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2 years ago

7

8. Measurement Jillian measured the distance around a small fishpond as 27 yards Which would be a good estimate for the distance

across the pond 14 yards 9 yards or 7 yards Explain how you decided

1 answer:

Anuta_ua [19.1K]2 years ago

3 0

May I see the picture of the pond if there is one?

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2 years ago

Amelia launched her science fair rocket, and then backed away. The path of the rocket is given by the equation below, where y is

Mamont248 [21]

Answer:

1)The rocket hit the ground at $x = \frac{5}{4}$

2)The maximum height of the rocket = 12.468 feet

Step-by-step explanation:

<u><em>Step(i):-</em></u>

Given equation

y = -2 x² + 5 x + 7 ...(i)

Differentiating equation (i) with respective to 'x' , we get

$\frac{dy}{dx} = -2( 2x) +5(1) = -4x +5$

Equating zero

$\frac{dy}{dx} = 0$

⇒ -4 x +5 =0

⇒ -4 x = -5

⇒ $x = \frac{5}{4}$

<em> The rocket hit the ground at </em> $x = \frac{5}{4}$ <em></em>

<u><em>Step(ii):</em></u>-

$\frac{dy}{dx} = -4x +5$ ...(ii)

Again differentiating equation (ii) with respective to 'x' , we get

$\frac{d^{2} y}{dx^{2} } = - 4(1)$

The maximum height at x = $\frac{-5}{4}$

y = -2 x² + 5 x + 7

$y = -2 (\frac{5}{4})^{2} + 5 (\frac{5}{4} ) + 7$

$y = \frac{-2(25)+ 25 (16)+7(64)}{64}$

$y = \frac{798}{64} = 12.468 feet$

<em>The maximum height of the rocket = 12.468 feet</em>

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2 years ago