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erastovalidia [21]
3 years ago
12

A ball, thrown vertically upwards, from the ground, has its height h (in meters) expressed as a function of time t (in seconds),

elapsed after the launch, by the law h(t) = 20t - 5t2. According to this information, determine the height at which the ball is 3 seconds after the throw and the maximum height reached by the ball.
Mathematics
1 answer:
zhuklara [117]3 years ago
5 0
Height at 3 sec: 15 meters

Max height: 20 meters
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If y is proportional to the sqaure root of x and y equal x when x equal 5,evaluate y when x eqaul 9.​
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Answer:

y = 3\, \sqrt{5} when x = 9.

Step-by-step explanation:

The question states that y is proportional to \sqrt{x}. In other words, there is a constant a (a \ne 0) such that y = a\, \sqrt{x} for all x \ge 0.

The question also states that y = x when x = 5. Make use of this equality to find the value of a.

Since x = 5 and y = x, it must be true that y = 5. Substitute x = 5\! and y = 5\! into the equation y = a\, \sqrt{x} and solve for a:

5 = a\, \sqrt{5}.

\begin{aligned}a &= \frac{5}{\sqrt{5}} \\ &= \sqrt{5}\end{aligned}.

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Substitute in the value x = 9 to find the corresponding value of y:

\begin{aligned} y &= \sqrt{5} \, (\sqrt{9}) \\ &= \sqrt{5} \times 3 \\ &= 3\, \sqrt{5}\end{aligned}.

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