$\bf \textit{vertex of a vertical parabola, using coefficients} \\\\ f(x)=\stackrel{\stackrel{a}{\downarrow }}{3}x^2\stackrel{\stackrel{b}{\downarrow }}{-24}x\stackrel{\stackrel{c}{\downarrow }}{+8} \qquad \qquad \left(-\cfrac{ b}{2 a}~~~~ ,~~~~ c-\cfrac{ b^2}{4 a}\right) \\\\\\ \left(-\cfrac{-24}{2(3)}~~,~~8-\cfrac{(-24)^2}{4(3)} \right)\implies (4~~,~~8-48)\implies (4~~,~-40)$

5 0

3 years ago

A rectangular

igor_vitrenko [27]

A = length x width

15,000 = (w + 30) x w
15,000 = $w^{2}$ + 30w
0 = $w^{2}$ + 30w - 15,000

Use quadratic formula to find that w= -15 + or - 5 $\sqrt{609}$ . Because distance cannot be negative, the width is -15 + 5 $\sqrt{609}$ meters or approximately 108.39 meters. This means that the length is approximately 138.39 meters.

8 0

3 years ago

Sin^2x + sin2x +2cox^2x = 2

Effectus [21]

Answer:

Step-by-step explanation:

$sin^2 \ x + sin ^2 \ x + 2cos^ 2\ x = 2\\\\2sin^2 \ x + 2 cos^2 \ x = 2\\\\2 ( sin^2 \ x + cos^2 \ x ) = 2 \\\\2 \times 1 = 2 \\\\2 = 2 \\\\LHS = RHS \\\\Hence \ proved.$

5 0

2 years ago