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3 years ago

Type your questiona circle has a diameter of 81 pie square units. what is the diameter of the circle?

1 answer:

7 0

I think your question should read "A circle has an AREA of 81 PI square units...)
Circle Area = PI * radius^2
81 PI = PI * radius ^2
radius^2 = 81 PI / PI
radius^2 = 81
radius = 9
Therefore circle diameter = 9 * 2 = 18

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Find the equation of the tangent of x^2- xy + y^2 =7 at (-1, 2)

Citrus2011 [14]

Answer:

It is 3y = 4x + 10

Step-by-step explanation:

Let's first get the slope of the curve.

[ slope is the derivative of the equation ]

${x}^{2} - xy + {y}^{2} = 7$

introduce dy/dx :

$\frac{d}{dx} ( {x}^{2} - xy + {y}^{2} ) = \frac{d}{dx} (7) \\ \\ 2x - (y + \frac{dy}{dx} ) + 2y \frac{dy}{dx} = 0$

make dy/dx the subject:

$2x - y - \frac{dy}{dx} + 2y \frac{dy}{dx} = 0 \\ \\ 2y \frac{dy}{dx} - \frac{dy}{dx} = y - 2x \\ \\ \frac{dy}{dx} (2y - 1) = y - 2x \\ \\ \frac{dy}{dx} = \frac{y - 2x}{2y - 1}$

At point (-1, 2):

$\frac{dy}{dx} = \frac{2 - 2( - 1)}{2(2) - 1} \\ \\ slope = \frac{4}{3}$

but a tangent has the same slope as the curve:

$y = mx + c$

m is the slope

c is the y-intercept

At (-1, 2):

$2 = ( - 1 \times \frac{4}{3} ) + c \\ \\ c = 2 + \frac{4}{3} \\ \\ c = \frac{10}{3}$

equation:

$y = \frac{4}{3} x + \frac{10}{3} \\ \\ { \boxed{3y = 4x + 10}}$

8 0

3 years ago

Read 2 more answers

Answer this problem: What is 4x2?

tiny-mole [99]

Answer:

Step-by-step explanation:

1 2 3 4 5 6 7 8

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3 years ago

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A change in heat energy can lead to a change in phase of or state of matter

ziro4ka [17]

Answer:

true

Step-by-step explanation:

if an object is losing heat energy, it turns cold, and can turn into a solid, for example, water turning into ice. If you apply heat on ice, it's turns back to water. IF you apply heat to water, it vaporizes, and turns into gas.

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3 years ago

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dos aviones parten de una ciudad con direcciones S32°E y E57°N¿ cuál es el angulo que forma sus direcciones?

Elan Coil [88]

Answer:

El ángulo formado entre las dos direcciones es aproximadamente 115º.

Step-by-step explanation:

Las direcciones dadas en el enunciado significan lo siguiente:

S32ºE - 32º al este del sur.

E57ºN - 57º al norte del este.

Vectorialmente hablando, cada dirección es la siguiente:

S32ºE

$A(x,y) = (\sin 32^{\circ}, -\cos 32^{\circ})$

$A(x,y) = (0.530, -0.848)$

E57ºN

$B(x,y) = (\cos 57^{\circ},\sin 57^{\circ})$

$B(x,y) = (0.545, 0.839)$

El ángulo formado entre los dos vectores unitarios ( $\theta$ ), medido en grado sexagesimales, puede determinarse mediante la siguiente ecuación vectorial:

$\theta = \cos^{-1} \frac{A\,\bullet \,B}{\|A\|\cdot \|B\|}$

Donde:

$\|A\|$ - Norma de $A(x,y)$ .

$\|B\|$ - Norma de $B(x,y)$ .

Si sabemos que $A(x,y) = (0.530, -0.848)$ , $B(x,y) = (0.545, 0.839)$ , $\|A\| = 1$ y $\|B\| = 1$ , entonces el ángulo formado entre los dos vectores es: