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2 years ago

State the number of complex roots, the number of positive real roots and the number of negative real roots of

Mathematics

1 answer:

harkovskaia [24]2 years ago

8 0

9514 1404 393

Answer:

2 complex roots
2 positive real roots
0 negative real roots

Step-by-step explanation:

The signs of the terms are + - - +. There are two sign changes, so 0 or 2 positive real roots.

Negating the signs of the odd-degree terms, the signs are + + + +. There are no sign changes, so 0 negative real roots.

For x=0, the value of the quartic is +3. For x=1, the value is -3, so we know there are 2 positive real roots, one of which lies in the interval (0, 1).

The 4th-degree polynomial equation must have 4 roots, so the other two must be complex.

2 complex roots
2 positive real roots
0 negative real roots

_____

The roots are approximately 0.489999841592, 2.06573034434, −0.777865092969 ± 1.53582061225i

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Some friends went to

igomit [66]

Some friends went to lunch and split the bill equally. If each person paid $6.75, how many people went to lunch thinking. Use a diagram or equation to explain your thinking. The total is 27$. 27 divided by 6.75 is 4. Suppose

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2 years ago

A space telescope on a mountaintop is housed inside of a cylindrical building with a hemispheric dome. If the circumference of t

Vlad1618 [11]

Answer:

$185553.7\text{ feet}^3$

Step-by-step explanation:

GIVEN: A space telescope on a mountaintop is housed inside of a cylindrical building with a hemispheric dome. If the circumference of the dome is $84\text{ feet}$ , and the total height of the building up to the top of the dome is $91\text{ feet}$ .

TO FIND: what is the approximate total volume of the building.

SOLUTION:

let the height of the mountaintop be $h\text{ feet}$

As the dome hemispherical.

circumference of a hemisphere $=\frac{1}{2}\times2\pi\times radius$

$=\pi\times radius$

$\frac{22}{7}\times radius=84$

$radius=26.75\text{ feet}$

total height of the building up to the top of the dome $=\text{radius of hemisphere}+\text{height of mountaintop}$

$=26.75+h=91$

$h=64.25\text{ feet}$

Volume of building $=\text{volume of cylindrical mountaintop}+\text{volume of dome}$

$=\pi(radius)^2h+\frac{2}{3}\pi(radius)^3$

as radius of mountain top is same as dome

putting values

$=3.14(26.75)^264.75+\frac{2}{3}3.14(26.75)^3$

$=145484.6+40069.1$

$185553.7\text{ feet}^3$

Hence the total volume of the building is $185553.7\text{ feet}^3$

5 0

2 years ago

Can someone help out ??

kupik [55]

Answer:

120 cubes

Step-by-step explanation:

Find the volume of the prism and then divide it by the volume of one cube (which is 1/27 cm):

V = length*width*height = (5/3 cm)(4/3 cm)(2 cm) = 40/9 cm³.

Dividing this result by 1/27 yields

40 27 40*3

------ * ------ = -------------- = 120

9 1 1

120 cubes (answer)

7 0

2 years ago

You buy magazines for $5 and books for $10. You spent a total of $100. Let x represent the number of magazines and y represent t

bagirrra123 [75]

The answer would be 10x+5y=100

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1 year ago

The table shows the ratio between the number of tickets ordered and their cost: Number of Tickets Cost (dollars) 5 20 7 28 9 36

Charra [1.4K]

9514 1404 393

Answer:

(1, 4)
(2, 8)
(3, 12)

Step-by-step explanation:

The ratios all have ...

first number : second number = 1 : 4

Using first numbers of 1, 2, 3, the second numbers can be found by multiplying these by 4. (1, 4), (2, 8), (3, 12)

You plot these (x, y) points the same way you plot <em>any</em> point on a coordinate grid. The first (x) value is the horizontal distance from the vertical axis. Positive is to the right. The second (y) value is the vertical distance from the horizontal axis. Positive is up.

Of course, the origin is where the horizontal and vertical axes meet. It can be convenient to find one of the coordinates on its respective axis, then use the other coordinate to find the point at the desired distance from that axis.

Usually, you would choose the axis on the basis of how easy it is to determine exactly where the coordinate lies. If the y-axis is marked every 5, for example, it might be hard to determine where a multiple of 4 will lie. Locating the x-coordinate on the x-axis may be an easier way to start.

7 0

2 years ago