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3 years ago

The endpoints of a diameter of a circle are located at (5,9) and (11,17) which is an equation of the circle?

Mathematics

1 answer:

lord [1]3 years ago

8 0

Answer:

(x - 8)² + (y - 13)² = 25

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

The centre is located at the midpoint of the endpoints of the diameter.

Use the midpoint formula to find the centre

[ $\frac{x_{1}+x_{2} }{2}$ , $\frac{y_{1}+y_{2} }{2}$ ]

with (x₁, y₁ ) = (5, 9) and (x₂, y₂ ) = (11,17)

centre = ( $\frac{5+11}{2}$ , $\frac{9+17}{2}$ ) = (8, 13)

The radius is the distance from the centre to either end of the diameter

Calculate r using the distance formula

r = √ (x₂ - x₁ )² + (y₂ - y₁ )²

with (x₁, y₁ ) = (8, 13) and (x₂, y₂ ) = (5, 9)

r = $\sqrt{(5-8)^2+(9-13)^2}$

= $\sqrt{(-3)^2+(-4)^2}$

= $\sqrt{9+16}$ = $\sqrt{25}$ = 5 ⇒ r² = 25

Hence

(x - 8)² + (y - 13)² = 25

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TRUE OR FALSE:

enot [183]

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Yes, this is true.
That's because an obtuse angle just means it's more than 90 but less than 180 degrees.

It is possible to have a right triangle that also contains a 110° angle.
No, this is false.
That's because a right triangle already has 90. That means that the two remaining angles must add up to 90 and not more or less.

It is possible to have an acute triangle that also contains a 70° angle.
Yes, this is true.
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Hope this helps :)

7 0

4 years ago

Walters savings account has a balance of $273. After 5 years, what will the amount of interest be at 5% compounded quarterly?

I am Lyosha [343]

The answer is $350

The formula is as follows: $P(1+r/n) ^{nt}$

P: Principal Amount : $273
r: Rate of interest: 5%
n: number of times the interest is compounded: 4 (Since Quarterly)
t: number of years : 5

7 0

4 years ago

The amount of polonium-210 remaining, p(t), after t days in a sample can be modeled by the exponential function p(t) = 100e−0.00

Archy [21]

Answer:

% Po lost = 100[1 - e^(-0.005t)] %; 73.0 g

Step-by-step explanation:

p(t) = 100e^(-0.005t)

Initial amount: p(0) = 100

Amount remaining: p(t) = 100e^(-0.005t)

Amount lost: p(0) – p(t) = 100 - 100e^(-0.005t) = 100[1 - e^(-0.005t)]

% of Po lost = amount lost/initial amount × 100 %

= [1 - e^(-0.005t)] × 100 % = 100[1 - e^(-0.005t)] %

p(63) = 100e^(-0.005 × 63) = 100e^(-0.315) = 100 × 0.730 = 73 g

The mass of polonium remaining after 63 days is 73 g.

4 0

3 years ago

<img src="https://tex.z-dn.net/?f=%28%5Cfrac%7B1%7D%7B4%7D%20%2B%5Cfrac%7B5%7D%7B4%7D%20%29%5E%7B2%7D%20%2B%5Cfrac%7B3%7D%7B4%7D

Assoli18 [71]

Answer:

Should be 3

Step-by-step explanation:

To add the fractions find the LCD then combine

4 0

3 years ago

Read 2 more answers

Type the correct answer in each box. If necessary, use /for the fraction bars

Vikentia [17]

Answer:

The experimental probability of rolling an odd number is 60%, which is 10% more than the theoretical probability.

Step-by-step explanation:

The complete question is:

Type the correct answer in each box. Use numerals instead of words. If necessary, use/ for the fraction bar(s).

A special 8-sided die is marked with the numbers 1 to 8. It is rolled 20 times with these outcomes.

3, 4, 5, 2, 7, 1, 3, 7, 2, 6, 2, 1, 7, 3, 6, 1, 8, 3, 5, 6

The experimental probability of rolling an odd number is _%, which is _% more than the theoretical probability.

Solution:

The possible outcomes of rolling an 8-sided die are:

S = {1, 2, 3, 4, 5, 6, 7, 8}

The odd numbers are:

Odd = {1, 3, 5, 7} = 4 outcomes

The theoretical probability of rolling an odd number is:

$P_{T}(\text{Odd})=\farc{4}{8}=\frac{1}{2}=50\%$

Now from the given 20 outcomes the odd values are:

Odd = {3, 5, 7, 1, 3, 7, 1, 7, 3, 1, 3, 5} = 12 outcomes

Compute the experimental probability of rolling an odd number as follows:

$P_{E}(\text{Odd})=\frac{12}{20}=\frac{3}{5}=60\%$

Thus, the experimental probability of rolling an odd number is 60%, which is 10% more than the theoretical probability.

6 0

3 years ago