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3 years ago

5

A central angle in a circle with a radius of 7in. intercepts an arc with a length of 9in. What is the radian measure of the cent

ral angle?

1 answer:

Vitek1552 [10]3 years ago

8 0

A central angle in a circle with a radius of 7in. intercepts an arc with a length of 9in. What is the radian measure of the central angle?

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Find the equation of the normal to the circle, whose equation is given below, at the point (1,2).( x − 3 ) 2 + ( y + 2 ) 2 = 20

grandymaker [24]

Answer:

The equation of the normal is y = 4 - 2·x

Step-by-step explanation:

The given equation of the circle, is presented as follows;

(x - 3)² + (y + 2)² = 20

The point of the normal of the circle = (1, 2)

The equation of the normal to a circle, x² + y² + D·x + E·y + F = 0 at a point P(x₁, y₁) is given as follows;

$\dfrac{y - y_1}{x - x_1} = \dfrac{2 \cdot y_1 + D}{2 \cdot x_1 + E}$

Expanding the given equation of the circle, gives;

(x - 3)² + (y + 2)² = x² + y² - 6·x + 4·y + 13 = 20

∴ x² + y² - 6·x + 4·y + 13 - 20 = x² + y² - 6·x + 4·y - 7 = 0

x² + y² - 6·x + 4·y - 7 = 0

∴ x₁ = 1, y₁ = 2, D = -6, E = 4, and F = 13

Which gives;

$\dfrac{y - 2}{x - 1} = \dfrac{2 \times 2 + 4}{2 \times 1 + (-6)} = \dfrac{8}{-4} = -2$

∴ y - 2 = -2 × (x - 1) = 2 - 2·x

y = 2 - 2·x + 2 = 4 - 2·x

The equation of the normal to the circle with equation (x - 3)² + (y + 2)² = 20, at the point (1, 2) is y = 4 - 2·x

8 0

3 years ago

Unit rate for 3 ounces for every 3/4 cup

Vanyuwa [196]

Answer:

4 ounces per cup

Step-by-step explanation:

To find the unit rate, we take the ounces and divide by cups. We want a 1 in the denominator

3 ounces÷3/4 cup

Copy dot flip

3 ounces * 4/3 per cup

4 ounces per cup

7 0

3 years ago

. A binary string containing M 0’s and N 1’s (in arbitrary order, where all orderings are equally likely) is sent over a network

Sophie [7]

Answer:

$P(k) = \frac{\binom{N}{k} \binom{(M+N) - N}{r-k}}{\binom{M+N}{r}}$

Step-by-step explanation:

We can model the string as a hypergeometric distribution, as each bit has two possible values, 1 or 0, and the chance of a 1 or 0 changes with every bit, as there are a finite number M of 0's and N of 1's and every bit takes one of those values.

If M+N (total size of the string) >> r (number of trials), we could model it as a binomial distribution as the probability of a 1 or 0 wouldn't change in a significant amount with every bit, but as we don't know the magnitude of M+N and r, we follow up with hypergeometric distribution.

The distribution has the following formula for probability:

$P(k) = \frac{\binom{K}{k} \binom{N - K}{n-k}}{\binom{N}{n}}$

Where k is the number of sucesses, K is how many total sucess states are in the population, N is the population size and n is the number of draws.

For our case, a 1 would be a sucess, i.e. k the number of 1's we want to know the probability, N our total number of 1's, M+N the length of the string (population size) and we want to analyse what happens in the first r bits (number of draws):

$P(k) = \frac{\binom{N}{k} \binom{(M+N) - N}{r-k}}{\binom{M+N}{r}}$

8 0

3 years ago

1. Write the word sentence as an equation. 2. Then solve the equation. 5/7a=25

seropon [69]

Answer:

a = 35

Step-by-step explanation:

5/7a = 25

multiply both sides by 7:

5a = 175

divide by 5:

a = 35

Hope this helps !!!

7 0

2 years ago

Arrange the following in descending order

nekit [7.7K]

Answer:

0, -3, -5, -8, -12

Step-by-step explanation:

6 0

2 years ago

Read 2 more answers