What quadrant is the point (-4,7) in?

Mathematics

1 answer:

Vikentia [17]3 years ago

3 0

Answer:

Quadrant 2

Step-by-step explanation:

Quadrant 1: Positive x and Positive y

Quadrant 2: Negative x and Positive y

Quadrant 3: Negative x and Negative y

Quadrant 4: Positive x and Negative y

For point (-4, 7), we have a Negative x and Positive y so it belongs in Quadrant 2.

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Which of the following represents the polar equation r = (cot 2θ)(csc θ) as a rectangular equation?

STALIN [3.7K]

The option that depicts the polar equation r = (cot 2θ)(csc θ) as an equation that is rectangular is: y² = 2x.

<h3>What is a polar equation?</h3>

A polar expression is any equation that describes the correlation between r and θ, where r signifies the anticlockwise angle formed by a point on a curve, the pole, and the positive x-axis, and means the breadth between the origin and a location on a curve.

<h3>What is the solution to the equation above?</h3>

Step 1 - expand the polar equation

r = 2cosθ * cscθ

Step 2 - convert csc and cos to their equivalents in tan and sin

r = 2 * (1/tanθ) * (1/sinθ) * sinθ

r = 2 * (1/tanθ) * sinθ/sinθ

r = 2 * 1/tanθ

r = 2/tanθ, making 2 the subject of the formula, we have

rtanθ = 2

Note that rectangular coordinates of a point will be depicted as (x,y) and it's plolar coordinate will be (r, θ).

This mean

x = r cos θ; and

y = r sinθ

From the above, we can state that:

Since y = r sinθ
⇒ tanθ = y/x

⇒ (rsinθ/y) * tanθ = 2

Thus y * (y/x) = 2

Therefore,

y²/x = 2

y² = 2x

Learn more about polar equation at:

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5 0

2 years ago

En una panadería se elaboraron 140 panes diarios, el 25% son conchas, 10% cortadillos, 40% donas y 25% bolillos. Cada pieza de p

torisob [31]

Answer:

Se obtuvo $ 448 de ganancia por la venta de donas.

Se obtuvo $ 280 de ganancia por la venta de bolillos.

Step-by-step explanation:

1) <em>¿Cuanta ganancia se obtuvo en la venta de donas?</em>

La ganancia es el producto del porcentaje producido de donas, expresado como razón, el precio unitario de la dona y el total producido de panes. Es decir:

$C = \frac{40\,donas}{100\,panes}\times (140\,panes)\times \left(8\,\frac{USD}{dona} \right)$

$C = 448\,USD$

Se obtuvo $ 448 de ganancia por la venta de donas.

2) <em>¿Cuanta ganancia se obtuvo en la venta de bolillos?</em>

La ganancia es el producto del porcentaje producido de bolillos, expresado como razón, el precio unitario del bolillo y el total producido de panes. Es decir:

$C = \frac{25\,bolillos}{100\,panes}\times (140\,panes)\times \left(8\,\frac{USD}{bolillo}\right)$