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2 years ago

PLEASE I NEED HELP!!!!!!!!

Mathematics

1 answer:

Yanka [14]2 years ago

7 0

Answer:

1) x= 3i, x= - 3i

2) x= +i $\sqrt{7}$ , x = - i

Step-by-step explanation:

1) x^2+9=0

(x+3i)(x-3i)=0

x= 3i, x=-3i

2) x^2-4=-11

x^2=-7

x= ±i $\sqrt{7}$

x= +i $\sqrt{7}$ , x = - i

hope this helps!! :))

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If a fire is burning a building and it takes 2 hours to put it out using 2000 gal./min., what minimum diameter cylindrical tank

strojnjashka [21]

Answer:

The minimum diameter of the cylindrical tank needed to store the quantity needed to put out the fire is approximately 58.415 feet.

Step-by-step explanation:

A gallon equals 0.134 cubic feet. First, we determine the amount of water ( $Q$ ), measured in cubic feet, needed to put out the fire under the assumption that water is consumed at constant rate:

$Q = \dot Q \cdot \Delta t$ (1)

Where:

$\dot Q$ - Volume rate, measured in feet per minute.

$\Delta t$ - Time, measured in minutes.

If we know that $\dot Q = 2000\,\frac{gal}{min}$ and $\Delta t = 120\,min$ , then the amount of water is:

$Q = \left(2000\,\frac{gal}{min} \right)\cdot (120\,min) \cdot \left(0.134\,\frac{ft^{3}}{gal} \right)$

$Q = 32160\,ft^{3}$

And the diameter of the cylindrical tank based on the capacity found above is determined by volume formula for a cylinder:

$Q = \frac{\pi}{4}\cdot D^{2}\cdot h$ (2)

Where:

$D$ - Diameter, measured in feet.

$h$ - Height, measured in feet.

If we know that $Q = 32160\,ft^{3}$ and $h = 12\,ft$ , then the minimum diameter is:

$D^{2} = \frac{4\cdot Q}{\pi\cdot h}$

$D = 2\cdot \sqrt{\frac{Q}{\pi\cdot h} }$

$D = 2\cdot \sqrt{\frac{32160\,ft^{3}}{\pi\cdot (12\,ft)} }$

$D \approx 58.415\,ft$

The minimum diameter of the cylindrical tank needed to store the quantity needed to put out the fire is approximately 58.415 feet.

8 0

2 years ago

Using the segment addition postulate, which is true? What is the measure of AngleDCF? Three lines extend from point C. The space

Flura [38]

Answer:

129

Step-by-step explanation:

If three lines CD, CE and CF extend from point C, then the following addition postulate is true;

<DCE + <ECF = <DCF

If the space between line C D and C E is 75 degrees, then <DCE = 75

If the space between lines C E and C F is 54, then <ECF = 54.

Substitute the given values into the expression above will give;

<DCF =<DCE + <ECF

<DCF = 75+54

<DCF = 129

Hence the measure of <DCF is 129°

8 0

3 years ago

EASY QUESTION PLEASE HELP

IgorC [24]

Answer:

9x,2,8y

Step-by-step explanation:

4 0

3 years ago

What is 11 1/2 + 10 11/16=

ahrayia [7]

Hey!

To solve this equation, we must first convert the mixed numbers into improper fractions. To do that we'll multiply the denominator by the whole number and add the total to the numerator.

Original Equation :

$11\frac{1}{2} + 10\frac{11}{16} = ?$

New Equation {Converted Mixed Numbers Into Improper Fractions} :

$\frac{23}{2} + \frac{171}{16} = ?$

Now that we've successfully changed our equation, we'll move onto the next step. Next we'll have change the fractions one more time so that the denominators are the same. To do that we'll multiply two by eight to get sixteen. We'll also be multiplying the top portion of the fraction by eight, because whatever you do to the bottom must also be done to the top; And vise versa.

Fraction Conversion :

$\frac{23*8}{2*8} = \frac{184}{16}$

So, now that we have our new fraction we can go ahead and plug that into our equation so we can start adding. Remember, we don't add the denominators, just the numerators.

Old Equation :

$\frac{23}{2} + \frac{171}{16} = ?$

New Equation {Input New Fraction With Common Denominator} :

$\frac{184}{16} +\frac{171}{16} = ?$

Solution {New Equation Solved} :

$\frac{355}{16}$

Now I'm not exactly sure how your instructor will accept your answer, but most prefer the final answer to be in the simplest form. In other words, they don't want it in the form of an improper fraction. They'd most likely rather have it as a mixed number.

New Solution {Converted to a Mixed Number} :

$22\frac{3}{16}$

Since the fraction cannot be simplified anymore, this should be our final answer.

So, this means that the answer to the equation is $22\frac{3}{16}$ .

Hope this helps!

- Lindsey Frazier ♥

5 0

3 years ago

Read 2 more answers

Trying to understand long division formula. 5 divided by 285.I have it down to 28-25 and i have 035 but why is 35 subtracted by

Sergeeva-Olga [200]

Explanation:

At each step, the product of the quotient digit and the divisor is subtracted from the dividend. This gives you the new dividend.

When the quotient digit is 7, the product of 7 and 5 is subtracted from the dividend. The dividend at that point is 35, so you have 35 - 35 = 0. The 0 is the next dividend. Among other things, that tells you you're done. (Any additional quotient digits will be zero.)

5 0

3 years ago