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ValentinkaMS [17]

3 years ago

5

If Joanne can paint a room in 3 hours and her sister Angela can paint the same room in 4 hours, how long (in h) would it take Jo

anne and Angela to paint the room working together? Round to the nearest tenth.

1 answer:

Gala2k [10]3 years ago

7 0

Answer:

Step-by-step explanation:

If J can paint a room in 3 hours, in 1 hour she gets $\frac{1}{3}$ of the job done.

If A can paint a room in 4 hours, in 1 hour she gets $\frac{1}{4}$ of the job done. We need to find out how long it takes them if they paint together. The equation for this is:

$\frac{1}{3}+\frac{1}{4}=\frac{1}{x}$ where x is the number of hours it takes them to get the job done together. Multiply everything through by 12x to get

4x + 3x = 12 so

7x = 12 and

x = 1.7 hours to get the room painted together.

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**Spam answers will not be tolerated**

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

What is the answer to 20/8x+16

Readme [11.4K]

Answer:

Step-by-step explanation:

It is 40

8 0

3 years ago

Read 2 more answers

What is are indices

White raven [17]

Answer:

The index of a number says how many times to use the number in a multiplication. It is written as a small number to the right and above the base number. In this example: 82 = 8 × 8 = 64. The plural of index is indices. (Other names for index are exponent or power.)

Step-by-step explanation:

8 0

3 years ago

The area of the U.S. is about 3.931 million square miles. Approximately 570000 square miles are worked for food production. What

PSYCHO15rus [73]

Answer:

Step-by-step explanation:

Just estimating, about 15%

% = Land used for food production/ Total Area * 100

% = (570000 / 3.931 * 10^6) * 100%

% = 14.5%

3 0

3 years ago

Lamar hikes Trail B, which is 2 1/2. He stops every 5/6. How many stops does he make?

Dahasolnce [82]

Answer:

2

Step-by-step explanation:

To solve this equation, you need to convert 2 1/2 into an improper fraction:

2 1/2 = 5/2

Then, you convert this into 6ths:

5/2 = 15/6

Next, you divide 15/6 by 5/6:

15/6 / 5/6 = 3

Because Jamal wouldn't make a stop at the end (it wouldn't be considered a stop because he is done), you subtract 1:

3-1=2

The answer is 2 (hope this helps, sorry if i got it wrong)

4 0

3 years ago