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3 years ago

A teapot is

Mathematics

1 answer:

lions [1.4K]3 years ago

7 0

Answer:

If you mean 1/3 and 2/3; The answer is (1/2) teacup = 1 full container.

Step-by-step explanation:

(1/3)t = (2/3)c, the t for teapot and c for the container.

Multiply both sides by (3/2) in order to get 1 on the right-hand side.

(3/2)(1/3)t = (3/2)(2/3)C

(1/2) teacup = 1 full container.

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1. For centuries, mathematicians believed that quadratic equations, like the one below, had no solutions and were not solvable.

7nadin3 [17]

Answer:

See below.

Step-by-step explanation:

(a) Because the solution led to a square root of a negative number:

x^2 -10x+40=0

x^2 - 10x = -40 Completing the square:

(x - 5)^2 - 25 = -40

(x - 5)^2 = -15

x = 5 +/-√(-15)

There is no real square root of -15.

(b) A solution was found by introducing the operator i which stands for the square root of -1.

So the solution is

= 5 +/- √(15) i.

These are called complex roots.

x^2 - 10 + 40:

((5 + √(-15)i)^2 - 10(5 + √(-15)i) + 40

= 25 + 10√(-15)i - 15 - 50 - 10√(-15)i + 40

= 25 - 15 - 50 + 40

= 0. So this checks out.

Now substitute 5 - √(-15)i

= 25 - 10√(-15)i - 15 - 50 + 10√(-15)i + 40

= 25 - 15 - 50 + 40

= 0. This checks out also.

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Answer:

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Step-by-step explanation:

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