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3 years ago

Which number line best shows how to solve −8 − (−2)?

Mathematics

1 answer:

Flauer [41]3 years ago

7 0

Answer:

It would be the third one

Step-by-step explanation:

The one with the shortest top arrow because if you have -8 and you minus that by -2 that cancels out and instead the minus turns into a plus and the 2 becomes positive therefore it becomes -6

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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

A value of 500 increases by 12%

Blizzard [7]

Value of 500 increased by 12% is 560

4 0

3 years ago

The weight, in pounds, of a newborn baby t months after birth can be modeled by W. A graph of W is shown below. Write an equatio

Agata [3.3K]

the First we need to choose two points in the graph

(0,6)=(t1,w1)

(1,7)=(t2,w2)

the variables are t and w

then we can calculate the slope

$m=\frac{w2-w1}{t2-t1}=\frac{7-6}{1-0}=\frac{1}{1}=1$

the equation of W is

where

m=1 ---> slope

b=6 ---> y-intercept

$\begin{gathered} W=mt+b \\ W=1\cdot t+6 \\ W=t+6 \end{gathered}$

the answers are

W=t+6

slope of the function 1

the answer is the third option

5 0

1 year ago

I need help with number 3

Lynna [10]

The hexagon divides the circle into 6 parts. That means the angle projecting each side is: 360°÷ 6 = 60°

The area of a circle is: πr²
78.54 in² divided by pi is 25 making the radius = 5

I would then use SOH CAH TOA to solve for the side.. knowing the hypotenuse is the radius and the angle to split it into a right triangle is 30°

Sin(30) = s/5
5*Sin(30) = s

12*s = perimeter hexagon
(remember s is half the hexagon side)

12*5*Sin(30) = perimeter hexagon
30 inches = perimeter

6 0

4 years ago

in a farm 20% of animals are cows . 0.4 are goat and the rest are sheep.How many cows are there if there are 40 sheeps

Zolol [24]

Step-by-step explanation:

20%=cows 0.4(40%)=goat 40%=sheep

if 40%sheep=40 sheeps

20% cow=x

20%×40=40%×x

8=40%x

x=8/40%

x=20

..so there are 20 cows

sorry...not sure

3 0

3 years ago

Read 2 more answers