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1 year ago

Find the distance between each pair of points (round answer to the nearest tenth if necessary)

Mathematics

2 answers:

Delvig [45]1 year ago

8 0

Answer: d=5

$d=\sqrt{(7-7)^2+(-3-(-8))^2} \\d=\sqrt{(0)^2+(5)^2}\\ d=\sqrt{0+25}\\ d=\sqrt{25}\\ d=5$

Step-by-step explanation: I hope this helps.

Elden [556K]1 year ago

4 0

Answer: 5

Step-by-step explanation:

$(7,-8)\ \ \ \ (7,-3)\\\\L=\sqrt{(7-7)^2+(-3-(-8)^2)}\\\\L=\sqrt{0^2+(-3+8)^2} \\\\L=\sqrt{0+5^2} \\\\L=\sqrt{5^2} \\\\L=5$

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A ball is thrown from an initial height of 7 feet with an initial upward velocity of 24 fts. The ball's height h (in feet) after

Montano1993 [528]

Answer:

The ball's height is 11 feet at t = 0.19s and t = 1.31s

Step-by-step explanation:

The ball's height h (in feet) after seconds is given by the following function:

$h(t) = 7 + 24t - 16t^{2}$

Find all values of t for which the ball's height is 11 feet.

This is t when $h(t) = 11$ .

We will need to solve a quadratic equation for this.

Solving a quadratic equation

Given a second order polynomial expressed by the following equation:

$ax^{2} + bx + c, a\neq0$ .

This polynomial has roots $x_{1}, x_{2}$ such that $ax^{2} + bx + c = (x - x_{1})*(x - x_{2})$ , given by the following formulas:

$x_{1} = \frac{-b + \sqrt{\bigtriangleup}}{2*a}$

$x_{2} = \frac{-b - \sqrt{\bigtriangleup}}{2*a}$

$\bigtriangleup = b^{2} - 4ac$

In this problem:

$h(t) = 11$

$7 + 24t - 16t^{2} = 11$

$16t^{2} - 24t + 4 = 0$

Simplifying by 4

$4t^{2} - 6t + 1 = 0$

So $a = 4, b = -6, c = 1$

$\bigtriangleup = (-6)^{2} - 4*(4)*1 = 20$

$x_{1} = \frac{-(-6) + \sqrt{20}}{2*4} = 1.31$

$x_{2} = \frac{-(-6) - \sqrt{20}}{2*4} = 0.19$

The ball's height is 11 feet at t = 0.19s and t = 1.31s

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