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3 years ago

X + 2y – 4z = 1 -2x – 4y + 4z = 6 -4x – 3y – 4z = 21

Mathematics

1 answer:

elena55 [62]3 years ago

6 0

Answer:

x = - 1

y = - 3

z = -2

Step-by-step explanation:

Please see steps in the image attached here.

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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

2 years ago

What is a real world word problem for 57.5=p(250)

sladkih [1.3K]

If p(x) is a function, then a real-world example might be

The amount of fish food, in grams required for the giant koi fish in the pond can be represented by the function $p(f)=\frac{f}{50} +7.5$ . If there are 50 fish, how many grams of fish food will you need?

$p(250)=\frac{250}{50} +7.5$
$p(250)=50 +7.5$
$p(250) = 57.5$

3 0

3 years ago

Read 2 more answers

(Apex 2.2.4 math 8)

Gennadij [26K]

Answer: D

Step-by-step explanation: slope = "rise over run" = 1.5/18 = 3/36 = 1/12 for the 1st section to the landing

slope is the change in height, the vertical change, divided by the change in horizontal distance

2nd section has slope 1/18 and covers 9 feet. That means it rises 1/2 foot

slope = 1/18 = (1/2)/9

the door is 2 feet higher than the ground level, 1.5 + .5 = 2 feet change vertically

5 0

2 years ago

Read 2 more answers

Number of rides marine can go on ?

saul85 [17]

Answer:

Check step by step explanation

Step-by-step explanation:

a) Let x represent the amount of rides she takes, the 6 and 2.5 represent the amount of money required to enter

A(x) = 1.5x + 6

B(x) = 2x + 2.5

b) You can find this by making the 2 equations equal to each other and solving for x

1.5x + 6 = 2x + 2.5

3.5 = .5x

7 = x

7 rides make them equal cost

c) Plug in 5 for each of the equations and find out which one is cheaper

A(5) = 1.5 * 5 + 6

A(5) = $13.50

B(5) = 2 * 5 + 2.5

B(5) = $12.50

Carnival B is cheaper

4 0

3 years ago

You own a lawn care business. in a typical week you drive 600 miles and use 40 gallons of gasoline. gasoline costs $1.25 per gal

iVinArrow [24]

42.50$ ? 21 times 1.25 plus 13 times 1.25 = 42.50?

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3 years ago