Mathematics, 23.02.2021 02:20 whocaresfasdlaf9341

A bullet is fired straight upward with an initial speed of 720 ft/s. It’s path is modeled by the equation h=-16t^2 + 720t, where h is the height of the bullet t seconds after it was fired. When does the bullet reach a height of 4,000 feet?

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Answer from: 1119diamondlord

The bullet reaches a height of 4000 feet after 6.49 seconds, and then, coming back down, after 38.5 seconds.

Step-by-step explanation:

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 $ax^{2} + bx + c = a(x - x_{1})*(x - x_{2})$ , given by the following formulas:

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

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

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

The height of the bullet after t seconds is given by:

h(t) = -16t^2 + 720t

When does the bullet reach a height of 4,000 feet?

This is t for which h(t) = 4000 . So

4000 = -16t^2 + 720t

16t^2 - 720t + 4000 = 0

Dividing by 16

t^2 - 45t + 250 = 0

So a = 1, b = -45, c = 250

$\bigtriangleup = b^{2} - 4ac = (-45)^2 - 4(1)(250) = 1025$

$t_{1} = \frac{-(-45) + \sqrt{1025}}{2} = 38.5$

$t_{2} = \frac{-(-45) - \sqrt{1025}}{2} = 6.49$

The bullet reaches a height of 4000 feet after 6.49 seconds, and then, coming back down, after 38.5 seconds.

Answer from: Quest

the system of inequity is

$y\leq -x+4$

$3y> x$

step-by-step explanation:

from the given graph it is noticed that we have two related lines. one is solid and another is dashed.

if a line passing through two points, then the equation of line is

$y-y_1=\frac{y_2-y_1}{x_2-x_1}(x-x_1)$

the solid line passing through the points (0,4) and (4,0).

$y-4=\frac{0-4}{4-0}(x-0)$

$y=-x+4$

the related equation of solid line is $y=-x+4$ .

similarly, find the related equation of dashed line. the dashed liune passing through the points (0,0) and (3,1).

$y-0=\frac{0-1}{3-0}(x-0)$

$3y=x$

the related equation of dashed line is $3y=x$

from the given graph it is noticed that the point (0,1) lies on the shaded region, therefore the point (0,1) must be satisfied by the related equations.

check the related equations by the point (0,1).

$1=-0+4$

$1=4$

this statement is true if the sign of inequality is < instead of equality. since it is an solid line therefore the sign of inequality will be $\leq$ . the required inequality is

$y\leq -x+4$

similarly, check the second related equation.

$3(1)=0$

it is a dashed line, so this statement is true if the sign of inequality is > . the required inequality is

$3y> x$

15 points write a system of inequalities to represent the shaded portion of the graph

Answer from: Quest

the correct answer is

c. 4

step-by-step explanation:

the given polynomial is

$-4x^4$

the degree of the polynomial is the highest exponent which is 4.

the -4 is called the leading coefficient.

this polynomial has only one term so it is a monomial.

the correct answer is option c.

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