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3 years ago

The equation of a circle in general form is x2+y2+20x+12y+15=0 .

Mathematics

1 answer:

Harlamova29_29 [7]3 years ago

5 0

Answer:

$(x +10)^2 + (y+6)^2 = 121$

Step-by-step explanation:

Given equation :

$x^2 + y^2 + 20x +12y + 15 = 0$

Standard equation of circle :

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

We will consider the x terms in the equation first to find a.

$(x-a)^2 = x^2 - 2ax + a^2$

-2ax = 20x

a = -20x/2x = -10

a = -10

Next consider the y terms to find b.

$(y - b)^2 = y^2 -2by + b^2$

-2by = 12y

b = -12y /2y = -6

b = -6

$(x+10)^2 + (y-6)^2 = x^2 +20x +100 + y^2 +12y + 36$

$=x^2 + y^2 + 20x +12y + 136\\$

But the given equation constant is 15. So find the difference between 136 and 15 to find the radius : 136 - 15 = 121

Therefore, radius = √121 = 11

<em><u>Equation in standard form : </u></em>

$(x +10)^2 + (y+6)^2 = 121$

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3 years ago

What is the area of the square adjacent to the third side of the triangle?

Naddik [55]

Answer:

85 units^2 = Area of Blue Square

and

x = 5 units

Step-by-step explanation:

To do this we use the Pythagorean theorem (a^2 + b^2 = c^2). a and b represent the legs of the triangle whereas c represents the longest side of the triangle, or the hypotenuse.

Since we know the area of a square is the side length multiplied by itself (or the side length squared), $\sqrt{35}$ is the side length of the pink square and $\sqrt{50}$ is the side length of the green square.

That means a = $\sqrt{35}$ and b = $\sqrt{50}$ , so...

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Now we need to square the square root of 85 to find the area of the blue square.

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85 units^2 = Area of Blue Square

To solve the other question we use the same formula again.

$x^2 + 12^2 = 13^2\\x^2 +144 = 169\\-144\\x^2 = 25\\x=\sqrt{25} \\x=5$

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3 0

3 years ago

If a person takes a prescribed dose of 10 milligrams of Valium, the amount of Valium in that person's bloodstream at any time ca

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Answer:

(a)8.0mg

(b)36.87 hours

(c)-0.168

Step-by-step explanation:

The amount of Valium in that person's bloodstream at any time can be modeled with the exponential decay function $A ( t ) = 10 e^{ -0.0188 t$ (t in hours)

(a)After 12 Hours

$A ( 12) = 10 e^{ -0.0188*12}\\=7.98\\\approx 8.0 mg $(to the nearest tenth of a milligram)$

(b)If A(t)=5mg

Then:

$5= 10 e^{ -0.0188 t}\\$Divide both sides by 10\\0.5=e^{ -0.0188 t}\\$Take the natural logarithm of both sides\\ln (0.5)=-0.0188 t\\t=ln (0.5) \div (-0.0188)\\$t=36.87 hours (to two decimal places.)$

(c)

$A ( t ) = 10 e^{ -0.0188 t}\\A'(t)=10(-0.0188)e^{ -0.0188 t}\\A'(t)=-0.188e^{ -0.0188 t}\\$At 6 hours, the rate at which the amount of Valium is decaying therefore is:\\A'(6)=-0.188e^{ -0.0188*6}\\$=-0.168 ( to three decimal places)$

3 0

2 years ago

Please answer 26 and 27 please thank you

ser-zykov [4K]

Answer:

Part 26) $3\frac{1}{4}\ in$

Part 27) $2\frac{2}{3}\ cups$

Step-by-step explanation:

Part 26)

we know that

The length of Alana's hair was 9 3/4 inches

After her haircut, the length was 6 1/2 inches

To find out how many inches did she have cut subtract 6 1/2 from 9 3/4

but first

Convert mixed number to an improper fraction

$9\frac{3}{4}\ in=\frac{9*4+3}{4}=\frac{39}{4}\ in$

$6\frac{1}{2}\ in=\frac{6*2+1}{2}=\frac{13}{2}\ in$

Find the difference

$\frac{39}{4}-\frac{13}{2}=\frac{39-26}{4}=\frac{13}{4}\ in$

Convert to mixed number

$\frac{13}{4}\ in=\frac{12}{4}+\frac{1}{4}=3\frac{1}{4}\ in$

Part 27)

we have that

Emeril used a total of 7 1/4 cups of flour to make three pastries

He used 2 1/4 cup of flour for the first and 2 1/3 cups of flour for the second

To find out how much cups of flour Emeril use for the third pastry, subtract the sum of the cups of flour used in the first and second pastry from the total cups of pastry used

Let

x ----> number of cups of flour used in the third pastry

$x=7\frac{1}{4}-(2\frac{1}{4} +2\frac{1}{3})$