How many real roots and how many complex roots does this expression have? (x+7)^7

Mathematics

1 answer:

Feliz [49]3 years ago

3 0

Answer:

One real root, with multiplicity 7.

Step-by-step explanation:

The given expresion is

${(x + 7)}^{7}$

This is a seventh degree polynomial.

According to the fundamental theorem of Algebra, the expression has a potential 7 roots both real and complex.

This expression has one real root, with multiplicity , 7.

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The region bounded by y=(3x)^(1/2), y=3x-6, y=0

Ganezh [65]

Answer:

4.5 sq. units.

Step-by-step explanation:

The given curve is $y = (3x)^{\frac{1}{2} }$

⇒ $y^{2} = 3x$ ...... (1)

This curve passes through (0,0) point.

Now, the straight line is y = 3x - 6 ....... (2)

Now, solving (1) and (2) we get,

$y^{2} - y - 6 = 0$

⇒ (y - 3)(y + 2) = 0

⇒ y = 3 or y = -2

We will consider y = 3.

Now, y = 3x - 6 has zero at x = 2.

Therefor, the required are = $\int\limits^3_0 {(3x)^{\frac{1}{2} } } \, dx - \int\limits^3_2 {(3x - 6)} \, dx$

= $\sqrt{3} [{\frac{x^{\frac{3}{2} } }{\frac{3}{2} } }]^{3} _{0} - [\frac{3x^{2} }{2} - 6x ]^{3} _{2}$

= $[\frac{\sqrt{3}\times 2 \times 3^{\frac{3}{2} } }{3}] - [13.5 - 18 - 6 + 12]$

= 6 - 1.5

= 4.5 sq. units. (Answer)

7 0

3 years ago

A ball is dropped from a height of 10 meters. Each time it bounces, it reaches 50 percent of its previous height. The total vert

xz_007 [3.2K]

After every drop,the ball bounces to half it's previous height. With that understood.

1st drop -The ball drops 10m

1st bounce - 5m up
2nd drop - 5m down

2nd bounce - 2.5m up
3rd drop - 2.5m down

3rd bounce - 1.25m up
4th drop - 1.25m down

4th bounce - 0.625m up
5th/last drop - 0.625m down

To find the total vertical distance, you add them all.

10+5+5+2.5+2.5+1.25+1.25+0.625+0.625
=29.25m travelled in all.

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3 years ago

I need help please please I appreciate it! ):

telo118 [61]

Answer:

!. Scale factor = 5

2. Scale factor = $\frac{1}{5}$