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3 years ago

6

What is the solution of the system of equations? {4x−3y=152x+2y=4

1 answer:

trasher [3.6K]3 years ago

8 0

Start by solving one equation for x or y, this time I'm choosing x. 2x = 4 - 2y, then x = 2 - y. Now substitute in x in the other equation. 4(2-y) - 3y = 15. This simplifies to 8 - 4y - 3y = 15. This simplifies to -7y = 7. Divide both sides by -7, and y = -1. Now plug the y value into the other equation: 2x + 2(-1) = 4. This simplifies to 2x = 6, and x = 3.
X = 3, Y = -1 or (3,-1)

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2 years ago

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.

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

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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:

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

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

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3 years ago

A number,M, is rounded to 1 decimal place. the result is 9.4 complete the error interval for M

ivann1987 [24]

Answer:

$9.35 \le M \le 9.45$

Step-by-step explanation:

Given

$M = 9.4$ to 1 d p

Required

The error interval

The error interval is represented as:

$Lower \le M \le Upper$

Where

$Lower = M - 0.05$

$Upper = M + 0.05$

So, we have:

$Lower = M - 0.05$

$Lower = 9.4 - 0.05$

$Lower = 9.35$

$Upper = M + 0.05$

$Upper = 9.4 + 0.05$

$Upper = 9.45$

Hence, the error interval: $Lower \le M \le Upper$ is:

$9.35 \le M \le 9.45$

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