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3 years ago

H=64t-32t^2 find the maximum height attained by the obiect

Mathematics

1 answer:

pshichka [43]3 years ago

5 0

Check the picture below.

so if we just find its vertex, we know how many feet it went up by its y-coordinate.

$\bf h=64t-32t^2\implies h=-32t^2+64t+0 \\\\[-0.35em] ~\dotfill$

$\bf \textit{vertex of a vertical parabola, using coefficients} \\\\ h=\stackrel{\stackrel{a}{\downarrow }}{-32}t^2\stackrel{\stackrel{b}{\downarrow }}{+64}t\stackrel{\stackrel{c}{\downarrow }}{+0} \qquad \qquad \left(-\cfrac{ b}{2 a}~~~~ ,~~~~ c-\cfrac{ b^2}{4 a}\right) \\\\\\ \left(-\cfrac{64}{2(-32)}~~,~~0-\cfrac{64^2}{4(-32)} \right)\implies \left( \stackrel{\stackrel{\textit{how many}}{\textit{seconds}}}{1}~~,~~\stackrel{\stackrel{\textit{how many feet}}{\textit{it went up}}}{32} \right)$

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garri49 [273]

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3 years ago

Catherine says that you can use the fact 24÷4=6 to find 240÷4.

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240÷4=60

Step-by-step explanation:

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3 years ago

At the school store, 3 pens and 2 notebooks cost a total of $12, while 1 pen and 3 notebooks cost a total of $11. This can be re

jasenka [17]

Answer:

Step-by-step explanation:

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3 years ago

Read 2 more answers

ANSWER PLEASE!!!!! ASAP!!! THANKS!!

GREYUIT [131]

Answer:

The answer is 64.

Step-by-step explanation:

To find the volume of a prism, you multiply l x w x h (length x width x height). The length is 8, width is 4, height is 2. 8 x 4 = 32, 32 x 2 = 64.

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3 years ago

Explain the steps to finding the vertex of g(x) = 3x2 + 12x + 15

RUDIKE [14]

Answer:

The vertex of this parabola, $(-2, 3)$ , can be found by completing the square.

Step-by-step explanation:

The goal is to express this parabola in its vertex form:

$g(x) = a\, (x - h)^2 + k$ ,

where $a$ , $h$ , and $k$ are constants. Once these three constants were found, it can be concluded that the vertex of this parabola is at $(h,\, k)$ .

The vertex form can be expanded to obtain:

$\begin{aligned}g(x)&= a\, (x - h)^2 + k \\ &= a\, \left(x^2 - 2\, x\, h + h^2\right) + k = a\, x^2 - 2\, a\, h\, x + \left(a\,h^2 + k\right)\end{aligned}$ .

Compare that expression with the given equation of this parabola. The constant term, the coefficient for $x$ , and the coefficient for $x^2$ should all match accordingly. That is:

$\left\lbrace\begin{aligned}& a = 3 \\ & -2\,a\, h = 12 \\& a\, h^2 + k = 15\end{aligned}\right.$ .

The first equation implies that $a$ is equal to $3$ . Hence, replace the " $a\!$ " in the second equation with $3\!$ to eliminate $\! a$ :

$(-2\times 3)\, h = 12$ .

$h = -2$ .

Similarly, replace the " $a$ " and the " $h$ " in the third equation with $3$ and $(-2)$ , respectively:

$3 \times (-2)^2 + k = 15$ .

$k = 3$ .

Therefore, $g(x) = 3\, x^2 + 12\, x + 15$ would be equivalent to $g(x) = 3\, (x - (-2))^2 + 3$ . The vertex of this parabola would thus be:

$\begin{aligned}&(-2, \, 3)\\ &\phantom{(}\uparrow \phantom{,\,} \uparrow \phantom{)} \\ &\phantom{(}\; h \phantom{,\,} \;\;k\end{aligned}$ .

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3 years ago