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3 years ago

a rocket is launched from the ground at an initial velocity of 39.2 meters per second. which equation can be used to model the h

eight of the rocket after t seconds?

Mathematics

1 answer:

Sonbull [250]3 years ago

4 0

$\bf ~~~~~~\textit{initial velocity} \\\\ \begin{array}{llll} ~~~~~~\textit{in meters} \\\\ h(t) = -4.9t^2+v_ot+h_o \end{array} \quad \begin{cases} v_o=\stackrel{39.2}{\textit{initial velocity of the object}}\\\\ h_o=\stackrel{\textit{from the ground, so }0}{\textit{initial height of the object}}\\\\ h=\stackrel{}{\textit{height of the object at "t" seconds}} \end{cases} \\\\\\ h(t)=-4.9t^2+39.2t+0\implies h(t)=-4.9t^2+39.2t$

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2 years ago

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IrinaK [193]

Answer:

The rule of the arithmetic sequence is 13 - 2n

The 30th term is -47

Step-by-step explanation:

∵ f(n) = 11 and g(n) = -2(n - 1) = -2n + 2

∴ f(n) + g(n) = 11 + -2n + 2 = 13 - 2n

Use n = 1 , 2 , 3 , 4 to check the type of the sequence

∵ n = 1 ⇒ 13 - 2(1) = 11

∵ n = 2 ⇒ 13 - 2(2) = 13 - 4 = 9

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∵ 11 , 9 , 7 , 5 is an arithmetic sequence with difference -2

∴ The rule of the arithmetic sequence is 13 - 2n

∴ The 30th term = 13 - 2(30) = -47

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3 years ago

Read 2 more answers

Find all solutions to the equation:

crimeas [40]

Let z = sin(x). This means z^2 = (sin(x))^2 = sin^2(x). This allows us to go from the equation you're given to this equation: 7z^2 - 14z + 2 = -5

That turns into 7z^2 - 14z + 7 = 0 after adding 5 to both sides. Use the quadratic formula to solve for z. The only solution is z = 1 (see attached image). Since we made z = sin(x), this means sin(x) = 1. All solutions to this equation will be in the form x = (pi/2) + 2pi*n, which is the radian form of the solution set. If you need the degree form, then it would be x = 90 + 360*n

The 2pi*n (or 360*n) part ensures we get every angle coterminal to pi/2 radians (90 degrees), which captures the entire solution set.

Note: The variable n can be any integer.

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3 years ago

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sergejj [24]

Answer:

Step-by-step explanation:

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To find ( f - g)(x) , subtract g(x) from f(x)

That's

$( f - g)(x) = \frac{2x + 6}{3x} - \frac{ \sqrt{x} - 8}{3x}$

Since they have a common denominator that's 3x we can subtract them directly

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$\frac{2x + 6}{3x} - \frac{ \sqrt{x} - 8}{3x} = \frac{2x + 6 - ( \sqrt{x} - 8) }{3x} \\ = \frac{2x + 6 - \sqrt{x} + 8 }{3x} \\ = \frac{2x - \sqrt{x} + 6 + 8 }{3x}$

We have the final answer as

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