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3 years ago

The height of a rocket a given number of seconds after it is released is modeled by . What does t represent?

1 answer:

6 0

$\bf ~~~~~~\textit{initial velocity} \\\\ \begin{array}{llll} ~~~~~~\textit{in feet} \\\\ h(t) = -16t^2+v_ot+h_o \\\\ ~~~~~~\textit{in meters} \\\\ h(t) = -4.9t^2+v_ot+h_o \end{array} \quad \begin{cases} v_o=\stackrel{}{\textit{initial velocity of the object}}\\\\ h_o=\stackrel{}{\textit{initial height of the object}}\\\\ h=\stackrel{}{\textit{height of the object at "t" seconds}} \end{cases}$

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Find the vertex, focus, directrix, and focal width of the parabola. (5 points)

Anarel [89]

$\bf \textit{vertical parabola vertex form with focus point distance} \\\\ 4p(y- k)=(x- h)^2 \qquad \begin{cases} \stackrel{vertex}{(h,k)}\qquad \stackrel{focus~point}{(h,k+p)}\qquad \stackrel{directrix}{y=k-p}\\\\ p=\textit{distance from vertex to }\\ \qquad \textit{ focus or directrix}\\\\ \stackrel{"p"~is~negative}{op ens~\cap}\qquad \stackrel{"p"~is~positive}{op ens~\cup} \end{cases} \\\\[-0.35em] \rule{34em}{0.25pt}$

$\bf -\cfrac{1}{20}x^2=y\implies \cfrac{x^2}{-20}=y\implies x^2=-20y\implies (x-0)^2=-20(y-0) \\\\\\ (x-\stackrel{h}{0})^2=4(\stackrel{p}{-5})(y-\stackrel{k}{0})$

something noteworthy is that the squared variable is the "x", thus the parabola is a vertical one, the "p" value is negative, so is opening downwards, and the h,k is pretty much the origin,

vertex is at (0,0)

the focus point is "p" or 5 units down from there, namely at (0, -5)

the directrix is "p" units on the opposite direction, up, namely at y = 5

the focal width, well, |4p| is pretty much the focal width, in this case, is simply yeap, you guessed it, 20.

8 0

3 years ago

Find the circumference of the circle. Use 3.14 for . Round to the nearest hundredth,.12.5 in. The circumference of the circle is

attashe74 [19]

69r + E is the answer

5 0

3 years ago

There are 34 beads on Brenda's necklace. 24 of the beads are pink and the rest are purple.

djyliett [7]

the correct answer is 24:10

6 0

3 years ago

Using subtraction what is 4 1/6-1 5/6

krek1111 [17]

Answer:

Step-by-step explanation:

the answer is 4 because 2.33333333333

is 4

4 0

3 years ago

Use a two-column proof to prove the Triangle Proportionality Theorem:

photoshop1234 [79]

Answer:

Step-by-step explanation:

From the picture attached,

Statements Reasons

1). In ΔABC, DE intersects AB and AC 1). Given

2). DE║BC 2). Given

3). ∠ADE ≅ ABC 3). Corresponding angles postulate

4). ∠AED ≅ ∠ACB 4). Corresponding angles postulate

5). ΔADE ~ ΔABC 5). AA similarity postulate

6). $\frac{AD}{AB}=\frac{AE}{AC}$ 6). Definition of two similar triangles

Hence proved.

4 0

3 years ago