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3 years ago

which function increases at a faster rate on 0 to infinity, f(x) = x2 or g(x) = 2x? explain your reasoning

Mathematics

2 answers:

Helga [31]3 years ago

8 0

Answer:

Using a table of values, the outputs of f(x) for whole numbers are 0, 1, 4, 9, 16, 25, 36, and so on. For the same input values, g(x) has outputs of 1, 2, 4, 8, 16, 32, and 64. Continuing to double the output each time results in larger outputs than those of f(x). The exponential function, g(x), has a constant multiplicative rate of change and will increase at a faster rate than the quadratic function.

Step-by-step explanation:

Tcecarenko [31]3 years ago

7 0

F(x) = x² increases at a faster rate than g(x) = 2x.

f(x)

Reason:

x = 0, 1, 2, 3, 4, 5, 6, 7

f(x) = 0, 1, 4, 9, 16, 25, 36, 49

g(x) = 0, 2, 4, 6, 8, 10, 12, 14.

Comparing the values of f(x) and g(x), we can see that that of f(x) are far higher than that of g(x) for the same values of x.

So f(x) increases at a faster rate.

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You want to place a towel bar that is 10 1⁄4 inches long in the center of a door that is 26 1⁄3 inches wide. How far should you

mestny [16]

$\frac{26 \frac{1}{3} -10 \frac{1}{4}}{2}=\\ \frac{ \frac{79}{3} - \frac{41}{4} }{2} =\\ \frac{ \frac{79}{3} * \frac{4}{4} - \frac{41}{4} * \frac{3}{3} }{2} =\\ \frac{ \frac{356}{12}- \frac{123}{12} }{2} =\\ \frac{ \frac{233}{12} }{2} =\\ \frac{233}{24} =\\ 9\frac{17}{24}$

9 17/24 inches.

8 0

3 years ago

Read 2 more answers

The half-life of Radium-226 is 1590 years. If a sample contains 200 mg, how many mg will remain after 1000 years?

adell [148]

Answer: 129.33 g

Step-by-step explanation:

$$$Let $p=A \cdot e^{n t}$ \\$(p=$ present amount, $A=$ initial amount, $n=$ decay rate, $t=$ time)$

$\begin{aligned}&\Rightarrow \text { Given } p=\frac{A}{2} \ a t \ t=1590 \\&\Rightarrow \frac{1}{2}=e^{1590n} \Rightarrow n=\frac{\ln (1 / 2)}{1590}=-0.00043594162\end{aligned}$

$If $A=200 \mathrm{mg}$ and $t=1000$ then,$$\begin{aligned}P &=200 e^{\left(\frac{\ln \left(1/2\right)}{1590}\right) \cdot 1000} \text \\\\&=129.33 \text { grams}\end{aligned}$

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2 years ago

Samuel can type nearly 40 words per minute. Use this information to find the number of hours it would take him to type 3.8 × 105

lora16 [44]

Answer:

Step-by-step explanation:

3 0

3 years ago

Read 2 more answers

Can someone PLEASE help me with Trigonometry???

Svetach [21]

$\bf sin^2(2\theta)-7sin(2\theta)-1=0\\\\
-------------------------------\\\\
sin(2\theta)=\cfrac{7\pm\sqrt{49-4(1)(-1)}}{2(1)}\implies sin(2\theta)=\cfrac{7\pm\sqrt{49+4}}{2}
\\\\\\
sin(2\theta)=\cfrac{7\pm\sqrt{53}}{2}\implies 2\theta=sin^{-1}\left( \frac{7\pm\sqrt{53}}{2} \right)
\\\\\\
\theta=\cfrac{sin^{-1}\left( \frac{7\pm\sqrt{53}}{2} \right)}{2}$

but anyway, the numerator will give the angles, and θ is just half of each

$\bf \theta=\cfrac{sin^{-1}\left( \frac{7\pm\sqrt{53}}{2} \right)}{2}\\\\
-------------------------------\\\\
sin^{-1}\left( \frac{7+\sqrt{53}}{2} \right)\implies sin^{-1}(7.14)\impliedby \textit{greater than 1, no good}
\\\\\\
sin^{-1}\left( \frac{7-\sqrt{53}}{2} \right)\implies sin^{-1}(-0.14) \approx -8.05^o
\\\\\\
\theta=\cfrac{-8.05}{2}\implies \theta=-4.025$

ok... that's a negative tiny angle, is in the 4th quadrant, if we stick to the range given, from 0 to 360, so we have to use the positive version of it, 360-4.025

so the angle is 355.975°

now, the 3rd quadrant has another angle whose sine is negative, so... if we move from the 180° line down by 4.025, we end up at 184.025°

and those are the only two angles, because, on the 2nd and 1st quadrants, the sine is positive, so it wouldn't have an angle there

7 0

3 years ago

A bag contains red and blue marbles, such that the probability of drawing a blue marble is an experiment consists of drawing a

coldgirl [10]

Answer:

The range of the random variable is {0, 1, 2}.

Step-by-step explanation:

The bag contains red and blue marbles.

The experiments consists of two draws, with reposition.

The random variable assigns the number of blue marbles to each outcome.

If we have only two draws, we can only get 0, 1 or 2 blue marbles.

The range of the random variable is {0, 1, 2}.

8 0

3 years ago