2 more answers

8. A box is filled with candies in different colors. We have 40 white candies, 24 green ones, 12

Darya [45]

Answer:

$P(Green\ or\ Red) = 0.30$

Step-by-step explanation:

Given

$White = 40$

$Green = 24$

$Red = 12$

$Yellow = 24$

$Blue = 20$

Required

$P(Green\ or\ Red)$

The total numbe of candy is:

$Total = 40 + 24 + 12 + 24 + 20$

$Total = 120$

This probability is calculated as:

$P(Green\ or\ Red) = P(Green) + P(Red)$

For each, we have:

$P(Green\ or\ Red) = \frac{Green}{Total} + \frac{Red}{Total}$

Take LCM

$P(Green\ or\ Red) = \frac{Green+Red}{Total}$

$P(Green\ or\ Red) = \frac{24+12}{120}$

$P(Green\ or\ Red) = \frac{36}{120}$

$P(Green\ or\ Red) = 0.30$

8 0

2 years ago

The centers for disease control and prevention reported that 25% of baby boys 6-8 months old in the united states weigh more tha

melisa1 [442]

Answer:

0.1971 ( approx )

Step-by-step explanation:

Let X represents the event of weighing more than 20 pounds,

Since, the binomial distribution formula is,

$P(x)=^nC_r p^r q^{n-r}$

Where, $^nC_r=\frac{n!}{r!(n-r)!}$

Given,

The probability of weighing more than 20 pounds, p = 25% = 0.25,

⇒ The probability of not weighing more than 20 pounds, q = 1-p = 0.75

Total number of samples, n = 16,

Hence, the probability that fewer than 3 weigh more than 20 pounds,

$P(X$

$=^{16}C_0 (0.25)^0 (0.75)^{16-0}+^{16}C_1 (0.25)^1 (0.75)^{16-1}+^{16}C_2 (0.25)^2 (0.75)^{16-2}$

$=(0.75)^{16}+16(0.25)(0.75)^{15}+120(0.25)^2(0.75)^{14}$

$=0.1971110499$

$\approx 0.1971$

3 0

2 years ago

Find the equation of the circle in standard form for the given center (h, k) and radius r: (h, k) = (0, 0), r = 4

Ad libitum [116K]

Answer:

$x^2+y^2=16$

Step-by-step explanation:

The equation of a circle with center (h,k) and radius r is given by the formula;

$(x-h)^2+(y-k)^2=r^2$

Given (h,k)=(0,0) and r=4, we substitute the values to obtain;

$(x-0)^2+(y-0)^2=4^2$

The required equation is

$x^2+y^2=16$

8 0

2 years ago

The second step in the process for factoring the trinomial is to:

emmainna [20.7K]

Example: the second step in the process for factoring the trinomial x^2-3x-40 is to: Well you really should find the sum of the factors of −40 (not 40) 
But before you can do that, you need to LIST the factors of −40 (not 40) 
−1 * 40 
−2 * 20 
−4 * 10 
−5 * 8 
−8 * 5 
−10 * 4 
−20 * 2 
−40 * 1 

NOW we find the sum of the factors of −40 
−1 + 40 = 39 
−2 + 20 = 18 
−4 + 10 = 6 
−5 + 8 = 3 
−8 + 5 = −3 
−10 + 4 = −6 
−20 + 2 = −18 
−40 + 1 = −39 

Then we choose the factors of −40 whose sum is −3 ---> −8 and 5 
x^2 − 3x − 40 = (x − 8) (x + 5) 

So FIRST step is B, SECOND step is C, and final step is factoring. 
What Rita did was combine these 2 steps together, which you will learn to do as you get better at factoring.

8 0

2 years ago