All categories

3 years ago

Which point lies on a circle with a radius of 5 units and center at P(6, 1)?

Mathematics

2 answers:

BabaBlast [244]3 years ago

5 0

Answer:

Step-by-step explanation:

The equation of a circle in standard form is

(x - h)² + (y - k)² = r²

where (h, k) are the coordinates of the centre and r is the radius

here (h, k) = (6, 1) and r = 5, thus

(x - 6)² + (y - 1)² = 25 ← equation of circle

To determine which point lies on the circle, substitute the coordinates into the left side and if equal to the right side then point is on the circle

A (1, 11)

(1 - 6)² + (11- 1)² = (- 5)² + 10² = 25 + 100 = 125 ≠ 25 ← not on circle

B (2, 4)

(2 - 6)² + (4 - 1)² = (- 4)² + 3² = 16 + 9 = 25 ← lies on circle

C (4, - 4)

(4 - 6)² + (- 4 - 1)² = (- 2)² + (- 5)² = 4 + 25 = 29 ≠ 25 ← not on circle

D (9, - 2)

(9 - 6)² + (- 2 - 1)² = (- 3)² + (- 3)² = 9 + 9 = 18 ≠ 25 ← not on circle

The only point that lies on the circle is R(2, 4)

guapka [62]3 years ago

3 0

Answer:

R (2,4)

soln

center(h,k)=(6,1)

radius (r)=5units

eqn of circle is (x-6)^2+(y-1)^2=5^2

2 2

or, 25=x +y -12x-2y+36+1 now , only the given point (6,1)satisfies the eqn so this point lies on circle

You might be interested in

If p is the hypothesis of a conditional statement and q is the conclusion, which is represented by ~p → ~q?

Bogdan [553]

It is equivalent to q -> p.

4 0

3 years ago

Find the length of the unknown side round your answer to the nearest whole number 18 and 4

EastWind [94]

Answer:

17.5

Step-by-step explanation:

90% sure

8 0

2 years ago

Which of the following is the graph of f(x) = 3 sin (2x)? (2 points)

TEA [102]

Answer:

Step-by-step explanation:

4 0

3 years ago

Find the area of a trapezoid with base 1 side = 10 base 2 side = 16 and 3

mart [117]

Answer:

Area of Trapezoid is 39 unit²

Step-by-step explanation:

Given as :

For A Trapezoid

The measure of base side 1 = $b_1$ = 10 unit

The measure of base side 2 = $b_2$ = 16 unit

The height of the Trapezoid = h = 3 unit

Let The Area of Trapezoid = A square unit

<u>Now, From Formula</u>

Area of Trapezoid = $\dfrac{1}{2}$ × (sum of opposite base) × height

I.e A = $\dfrac{1}{2}$ × ( $b_1$ + $b_2$ ) × h

Or, A = $\dfrac{1}{2}$ × (10 unit + 16 unit) × 3 unit

Or, A = $\dfrac{1}{2}$ × (26 unit) × 3 unit

Or, A = $\dfrac{1}{2}$ × 78 unit²

Or, A = $\dfrac{78}{2}$ unit²

I.e A = 39 unit²

So, The Area of Trapezoid = A = 39 unit²

Hence, The Area of Trapezoid is 39 unit² . Answer

6 0

3 years ago

At 95% confidence, how large a sample should be taken to obtain a margin of error of 0.03 for the estimation of a population pro

Gnom [1K]

Answer:

A sample of 1068 is needed.

Step-by-step explanation:

In a sample with a number n of people surveyed with a probability of a success of $\pi$ , and a confidence level of $1-\alpha$ , we have the following confidence interval of proportions.

$\pi \pm z\sqrt{\frac{\pi(1-\pi)}{n}}$

In which

z is the zscore that has a pvalue of $1 - \frac{\alpha}{2}$ .

The margin of error is:

$M = z\sqrt{\frac{\pi(1-\pi)}{n}}$

95% confidence level

So $\alpha = 0.05$ , z is the value of Z that has a pvalue of $1 - \frac{0.05}{2} = 0.975$ , so $Z = 1.96$ .

At 95% confidence, how large a sample should be taken to obtain a margin of error of 0.03 for the estimation of a population proportion?

We need a sample of n.

n is found when M = 0.03.

We have no prior estimate of $\pi$ , so we use the worst case scenario, which is $\pi = 0.5$

Then

$M = z\sqrt{\frac{\pi(1-\pi)}{n}}$

$0.03 = 1.96\sqrt{\frac{0.5*0.5}{n}}$

$0.03\sqrt{n} = 1.96*0.5$

$\sqrt{n} = \frac{1.96*0.5}{0.03}$

$(\sqrt{n})^{2} = (\frac{1.96*0.5}{0.03})^{2}$

$n = 1067.11$

Rounding up

A sample of 1068 is needed.

8 0

3 years ago