14.Write an equation of the line that passes through (2, 7)(2, 7) and (0, −5)

Mathematics

1 answer:

Rzqust [24]3 years ago

6 0

Answer:

Step-by-step explanation:

The slope-intercept form of an equation of a line:

$y=mx+b$

<em>m</em><em> - slope</em>

<em>b</em><em> - y-intercet → (0, b)</em>

The formula of a slope:

$m=\sdeac{y_2-y_1}{x_2-x_1}$

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14.

(2, 7), (0, -5) → <em>b = -5</em>

Calculate the slope:

$m=\dfrac{-5-7}{0-2}=\dfrac{-12}{-2}=6$

The equation of a line:

$y=6x-5$

15.

(-6, 0), (0, -24) → <em>b = -24</em>

Calculate the slope:

$m=\dfrac{-24-0}{0-(-6)}=\dfrac{-24}{6}=-4$

The equation of a line:

$y=-4x-24$

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NASA launches a rocket at t=0 seconds. Its height, in meters above sea-level, as a function of time is given by h(t)=−4.9t2+121t

Alenkasestr [34]

NASA launches a rocket at t = 0 seconds. Its height, in meters above sea-level, as a function of time is given by

$h(t)=-4.9t^2+121t+283$

The sea level is represented by h = 0, therefore, to find the corresponding time when h splashes into the ocean we have to solve for t the following equation:

$h(t)=0\implies-4.9t^2+121t+283=0$

Using the quadratic formula, the solution for our problem is

$\begin{gathered} t=\frac{-(121)\pm\sqrt{(121)^2-4(-4.9)(283)}}{2(-4.9)} \\ =\frac{121\pm142.083778...}{9.8} \\ =\frac{121+142.083778...}{9.8} \\ =26.8452834694... \end{gathered}$

The rocket splashes after 26.845 seconds.

The maximum of this function happens at the root of the derivative. Differentiating our function, we have