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Thepotemich [5.8K]
3 years ago
6

Plz

Mathematics
1 answer:
allsm [11]3 years ago
4 0
Top box is 2x
bottom box is 3
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Which formula represents Charles's law? ?
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The answer would be: V1/T1=V2/T2

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If xy + y² = 6, then the value of dy/dx at x= -1 is<br>​
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Hi there!

\large\boxed{\text{At (-1, -2), }\frac{dy}{dx} = -\frac{2}{5}}}

\large\boxed{\text{At (-1, 3), }\frac{dy}{dx} = -\frac{3}{5}}}

We can calculate dy/dx using implicit differentiation:

xy + y² = 6

Differentiate both sides. Remember to use the Product Rule for the "xy" term:

(1)y + x(dy/dx)  + 2y(dy/dx) = 0

Move y to the opposite side:

x(dy/dx) + 2y(dy/dx) = -y

Factor out dy/dx:

dy/dx(x + 2y) = -y

Divide both sides by x + 2y:

dy/dx = -y/x + 2y

We need both x and y to find dy/dx, so plug in the given value of x into the original equation:

-1(y) + y² = 6

-y + y² = 6

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(y - 3)(y + 2) = 0

Thus, y = -2 and 3.

We can calculate dy/dx at each point:

At y = -2: dy/dx = -(-2) / -1+ 2(-2) = -2/5.

At y = 3: dy/dx = -(3) / -1 + 2(3) = -3/5.

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3 years ago
describe how axioms about addition in particular could be helpful in developing theorems about multiplication.
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The axioms in addition help in developing theorems about multiplication because multiplication, in simple terms, repeated addition.
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Check the picture below.

let's recall that a straight-line has 180°, and that sum of all interior angles in a triangle is also 180°.

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