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3 years ago

The diameter of a circle has endpoints P(-12, -4) and Q(6, 12).

Mathematics

1 answer:

nexus9112 [7]3 years ago

3 0

9514 1404 393

Answer:

(x +3)² +(y -4)² = 145

Step-by-step explanation:

The center of the circle is the midpoint of the given segment PQ. If we call that point A, then ...

A = (P +Q)/2

A = ((-12, -4) +(6, 12))/2 = (-12+6, -4+12)/2 = (-6, 8)/2

A = (-3, 4)

The equation of the circle for some radius r is ...

(x -(-3))² +(y -4)² = r² . . . . . . where (-3, 4) is the center of the circle

The value of r² can be found by substituting either of the points on the circle. If we use Q, then we have ...

(6 +3)² +(12 -4)² = r² = 9² +8²

r² = 81 +64 = 145

Then the equation of the circle is ...

(x +3)² +(y -4)² = 145

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Exercise 2.4.2: Proving statements about rational numbers with direct proofs. About Prove each of the following statements using

IgorLugansk [536]

Answer:

See Explanation

Step-by-step explanation:

(a) Proof: Product of two rational numbers

Using direct proofs.

Let the two rational numbers be A and B.

Such that:

$A = \frac{1}{2}$

$B = \frac{2}{3}$

The product:

$A * B = \frac{1}{2} * \frac{2}{3}$

$A * B = \frac{1}{1} * \frac{1}{3}$

$A * B = 1 * \frac{1}{3}$

$A * B = \frac{1}{3}$

Proved, because 1/3 is rational

(b) Proof: Quotient of a rational number and a non-zero rational number

Using direct proofs.

Let the two rational numbers be A and B.

Such that:

$A = \frac{1}{2}$

$B = \frac{2}{3}$

The quotient:

$A / B = \frac{1}{2} / \frac{2}{3}$

Express as product

$A / B = \frac{1}{2} / \frac{3}{2}$

$A / B = \frac{1*3}{2*2}$

$A / B = \frac{3}{4}$

Proved, because 3/4 is rational

(c) x + y is rational (missing from the question)

Using direct proofs.

Let x and y be

Such that:

$x = \frac{1}{2}$

$y = \frac{2}{3}$

The sum:

$x + y = \frac{1}{2} + \frac{2}{3}$

Take LCM

$x + y = \frac{3+4}{6}$

$x + y = \frac{7}{6}$

Proved, because 7/6 is rational

<em>The above proof works for all values of A, B, x and y; as long as they are rational values</em>

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3 years ago

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Answer:

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Step-by-step explanation:

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2 years ago

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irina [24]

Answer:

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7 0

2 years ago

Read 2 more answers

sam ran 63,756 feet in 70 minutes what is sam rate in miles per hour there are 5,280 feet in one mile

topjm [15]

Answer:

simply convert first feets into miles

Given is 5280 feets=1 miles

63756 /5280=12.075 miles

70 minutes = 1.16666= 1.17 hrs

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Step-by-step explanation:

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3 years ago

Use the factor theorem to determine whether the first polynomial is a factor of the second polynomial

Diano4ka-milaya [45]

Answer:

not a factor

Step-by-step explanation:

If (x - 3) is a factor then f(3) = 0

f(x) = 2x² - 4x + 30

f(3) = 2(3)² - 4(3) + 30 = 18 - 12 + 30 = 36 ≠ 0

Since f(3) ≠ 0 then (x - 3) is not a factor of f(x)

3 0

3 years ago