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shepuryov [24]
3 years ago
8

the equation of a circle is x - y + 1 = 0 . if one end of the diameter is ( 3, p) and other end is ( a, 2 ) , find the equation

of the circle.

Mathematics
1 answer:
erma4kov [3.2K]3 years ago
8 0
I gave the answer earlier, but here is the solution again, along with a graph proving it is correct.

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MULTIPLE CHOICE
Dvinal [7]

Step 1) Multiply 2 by 3

<em>5x+6 = 2x+3x+6</em>

Step 2) Combine like terms

<em>5x+6 = 5x+6</em>

Step 3) Add 5x and 6 to both sides

Answer:

<em>0 = 0</em>

4 0
3 years ago
The table shows the maximum and minimum depths of two submarines. Find the range of depths for each submarine. Then determine wh
JulsSmile [24]

Answer:

Range A = 386ft

Range B = 427ft

B has the larger range.

Explanation:

To find the range, find the difference between the minimum and maximum depths for each submarine. Remember that your answer will be positive.

Sub A:

-146ft - (-532ft) = 386 ft

Sub B:

-194ft - (-621ft) = 427 ft

Submarine B has a larger range.

7 0
3 years ago
Determine all prime numbers a, b and c for which the expression a ^ 2 + b ^ 2 + c ^ 2 - 1 is a perfect square .
kogti [31]

Answer:

The family of all prime numbers such that a^{2} + b^{2} + c^{2} -1 is a perfect square is represented by the following solution:

a is an arbitrary prime number. (1)

b = \sqrt{1 + 2\cdot a \cdot c} (2)

c is another arbitrary prime number. (3)

Step-by-step explanation:

From Algebra we know that a second order polynomial is a perfect square if and only if (x+y)^{2} = x^{2} + 2\cdot x\cdot y  + y^{2}. From statement, we must fulfill the following identity:

a^{2} + b^{2} + c^{2} - 1 = x^{2} + 2\cdot x\cdot y + y^{2}

By Associative and Commutative properties, we can reorganize the expression as follows:

a^{2} + (b^{2}-1) + c^{2} = x^{2} + 2\cdot x \cdot y + y^{2} (1)

Then, we have the following system of equations:

x = a (2)

(b^{2}-1) = 2\cdot x\cdot y (3)

y = c (4)

By (2) and (4) in (3), we have the following expression:

(b^{2} - 1) = 2\cdot a \cdot c

b^{2} = 1 + 2\cdot a \cdot c

b = \sqrt{1 + 2\cdot a\cdot c}

From Number Theory, we remember that a number is prime if and only if is divisible both by 1 and by itself. Then, a, b, c > 1. If a, b and c are prime numbers, then  2\cdot a\cdot c must be an even composite number, which means that a and c can be either both odd numbers or a even number and a odd number. In the family of prime numbers, the only even number is 2.

In addition, b must be a natural number, which means that:

1 + 2\cdot a\cdot c \ge 4

2\cdot a \cdot c \ge 3

a\cdot c \ge \frac{3}{2}

But the lowest possible product made by two prime numbers is 2^{2} = 4. Hence, a\cdot c \ge 4.

The family of all prime numbers such that a^{2} + b^{2} + c^{2} -1 is a perfect square is represented by the following solution:

a is an arbitrary prime number. (1)

b = \sqrt{1 + 2\cdot a \cdot c} (2)

c is another arbitrary prime number. (3)

Example: a = 2, c = 2

b = \sqrt{1 + 2\cdot (2)\cdot (2)}

b = 3

4 0
3 years ago
Suppose it is known that for a given differentiable function y=f(x), its tangent line (local linearization) at the point where a
AleksandrR [38]

Answer:

y(-4) = 5

y'(-4) = -7

Step-by-step explanation:

Hi!

Since the tangent line T and the curve y must coincide at x=-4

y(-4) = T(-4) = 5

On the other hand, the derivative of the curve evaluated at -4 y'(x=-4) must be the slope of the tangent line. Which inspecting the tangent line T(x) is -7

That is:

y'(-4) = -7

6 0
2 years ago
solve the following word problem. use x for the unknown value. the average cost of a car in 2013 is said to be 5 less than twice
Rashid [163]
Let the average cost of car in 2009 be $x, then the average cost of a car in 2013 is 2x - 5
25,000 = 2x - 5
2x = 25,000 + 5 = 25,005
x = 25,005/2 = $12,502.50
7 0
3 years ago
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