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4 years ago

What is the range for this set of data? 7,15,12

2 answers:

5 0

To find the range of data, you first order the data least to greatest:
7, 12, 15
Then you subtract the smallest number from the largest:
15-7=8

The range is 8.

Oxana [17]4 years ago

5 0

8 is your answer because its just biggest to smallest.

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Morgarella [4.7K]

Answer:

$f'(x)=-\frac{2}{x^\frac{3}{2}}$

Step-by-step explanation:

So we have the function:

$f(x)=\frac{4}{\sqrt x}$

And we want to find the derivative using the limit process.

The definition of a derivative as a limit is:

$\lim_{h \to 0} \frac{f(x+h)-f(x)}{h}$

Therefore, our derivative would be:

$\lim_{h \to 0}\frac{\frac{4}{\sqrt{x+h}}-\frac{4}{\sqrt x}}{h}$

First of all, let's factor out a 4 from the numerator and place it in front of our limit:

$=\lim_{h \to 0}\frac{4(\frac{1}{\sqrt{x+h}}-\frac{1}{\sqrt x})}{h}$

Place the 4 in front:

$=4\lim_{h \to 0}\frac{\frac{1}{\sqrt{x+h}}-\frac{1}{\sqrt x}}{h}$

Now, let's multiply everything by (√(x+h)(√(x))) to get rid of the fractions in the denominator. Therefore:

$=4\lim_{h \to 0}\frac{\frac{1}{\sqrt{x+h}}-\frac{1}{\sqrt x}}{h}(\frac{\sqrt{x+h}\sqrt x}{\sqrt{x+h}\sqrt x})$

Distribute:

$=4\lim_{h \to 0}\frac{({\sqrt{x+h}\sqrt x})\frac{1}{\sqrt{x+h}}-(\sqrt{x+h}\sqrt x)\frac{1}{\sqrt x}}{h({\sqrt{x+h}\sqrt x})}$

Simplify: For the first term on the left, the √(x+h) cancels. For the term on the right, the (√(x)) cancel. Thus:

$=4 \lim_{h\to 0}\frac{\sqrt x-(\sqrt{x+h})}{h(\sqrt{x+h}\sqrt{x}) }$

Now, multiply both sides by the conjugate of the numerator. In other words, multiply by (√x + √(x+h)). Thus:

$= 4\lim_{h\to 0}\frac{\sqrt x-(\sqrt{x+h})}{h(\sqrt{x+h}\sqrt{x}) }(\frac{\sqrt x +\sqrt{x+h})}{\sqrt x +\sqrt{x+h})}$

The numerator will use the difference of two squares. Thus:

$=4 \lim_{h \to 0} \frac{x-(x+h)}{h(\sqrt{x+h}\sqrt x)(\sqrt x+\sqrt{x+h})}$

Simplify the numerator:

$=4 \lim_{h \to 0} \frac{x-x-h}{h(\sqrt{x+h}\sqrt x)(\sqrt x+\sqrt{x+h})}\\=4 \lim_{h \to 0} \frac{-h}{h(\sqrt{x+h}\sqrt x)(\sqrt x+\sqrt{x+h})}$

Both the numerator and denominator have a h. Cancel them:

$=4 \lim_{h \to 0} \frac{-1}{(\sqrt{x+h}\sqrt x)(\sqrt x+\sqrt{x+h})}$

Now, substitute 0 for h. So:

$=4 ( \frac{-1}{(\sqrt{x+0}\sqrt x)(\sqrt x+\sqrt{x+0})})$

Simplify:

$=4( \frac{-1}{(\sqrt{x}\sqrt x)(\sqrt x+\sqrt{x})})$

(√x)(√x) is just x. (√x)+(√x) is just 2(√x). Therefore:

$=4( \frac{-1}{(x)(2\sqrt{x})})$

Multiply across:

$= \frac{-4}{(2x\sqrt{x})}$

Reduce. Change √x to x^(1/2). So:

$=-\frac{2}{x(x^{\frac{1}{2}})}$

Add the exponents:

$=-\frac{2}{x^\frac{3}{2}}$

And we're done!

$f(x)=\frac{4}{\sqrt x}\\f'(x)=-\frac{2}{x^\frac{3}{2}}$

5 0

3 years ago

Help ????????????????????

Degger [83]

Answer:

first one is 90

second one is 108

Step-by-step explanation:

7 0

4 years ago

What is the slope of the line (9,-6) and (-6- -9)?

Vlada [557]

Answer:

1/5

Step-by-step explanation:

Slope formula = (y2-y1)/(x2-x1)

((-6)- (-9))/ ((9)-(-6)

(-6 + 9)/ (9 + 6)

3/15

1/5

6 0

3 years ago

Read 2 more answers

Which step brings you closest to getting the variable alone on one side of the equation

Oliga [24]

Answer:

Adding 5 from both sides then dividing by 7

Step-by-step explanation:

The best way to isolate x is to add 5 to both sides first:

21 = 7x

Then to isolate x by itself divide both sides by 7

x = 3

That would be the value of x and your final answer.

5 0

3 years ago

Read 2 more answers

The equation y = kx represents a proportional relationship between x and y, where k is the constant of proportionality. For a mo

kvasek [131]

Answer:

Hello!!!

In this specific case the constant of proportionality is s (speed).

Step-by-step explanation:

The constant of proportionality stay "constant" (as the name suggests) in a certain case.

meaning, the speed itself remains constant at any given distance or time.

You can use the constant of proportionality and either distance or time to find the missing varliable since it remains constant.

you can also switch up the formula:

d=st

t=d/s

s=d/t

i really hope this helps!!!!!

3 0

2 years ago