So the formula for a volume of a sphere is 4/3 times pi times the radius cubed.
step one: 4/3 times 3.14 = 4.18666666667
Step two: then you cube 8.5 and get 592.45
the final answer is 2,480.3906

6 0

2 years ago

A baseball is thrown in a parabolic arc. It's position above the ground at a given point in time

FinnZ [79.3K]

If the ball was thrown straight up at 24 ft/sec when it was 5 ft above the ground, the ball reached a maximum height of 7.25 m

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<h3>Further explanation</h3>

Discriminant of quadratic equation ( ax² + bx + c = 0 ) could be calculated by using :

From the value of Discriminant , we know how many solutions the equation has by condition :

D < 0 → No Real Roots

D = 0 → One Real Root

D > 0 → Two Real Roots

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An axis of symmetry of quadratic equation y = ax² + bx + c is :

$\large {\boxed {x = \frac{-b}{2a} } }$

Let us now tackle the problem!

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Given:

$p(t) = 3gt^2 + v_ot + p_o$

$p(t) = 3(-32)t^2 + 24t + 5$

$p(t) = -64t^2 + 24t + 5$

Asked:

$p_{max} = ?$

Solution:

At the maximum height , velocity is 0 m/s:

$v = \frac{dp(t)}{dt}$

$v = \frac{d}{dt} ( -64t^2 + 24t + 5 )$

$v = (-64)(2)t^{2-1} + 24$

$v = -128t + 24$

$0 = -128t + 24$

$128t = 24$

$t = 24 \div 128$

$t = 3 \div 16$

$t = 0.1875 \texttt{ s}$

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$p(t) = -64t^2 + 24t + 5$

$p(0.1875) = -64(0.1875)^2 + 24(0.1875) + 5$

$p(0.1875) = 7.25 \texttt{ m}$

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<h3>Learn more</h3>

Solving Quadratic Equations by Factoring : brainly.com/question/12182022
Determine the Discriminant : brainly.com/question/4600943
Formula of Quadratic Equations : brainly.com/question/3776858

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<h3>Answer details</h3>

Grade: High School

Subject: Mathematics

Chapter: Quadratic Equations

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Keywords: Quadratic , Equation , Discriminant , Real , Number

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3 0

2 years ago

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