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ICE Princess25 [194]
2 years ago
12

Johanna, Elizabeth, and Dan are preparing a chemical solution for a research project. When

Mathematics
1 answer:
Bond [772]2 years ago
8 0

Using the together rate, it is found that they would prepare the solution in 1.71 minutes working together.

<h3>What is the together rate?</h3>

It is the sum of each separate rate.

In this problem, the rates are given by:

  • Johanna's: 1/6.
  • Elizabeth's: 1/6.
  • Dan's: 1/4.

Hence the together rate is given by:

\frac{1}{x} = \frac{1}{6} + \frac{1}{6} + \frac{1}{4}

\frac{1}{x} = \frac{1}{3} + \frac{1}{4}

\frac{1}{x} = \frac{4 + 3}{12}

7x = 12

x = 12/7

x = 1.71.

They would prepare the solution in 1.71 minutes working together.

More can be learned about the together rate at brainly.com/question/25159431

#SPJ1

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Find lim x→3 sqrt 2x+3-sqrt 3x/ x^2-3x. you must show your work or explain your work in words plsss I need help
sineoko [7]

I'm assuming the limit is supposed to be

\displaystyle\lim_{x\to3}\frac{\sqrt{2x+3}-\sqrt{3x}}{x^2-3x}

Multiply the numerator by its conjugate, and do the same with the denominator:

\left(\sqrt{2x+3}-\sqrt{3x}\right)\left(\sqrt{2x+3}+\sqrt{3x}\right)=\left(\sqrt{2x+3}\right)^2-\left(\sqrt{3x}\right)^2=-(x-3)

so that in the limit, we have

\displaystyle\lim_{x\to3}\frac{-(x-3)}{(x^2-3x)\left(\sqrt{2x+3}+\sqrt{3x}\right)}

Factorize the first term in the denominator as

x^2-3x=x(x-3)

The x-3 terms cancel, leaving you with

\displaystyle\lim_{x\to3}\frac{-1}{x\left(\sqrt{2x+3}+\sqrt{3x}\right)}

and the limand is continuous at x=3, so we can substitute it to find the limit has a value of -1/18.

7 0
3 years ago
Help me with this exercise
Vinil7 [7]
<em>The answer you are looking for is: </em>
<em><u>270 yards^{2} </u></em>
<em><u>15*18= 270 </u></em>
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6 0
3 years ago
Given: sin(18m-12)=cos(7m+2), find the value of m.
V125BC [204]

Answer:

m = -2/7 + π/14 + (π n_1)/7 for n_1 element Z

or m = 2/3 - (π n_2)/18 for n_2 element Z

Step-by-step explanation:

Solve for m:

-cos(7 m + 2) sin(12 - 18 m) = 0

Multiply both sides by -1:

cos(7 m + 2) sin(12 - 18 m) = 0

Split into two equations:

cos(7 m + 2) = 0 or sin(12 - 18 m) = 0

Take the inverse cosine of both sides:

7 m + 2 = π n_1 + π/2 for n_1 element Z

or sin(12 - 18 m) = 0

Subtract 2 from both sides:

7 m = -2 + π/2 + π n_1 for n_1 element Z

or sin(12 - 18 m) = 0

Divide both sides by 7:

m = -2/7 + π/14 + (π n_1)/7 for n_1 element Z

or sin(12 - 18 m) = 0

Take the inverse sine of both sides:

m = -2/7 + π/14 + (π n_1)/7 for n_1 element Z

or 12 - 18 m = π n_2 for n_2 element Z

Subtract 12 from both sides:

m = -2/7 + π/14 + (π n_1)/7 for n_1 element Z

or -18 m = π n_2 - 12 for n_2 element Z

Divide both sides by -18:

Answer: m = -2/7 + π/14 + (π n_1)/7 for n_1 element Z

or m = 2/3 - (π n_2)/18 for n_2 element Z

3 0
3 years ago
What is the length of the hypotenuse of a right triangle with legs of length 6 and 4 ?
liberstina [14]

Answer:

6²+4²=h²

36+16=h²

\sqrt{52}  = h \:  \:  \:  \:  \:  \\ hyphotenuse \: is \: 2 \sqrt{13  \:} \\ or \: 7.2111

6 0
4 years ago
Mentally estimate the total cost of items that have the following prices $1.85 $.98 $3.94 $9.78 and $6.18 round off the answer t
velikii [3]

the first 4 would be rounded up tot he nearest dollar and the last one rounded down to the nearest dollar

 doing that I estimate $23.00

Answer is C


7 0
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