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Alex777 [14]
3 years ago
14

Complete the parametric equations for the given rectangular equation.

Mathematics
1 answer:
Mama L [17]3 years ago
6 0

Answer:

1) x = 5√(1-sin^2t)

2) y = = -2+3t

Step-by-step explanation:

1)

Given rectangular equation:

x^2/25 + y^2 =1

Parametric equations y=-sint and x=?

Find parametric equation for x

Substituting value of y =-sint in given rectangular equation, we get

x^2/25 + (-sint )^2 =1

x^2/25 + sin^2t =1

x^2 + 25sin^2t = 25

x^2 =25 - 25sin^2t

taking square root on both sides

x= √(25 - 25sin^2t)

  = √25(1-sin^2t)

   = 5√(1-sin^2t)

2)

Given rectangular equation:

y=-3x+4

Parametric equations x=2-t and y=?

Find parametric equation for y

Substituting value of x=2-t  in given rectangular equation, we get

y= -3(2-t) +4

 = -6+3t+4

 = -2+3t !

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Answer:

a) f(x)=3x^{3}-6x^{2}-15x+30

Step-by-step explanation:

1) In this question we've been given "a", the leading coefficient. and two roots:

x_{1}=\sqrt{5}\:x_{2}=2

2) There's a theorem, called the Irrational Theorem Root that states:

If one root is in this form x'=\sqrt{a}+b  then its conjugate x''=\sqrt{a}-b. is also a root of this polynomial.

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x_3=-\sqrt{5}

3) So, applying this Theorem we can rewrite the equation, by factoring. Remembering that x is the root. Since the question wants it in this expanded form then:

f(x)=3(x-\sqrt{5})(x+\sqrt{5})(x-2)\Rightarrow 3x^{3}-6x^{2}-15x+30

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The slope-intercept form of the equation of the line through the given point with the given slope is y=-4x+1.

The given coordinate point is (-1, 5) and slope=-4.

<h3>What is the slope intercept form?</h3>

The slope intercept form of a straight line is one of the most common forms used to represent the equation of a line. The slope intercept formula can be used to find the equation of a line when given the slope of the straight line and the y-intercept.

The standard form of the slope intercept form is y=mx+c.

Substitute (x, y)=(-1, 5) and m=-4 in standard form of the slope intercept form, we get

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Substitute m=-4 and c=1 in y=mx+c, we get

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1 year ago
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Rudiy27

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parallel

Step-by-step explanation:

y=3/4x+2

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8y=6x+16

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3 years ago
A farmer sold 54 pumpkins the first weekend of a fall festival and 42 pumpkins the second weekend. Which expression uses the dis
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