Describe how to determine whether the parabola y = 3x2 + 3x + 6 is opening upward.

Mathematics

1 answer:

qaws [65]2 years ago

4 0

Answer:

Opening upward

Step-by-step explanation:

<u>Standard equation of parabola is:</u>

y = ax² + bx + c

The parabola is opening upward if a > 0 and opening downward if a < 0

The given parabola has a = 3 > 0, therefore it is opening upward

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Express in terms of logarithm without exponents

sdas [7]

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\\ \quad \\
% Logarithm of rationals
\\ \quad \\
% Logarithm of exponentials
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-----------------------------\\\\
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6 0

2 years ago

Fill in Sin, Cos, and tan ratio for angle x. <br> Sin X = 4/5 (28/35 simplified)

Fantom [35]

Answer:

Given: $\sin(x) = (4/5)$ .

Assuming that $0 < x < 90^{\circ}$ , $\cos(x) = (3/5)$ while $\tan(x) = (4/3)$ .

Step-by-step explanation:

By the Pythagorean identity $\sin^{2}(x) + \cos^{2}(x) = 1$ .

Assuming that $0 < x < 90^{\circ}$ , $0 < \cos(x) < 1$ .

Rearrange the Pythagorean identity to find an expression for $\cos(x)$ .

$\cos^{2}(x) = 1 - \sin^{2}(x)$ .

Given that $0 < \cos(x) < 1$ :

$\begin{aligned} &\cos(x) \\ &= \sqrt{1 - \sin^{2}(x)} \\ &= \sqrt{1 - \left(\frac{4}{5}\right)^{2}} \\ &= \sqrt{1 - \frac{16}{25}} \\ &= \frac{3}{5}\end{aligned}$ .