Mathematics, 12.11.2020 04:00 parcess

An object was dropped off the top of a building. The function f(x)=-16x^2+144f(x)=−16x 2 +144 represents the height of the object above the ground, in feet, xx seconds after being dropped. Find and interpret the given function values and determine an appropriate domain for the function.

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Answer from: Geo777

The domain of the function is required.

The domain of the function is the set of real numbers

$x\in(-\infty,\infty)$

The function is

f(x)=-16x^2+144

The y intercept of the function is

$y=-16\times 0+144\\\Rightarrow y=144$

(0,144)

The y intercept is the maximum height here.

The x intercepts are the points where the object is on the ground.

They are

$0=-16x^2+144\\\Rightarrow 16x^2=144\\\Rightarrow x=\pm\sqrt{\dfrac{144}{16}}\\\Rightarrow x=\pm3$

(3,0),(-3,0)

The domain of the function is the set of real numbers

$x\in(-\infty,\infty)$

The graph of the figure is attached.

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Answer from: wananikwecurley99

Step-by-step explanation:

Given the height at which an ogject dropped modelled by the function f(x)=-16x^2+144

The height of the body on the ground occurs at when f(x) = 0

0 =-16x^2+144

16x^2 = 144

x^2 = 144/16

x^2 = 9

x = 3

The ball reached the ground after 3 secs

The domain of a function is the input function that will make the function exist. Based on the function given, the function can exist on all given input value of x. Hence the domain of the function will be;

Domain =(-\infty, infty)

An object was dropped off the top of a building. The function f(x)=-16x^2+144f(x)=−16x 2 +144 repres

Answer from: Quest

step-by-step explanation:

let

we know that

the y-intercept is the y-coordinate of the point when the value of x is equal to zero

the y-coordinate of the point a is the y-intercept

the answer part a) is

the value of y-intercept is

part b) find the slope m

we know that

the value of the slope is equal to

substitute the values

therefore

the answer part b) is

the value of the slope is equal to

the general answer is

the slope is

the value of y-intercept is

Answer from: Quest

x =-.20752

step-by-step explanation:

4^(x+2)=12

take the log base 4 on each side

log 4 (4^(x+2) = log 4(12)

we know log b(a^y) = y log b (a)

(x+2) log 4(4) = log 4 (12)

x+2 = log 4 (12)

we know logb c = loga c/loga b

we want to convert to base 10 so a = 10

by default, we do not write the 10 c = 4 and b = 10

log4 10 = log 12/log 4

log4 10 = log 12/ log 4

x+2 = log 12/ log 4

subtract 2 from each side

x +2 -2 = log 12/ log 4 -2

x = 1.79248125 -2

x =-.20752

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An object was dropped off the top of a building. The function f(x)=-16x^2+144f(x)=−16x 2 +144 repres...