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9966 [12]
3 years ago
13

Quadrilateral ABCD ​ is inscribed in this circle.

Mathematics
1 answer:
miskamm [114]3 years ago
7 0

The measure of angle A is 65°

Explanation:

Given that ABCD is a quadrilateral inscribed in a circle.

The measure of angle A is \angle A=(2x+1)^{\circ}

The measure of angle B is \angle B=148^{\circ}

The measure of angle D is \angle D=x^{\circ}

We need to determine the measure of angle A.

Since, we know that the angles B and D are opposite angles and the opposite angles of a quadrilateral add up to 180°

Thus, we have,

\angle B+\angle D=180^{\circ}

Substituting the values, we have,

148^{\circ}+x=180^{\circ}

          x=32^{\circ}

Thus, the value of x is 32°

Substituting the value of x in the measure of angle A, we get,

\angle A=(2x+1)^{\circ}

\angle A=(2(32)+1)^{\circ}

\angle A=(64+1)^{\circ}

\angle A=65^{\circ}

Thus, the measure of angle A is 65°

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Step-by-step explanation:

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Marine biologists have determined that when a shark detectsthe presence of blood in the water, it will swim in the directionin w
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Solution :

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If the shark always swim in the direction of maximum increase of blood concentration, its direction at any point would coincide with the gradient vector.

Then we know the shark's path is perpendicular to the level curves it intersects.

b). We have :

$\triangledown C= \frac{\partial C}{\partial x}i+\frac{\partial C}{\partial y}j$

$\Rightarrow \triangledown C =-\frac{2}{10^4}e^{-(x^2+2y^2)/10^4}(xi+2yj),$ and

$\triangledown C$ points in the direction of most rapid increase in concentration, which means $\triangledown C$ is tangent to the most rapid increase curve.

$r(t)=x(t)i+y(t)j$  is a parametrization of the most $\text{rapid increase curve}$ , then

$\frac{dx}{dt}=\frac{dx}{dt}i+\frac{dy}{dt}j$ is a tangent to the curve.

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∴ $\frac{dy}{dx}=\frac{dy/dt}{dx/dt}=\frac{2y}{x}$

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$\frac{dy}{y}=2\frac{dx}{x}$

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$y=\frac{y_0}{x_0^2}x^2$

$y=y_0\left(\frac{x}{x_0}\right)^2$

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3 0
3 years ago
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