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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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Find the equation of the line perpendicular to y = 3x + 6 and containing the point (-9,-5).

neonofarm [45]

The equation of the line perpendicular to y = 3x + 6 and containing the point (-9,-5) is $y = \frac{-1}{3}x - 8$

Solution:

Given that line perpendicular to y = 3x + 6 and containing the point (-9, -5)

We have to find the equation of line

The slope intercept form is given as:

y = mx + c ------ eqn 1

Where "m" is the slope of line and "c" is the y - intercept

Let us first find the slope of line

The given equation of line is y = 3x + 6

On comparing the given equation of line y = 3x + 6 with eqn 1, we get,

m = 3

Thus the slope of given equation of line is 3

We know that product of slopes of given line and slope of line perpendicular to given line is equal to -1

Slope of given line $\times$ slope of line perpendicular to given line = -1

$3 \times \text{ slope of line perpendicular to given line }= -1$

$\text{ slope of line perpendicular to given line } = \frac{-1}{3}$

Let us now find the equation of line with slope $m = \frac{-1}{3}$ and containing the point (-9, -5)

Substitute $m = \frac{-1}{3}$ and (x, y) = (-9, -5) in eqn 1

$-5 = \frac{-1}{3}(-9) + c\\\\-5 = 3 + c\\\\c = -8$

Thus the required equation of line is:

Substitute $m = \frac{-1}{3}$ and c = -8 in eqn 1

$y = \frac{-1}{3}x - 8$

Thus the required equation of line perpendicular to given line is found

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3 years ago

Deside whether g(x) = 2x^3 - 7x^2 - 3x^-1

mina [271]

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5 0

3 years ago

5 1/6 minus 1 2/3 PLZ HELP NOW

Ivenika [448]

21/6 simplified 7/2 or 3 1/2

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3 years ago

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Enrique can spend at most $2240 to renovate his home. One roll of wallpaper costs $32, and one can of paint costs $28. He needs

umka2103 [35]

The possible solution is having 30 rolls of wallpaper and 20 can of paints or 30 rolls of wallpaper with 46 can of paint.

<h3>Inequality</h3>

Inequality is the non equal comparison of two or more numbers and variables.

Let x represent the number of wallpapers and y represent the number of cans.

He needs at least 30 rolls of wallpaper and at least 20 cans of paint. Hence:

x ≥ 30 (1);

y ≥ 20 (2)

Also:

32x + 28y ≤ 2240 (3)

Plotting the 3 equations using geogebra online graphing tool, the possible solution is:

(30, 20), (30, 46)

The possible solution is having 30 rolls of wallpaper and 20 can of paints or 30 rolls of wallpaper with 46 can of paint.

Find out more on Inequality at: brainly.com/question/24372553

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2 years ago

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Pavel [41]

Answer:

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3 years ago