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3 years ago

Write the equation in standard form of a circle with center (-3,6), tangent to the y-axis.

Mathematics

1 answer:

Romashka-Z-Leto [24]3 years ago

8 0

Answer:

$(x+3)^2+(y-6)^2=9$

Step-by-step explanation:

The equation of a circle in standard form is written as

$(x-a)^2+(y-b)^2=r^2$

where

(a, b) are the coordinates of the center

r is the radius of the circle

In this problem, the circle is centered at (-3,6), so we have

a = -3

b = 6

Also, we know that the circle is tangent to the y-axis, and the x-coordinate of its center is 3: this means that the horizontal distance between the point of the circle tangent to the y-axis and the centre of the circle is 3, therefore the radius of the circle is 3.

So, the equation of this circle is:

$(x-(-3))^2+(y-6)^2=3^2$

$(x+3)^2+(y-6)^2=9$

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The polynomial p(x)=3x^3-20x^2+37x-20 has a known factor of (x-4). Rewrite p(x) as a product of linear factors. p(x) =

vesna_86 [32]

Answer:

$p(x) = (3x^{2} - 8x + 5)(x - 4)$

Step-by-step explanation:

p(x) has degree 3

(x - 4) has degree 1

So p(x) can be rewritten as a polynomial of degree 2 multiplying (x-4)

$p(x) = (ax^{2} + bx + c)(x - 4)$

To find a, b and c, we have to divide p(x) by x - 4.

Finding a:

Dividing the first term of p(x) by x - 4.

$\frac{3x^{3}}{x - 4} = 3x^{2}$

So a = 3.

Now multiplying 3x² by, x - 4, we have:

$3x^{2}(x - 4) = 3x^{3} - 12x^{2}$

Subtracting p(x) from this:

$3x^{3} - 20x^{2} + 37x - 20 - (3x^{3} - 12x^{2}) = 3x^{3} - 20x^{2} + 37x - 20 - 3x^{3} + 12x^{2} = -8x^{2} + 37x - 20$

Finding b:

Dividing the first term, after the subtraction, by x - 4.

$\frac{-8x^{2}}{x - 4} = -8x$

So b = -8.

Multiplying -8x by x - 4, we have:

$-8x(x-4) = -8x^{2} + 32x$

Then

$-8x^{2} + 37x - 20 - (-8x^{2} + 32x) = -8x^{2} + 37x - 20 + 8x^{2} - 32x = 5x - 20$

Finding c:

$\frac{5x}{x - 4} = 5$

So c = 5.

Just to verify if the remainder is 0.

$5(x - 4) = 5x - 20$

$5x - 20 - (5x - 20) = 0$

Then:

$p(x) = (ax^{2} + bx + c)(x - 4)$

$p(x) = (3x^{2} - 8x + 5)(x - 4)$

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3 years ago

Find the amount of interest on a loan of $10,500, at 9% interest, for 124 days using the exact interest method.

mr Goodwill [35]

Step-by-step explanation:

I = PRT

I = 10,500 * 0.09 * (124/365)

I = 945 * 0.3397

I = 321.04

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3 years ago

The back frame of a dog house is in the shape of a triangle with an area of 6 square feet. The height of the frame is 4 feet. Wh

Soloha48 [4]

The area of a triangle is A = bh/2 (base times height divided by 2).
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3 years ago

What is the value of the expression 1/2-(-1/3+2/5)

11111nata11111 [884]

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Step-by-step explanation:

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3 years ago

Which ordered pair would form proportional relationship with the point graphed below ?

tangare [24]

Answer:

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this is the only pair achievable by proportion.

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3 years ago