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2 years ago

Dada la recta 3x +4y - 12=0 encontrar los puntos de interseccion de la parábola y^2=-9x

Mathematics

1 answer:

Radda [10]2 years ago

3 0

Answer:

(-4 , 6)

Step-by-step explanation:

3x +4y - 12=0

x = 1/3 × (12-4y)

y² = 9 × 1/3 × (12-4y) = 36 -12y

y² + 12y -36 =0

(y -6)² = 0

y = 6

x = -4

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Misha Larkins [42]

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2 years ago

A square has a diagonal length of 10 ft. Draw a diagram and determine the perimeter of the square.

denpristay [2]

The perimeter of the square is: $20\sqrt2$ ft

Step-by-step explanation:

The picture is attached with the answer.

the diagonal of a square divides it into two right angled-triangles.

We can use one of the triangle to find the length of side as the diagonal will be the hypotenuse of the triangle

Let a be the side of the square, then according to Pythagoras theorem

$d^2=a^2+a^2\\(10)^2 = 2a^2\\2a^2=100$

Dividing both sides by 2

$\frac{2a^2}{2}=\frac{100}{2}\\a^2=50$

Taking Square root on both sides

$\sqrt{a^2}=\sqrt{50}\\a=\sqrt{25*2}\\a=\sqrt{5^2 * 2}\\a=5\sqrt{2}\ ft$

Now,

$P = 4a\\P = 4 * 5\sqrt{2}\\=20\sqrt{2}\ ft$

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The perimeter of the square is: $20\sqrt2$ ft

Keywords: Perimeter, Pythagoras Theorem

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2 years ago

use green's theorem to evaluate the line integral along the given positively oriented curve. c 9y3 dx − 9x3 dy, c is the circle

Rina8888 [55]

The line integral along the given positively oriented curve is -216π. Using green's theorem, the required value is calculated.

<h3>What is green's theorem?</h3>

The theorem states that,

$\int_CPdx+Qdy = \int\int_D(\frac{\partial Q}{\partial x} - \frac{\partial P}{\partial y})dx dy$

Where C is the curve.

<h3>Calculation:</h3>

The given line integral is

$\int_C9y^3dx-9x^3dy$

Where curve C is a circle x² + y² = 4;

Applying green's theorem,

P = 9y³; Q = -9x³

Then,

$\frac{\partial P}{\partial y} = \frac{\partial 9y^3}{\partial y} = 27y^2$

$\frac{\partial Q}{\partial x} = \frac{\partial -9x^3}{\partial x} = 27x^2$

$\int_C9y^3dx-9x^3dy = \int\int_D(-27x^2 - 27y^2)dx dy$

⇒ $-27\int\int_D(x^2 + y^2)dx dy$

Since it is given that the curve is a circle i.e., x² + y² = 2², then changing the limits as

0 ≤ r ≤ 2; and 0 ≤ θ ≤ 2π

Then the integral becomes

$-27\int\limits^{2\pi}_0\int\limits^2_0r^2. r dr d\theta$

⇒ $-27\int\limits^{2\pi}_0\int\limits^2_0 r^3dr d\theta$

⇒ $-27\int\limits^{2\pi}_0 (r^4/4)|_0^2 d\theta$

⇒ $-27\int\limits^{2\pi}_0 (16/4) d\theta$

⇒ $-108\int\limits^{2\pi}_0 d\theta$

⇒ $-108[2\pi - 0]$

⇒ -216π

Therefore, the required value is -216π.

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1 year ago

The probability of winning a school raffle is 2%. What is the probability of not winning the raffle?

xeze [42]

Answer:

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Step-by-step explanation:

If the probability of winning a school raffle is 2%, the probability of not winning the raffle would be 98%.

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1 year ago

The area of the shaded region

lbvjy [14]

Answer:

27.74cm^2

Step-by-step explanation:

area of circle: 3 times 3 times pi = 28.26cm^2

area of square: 8 times 7 = 56cm^2

subtract area of circle from square

56-28.26=27.74cm^2

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2 years ago

Dada la recta 3x +4y - 12=0 encontrar los puntos de interseccion de la parábola y^2=-9x​

Dada la recta 3x +4y - 12=0 encontrar los puntos de interseccion de la parábola y^2=-9x