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Mathematics

1 answer:

marusya05 [52]2 years ago

4 0

Answer:

Area is 168

Step-by-step explanation:

(Base x height)

(12x14) = 168

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Derive the equation of the parabola with a focus at (-5,5) and a directix of y = -1

Paladinen [302]

Answer:

Step-by-step explanation:

From any point (x, y) on the parabola the focus and directrix are equidistant

Using the distance formula

$\sqrt{(x+5)^2+(y-5)^2}$ = | y + 1 |

Squaring both sides

(x + 5)² + (y - 5)² = (y + 1)^2 , that is

(y + 1)² = (x + 5)² + (y - 5)² ← subtract (y - 5)² from both sides

(y + 1)² - (y - 5)² = (x + 5)² ← expand left side and simplify

y² + 2y + 1 - y² + 10y - 25 = (x + 5)²

12y - 24 = (x + 5)² ← factor left side

12(y - 2) = (x + 5)² ← divide both sides by 12

y - 2 = $\frac{1}{12}$ (x + 5)² ← add 2 to both sides

y = $\frac{1}{12}$ (x + 5)² + 2

f(x) = $\frac{1}{12}$ (x + 5)² + 2 → D

7 0

3 years ago

Solving quadratic equations with complex solutions x2 + 4x + 8 = 0.

Daniel [21]

Answer:

$\large\boxed{x=-2\pm2i}$

Step-by-step explanation:

$x^2+4x+8=0\qquad\text{subtract 8 from both sides}\\\\x^2+4x+8-8=0-8\\\\x^2+2(x)(2)=-8\qquad\text{add}\ 2^2\ \text{to both sides}\\\\x^2+2(x)(2)+2^2=-8+2^2\qquad\text{use}\ (a+b)^2=a^2+2ab+b^2\\\\(x+2)^2=-8+4\\\\(x+2)^2=-4\iff x+2=\pm\sqrt{-4}\\\\x+2=\pm\sqrt{(4)(-1)}\qquad\text{use}\ \sqrt{ab}=\sqrt{a}\cdot\sqrt{b}\\\\x+2=\pm\sqrt4\cdot\sqrt{-1}\qquad\text{use}\ \sqrt{-1}=i\\\\x+2=\pm2\cdot i\qquad\text{subtract 2 from both sides}\\\\x=-2\pm2i$