All categories

3 years ago

The radius of the circle whose equation is (x-3)^2 + (y+1)^2 = 16 is

Mathematics

1 answer:

Firdavs [7]3 years ago

4 0

Answer:

Step-by-step explanation:

The general equation of a circle with center (a, b) and radius r is given by the equation;

$(x-a)^{2}+(y-b)^{2}=r^{2}$

The constant in the right hand side of the equation is simply the square of the radius;

We have been given the following equation;

(x-3)^2 + (y+1)^2 = 16

Comparing this with the general equation above;

$r^{2}=16\\\\r=\sqrt{16}=4$

You might be interested in

All real square roots of 0.0009

kompoz [17]

the real square root of 0.0009 is 0.03

6 0

3 years ago

Read 2 more answers

I WILL GIVE 20 POINTS TO THOSE WHO ANSWER THIS QUESTION RIGHT NOOOO SCAMS AND EXPLAIN WHY THAT IS THE ANSWER

Step2247 [10]

Answer:

$A = 297\pi$

Step-by-step explanation:

To solve this problem we need to be familiar with the formula for the surface area of a cone:

$A = \pi r(r + \sqrt{h^2+r^2})$

We are given the length of a side and the diameter, to calculate the radius divide the diameter in half:

$r = \frac{d}{2}\\r = \frac{18}{2}\\r = 9 cm$

To calculate the height of the cone, we must use the Pythagorean Theorem:

$C^2 = A^2 + B^2$

We can treat the side length as the hypotenuse $C$ , the radius as the base $A$ , and solve for height $B$ . Set the expression up like this:

$C^2 = A^2 + B^2\\24^2 = 9^2 + B^2\\B^2 = 24^2 - 9^2\\B = \sqrt{24^2 - 9^2}\\B = \sqrt{576 - 81}\\B = \sqrt{495}\\B \approx 22.25$

Now we can plug into our original formula:

$A = \pi r(r + \sqrt{h^2+r^2})\\A = \pi 9(9+\sqrt{\sqrt{495}^2+9^2}\\A = \pi 9(9+\sqrt{495 + 81}\\A = \pi 9(9+\sqrt{576})\\A = \pi 9(9 + 24)\\A = \pi 9(33)\\A = 297\pi$

5 0

2 years ago

Question 31 pts Prove the statement is true using mathematical induction: 2n-1 ≤ n! Use the space below to write your answer. To

Sladkaya [172]

Answer:

P(3) is true since 2(3) - 1 = 5 < 3! = 6.

Step-by-step explanation:

Let P(n) be the proposition that 2n-1 ≤ n!. for n ≥ 3

Basis: P(3) is true since 2(3) - 1 = 5 < 3! = 6.

Inductive Step: Assume P(k) holds, i.e., 2k - 1 ≤ k! for an arbitrary integer k ≥ 3. To show that P(k + 1) holds:

2(k+1) - 1 = 2k + 2 - 1

≤ 2 + k! (by the inductive hypothesis)

= (k + 1)! Therefore,2n-1 ≤ n! holds, for every integer n ≥ 3.

4 0

3 years ago

Hey yall, how is you doing?<br>

Klio2033 [76]

Answer:

doing well

Step-by-step explanation:

the reason i doing well is because nice people are giving me answers to questions that i need help with.

7 0

3 years ago

Read 2 more answers

Which of the following function rules represents the graph shown?

denpristay [2]

As the line raises from left to right, the slope must be positive, so only the function, f(x)=x-3, has a slope greater than zero. Additionally, at x=0, the y-value is at, or around, -3, confirming that f(x)=x-3 is the correct solution.

3 0

3 years ago

Read 2 more answers