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2 years ago

How many real third roots does -343 have? Explain your reasoning.

Mathematics

1 answer:

kupik [55]2 years ago

4 0

Answer: One root

Explanation:

x^3 = -343

x^3 + 343 = 0

x^3 + 7^3 = 0

(x+7)(x^2 - 7x + 7^2) = 0 .... sum of cubes factoring rule

(x+7)(x^2 - 7x + 49) = 0

Set each piece equal to zero and solve for x.

You should find that the first piece x+7 = 0 leads to x = -7 as the only real root.

The other piece x^2-7x+49 = 0 leads to two non-real roots, ie complex roots.

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How many and what type of solutions?

kolbaska11 [484]

Hello,

2k²-3k-9=0
==>k=3 or k=-3/2

Answer C two rational solutions.

3 0

3 years ago

A fluid moves through a tube of length 1 meter and radius r=0.006±0.00025 meters under a pressure p=4⋅105±2000 pascals, at a rat

iris [78.8K]

Answer:

Maximum error for viscosity is 17.14%

Step-by-step explanation:

We know that everything is changing with respect to the time, "r" is changing with respect to the time, and also "p" just "v" will not change with the time according to the information given, so we can find the implicit derivative with respect to the time, and since

$n = (\frac{\pi}{8}) (\frac{pr^4}{v})\\$

The implicit derivative with respect to the time would be

$\frac{dn}{dt} = \frac{\pi}{8} ( \frac{r^4}{v} \frac{dp}{dt} + \frac{4pr^3}{v}\frac{dr}{dt} )$

If we multiply everything by dt we get

$dn = \frac{\pi}{8} ( \frac{r^4}{v} dp + \frac{4pr^3}{v} dr})$

Remember that the error is given by $\frac{dn}{n}$ therefore doing some algebra we get that

$\frac{dn}{n} = 4 \frac{dr}{r} + \frac{dp}{p}$

Since, r = 0.006 , dr = 0.00025 , p = 4*105 , dp = 2000 we get that

$\frac{dn}{n} = 0.1714$

Which means that the maximum error for viscosity is 17.14%.

5 0

3 years ago

What is the value of x, when -9(x-5)=x+22 1/2

Kipish [7]

Answer:

x = 2.25

Step-by-step explanation:

-9(x - 5) = x + 22 1/2

Distribute the nine and then add 9x to both sides

-9x + 45 = x +22 1/2

+ 9x + 9x

Then try to get x alone

45 = 10x + 22 1/2

-22 1/2 -22 1/2

22.5 = 10x

$\frac{22.5}{10} = \frac{10x}{10}$

2.25 = x

4 0

3 years ago

Read 2 more answers

In the equation 6x – 2 = –4x + 2, Spencer claims that the first step is to add 4x to both sides. Jeremiah claims that the first

Nataliya [291]

The real way is to subtract the term with the variable on the right first, but both Spencer and Jeremiah are correct. When you do them both, they arrive at the same answer, only that Spencer's would be 2/5, and Jeremiah's would be -2/-5, which is 2/5, because you divide negative by a negative. It doesn't matter which term with the variable you would cancel out first. Either way, you still arrive at the correct answer.

7 0

3 years ago

Read 2 more answers

The lengths of the bases of a trapezoid are 17 inches and 10 inches. The trapezoid has an area of 189 square inches.

Mamont248 [21]

Answer:

height of this trapezoid is 14 inches.

Step-by-step explanation:

$\boxed{Area -of -trapezoid=\frac{a+b}{2} h}$