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2 years ago

Transform each polar equation to an equation in rectangular form.

Mathematics

1 answer:

pickupchik [31]2 years ago

4 0

The equation of the line in slope-intercept form is equal to y = √3x + b.

<h3>How to transform polar coordinates to rectangular coordinates?</h3>

In geometry, the relationship between a rectangular coordinate (x, y) and a polar coordinate (r, θ) based on the conversion rules is given by these polar functions:

x = rcosθ ....equation 1.

y = rsinθ ....equation 2.

<u>Where:</u>

θ is the angle.

r is the radius of a circle.

Also, the slope from this angle is given by:

θ = tan⁻¹(y/x)

tan⁻¹ (π/3) = (y/x)

√3 = (y/x)

y = √3x

Mathematically, the equation of the line in slope-intercept form is given by this formula;

y = √3x + b.

Read more on polar coordinates here: brainly.com/question/2193539

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jasenka [17]

Answer:

1. The correct option B.

2.The correct option A.

Step-by-step explanation:

The given function is

$f(d)=-0.6d^2+5.4d+0.8$

Where f(d) is the height of the ball at horizontal distance d.

Put f(d)=0, to find the distance where the ball touch the ground.

$0=-0.6d^2+5.4d+0.8$

Quadratic formula:

$d=\frac{-b\pm \sqrt{b^2-4ac}}{2a}$

Using the quadratic formula we get

$d=\frac{-5.4\pm \sqrt{(5.4)^2-4(-0.6)(0.8)}}{2(-0.6)}$

$d=-0.146,9.146$

Therefore the ball is in air between d=-0.146 to d=9.146.

The distance can not be negative, therefore the ball remains in the air between d=0 to d=9.146.

$9.146\approx 9.15$

Therefore the correct option is B.

The given equation is

$y=(x-1)^2+1$ .... (1)

The standard form of parabola is

$y=a(x-h)^2+h$ .... (2)

Where, a is constant and (h,k) is vertex.

On comparing (1) and (2), we get

$a=1$

$h=1$

$k=1$

Since the value of a is positive, therefore it is an upward parabola. The vertex of the parabola is (1,1).

Put x=0 in the given equation.

$y=(0-1)^2+1$

$y=1+1=2$

Therefore the y-intercept is (0,2) and option A is correct.

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MariettaO [177]

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3 years ago

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netineya [11]

Answer:

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Step-by-step explanation:

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Answer:

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