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3 years ago

If anyone knows this please help me. Please answer only if you know. Thanks! more points for you if answered!

Mathematics

1 answer:

Sauron [17]3 years ago

3 0

1a) Possible rational roots will be of the form
±{divisor of 10}/{divisor of 4}
Divisors of 10 are {1, 2, 5, 10}
Divisors of 4 are {1, 2, 4}

Then possible rational roots are
{±1/4, ±1/2, ±1, ±5/4, ±2, ±5/2, ±5, ±10}

1b) Your answer is correct.

2) One additional root will be the conjuate of the given complex root.
5 -3i

3) If one root is 5 -√7, another will be 5 +√7. Then your polynomial is
P(x) = (x -(5 -√7))*(x -(5 +√7)) = (x -5)^2 -(√7)^2
P(x) = x^2 -10x +18

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Let ????C be the positively oriented square with vertices (0,0)(0,0), (2,0)(2,0), (2,2)(2,2), (0,2)(0,2). Use Green's Theorem to

bonufazy [111]

Answer:

-48

Step-by-step explanation:

Lets call L(x,y) = 10y²x, M(x,y) = 4x²y. Green's Theorem stays that the line integral over C can be calculed by computing the double integral over the inner square of Mx - Ly. In other words

$\int\limits_C {L(x,y)} \, dx + M(x,y) \, dy = \int\limits_0^2\int\limits_0^2 (M_x - L_y ) \, dx \, dy$

Where Mx and Ly are the partial derivates of M and L with respect to the x variable and the y variable respectively. In other words, Mx is obtained from M by derivating over the variable x treating y as constant, and Ly is obtaining derivating L over y by treateing x as constant. Hence,

M(x,y) = 4x²y
Mx(x,y) = 8xy
L(x,y) = 10y²x
Ly(x,y) = 20xy
Mx - Ly = -12xy

Therefore, the line integral can be computed as follows

$\int\limits_C {10y^2x} \, dx + {4x^2y} \,dy = \int\limits_0^2\int\limits_0^2 -12xy \, dx \, dy$

Using the linearity of the integral and Barrow's Theorem we have

$\int\limits_0^2\int\limits_0^2 -12xy \, dx \, dy = -12 \int\limits_0^2\int\limits_0^2 xy \, dx \, dy = -12 \int\limits_0^2\frac{x^2y}{2} |_{x = 0}^{x=2} \, dy = -12 \int\limits_0^22y \, dy \\= -24 ( \frac{y^2}{2} |_0^2) = -24*2 = -48$

As a result, the value of the double integral is -48-

3 0

3 years ago

A system of linear equations is graphed. which ordered pair is the best estimate for the solution to the system?

OLga [1]

Answer:

The answer that gives the best estimate is (1,1)

Step-by-step explanation:

i) As can be seen on of the lines intercepts the y axis at (0,-1). So the y

intercept or $c_{1}$ = -1. Therefore the equation for this line can be written as

y = $m_{1}$ x + $c_{1}$ ⇒ y = $m_{1}$ x - 1 . It can also be seen from this graph that the

line passes through the point (2 , 2). Substituting these values for x and y

respectively we get 2 = 2 $m_{1}$ - 1 ∴ $m_{1}$ = $\frac{3}{2}$ . The equation of the first line

can be written as y = $\frac{3}{2}$ x - 1 ⇒ 2y - 3x = -2

ii) As can be seen on the other line the intercept on the y axis is at (0,2). So

the y intercept or $c_{2}$ = 2. Therefore the equation for this line can be

written as y = $m_{2}$ x + $c_{2}$ ⇒ y = $m_{2}$ x + 2 . It can also be seen from this

graph that the line passes through the point (1 , -1). Substituting these

values for x and y respectively we get 1 = 1 $m_{2}$ + 2 ∴ $m_{2}$ = -1 . The

equation of the second line can be written as y = - x + 2 or x + y = 2

iii) Solving the two equations of the two lines respectively as found in i) and

ii) we get y = 0.8. We multiply equation in ii) by 3 to get 3x + 3y = 6 and

when we add this to equation in i) we get 5y = 4 which means that y = 0.8.

If we substitute this value in ii) we get 0.8 + x = 2 , therefore x = 1.2.

iv) Therefore we get the solution of the two lines, which is the intersection

of the two lines as (1.2, 0.8). So the answer that gives the best estimate

is (1,1)

6 0

3 years ago

A point lies on AB and is the distance from A to B. Point A is located at (4, 8) and point B is located at (14, 10)

Rzqust [24]

Answer:

(9,9)

Step-by-step explanation:

Assuming the point is exactly halfway between A and B, to find it we just need to find the centre point between (4,8) and (14,10).

To find the midpoint, we just need to find the middle value, by dividing the difference between the x values by 2, and repeating the process with the y values.

This is because the point is in the middle, so it's y value will be in the middle of the given AB y values, and its x value will also be directly in the middle of the AB x values.

The x values are 4 and 14. The midpoint is

14-4=10

10/2=5 (the midpoint is 5 away from each reference point)

4+5=9

The midpoint is 9 for the x values. This means the x-value for the point is 9.

Repeat for y-values:

10-8=2

2/2=1

8+1=9

The midpoint is 9, therefore it has the y coordinate of 9.

Therefore the coordinates for the point are (9,9).

Hope this helped!

6 0

3 years ago

A used bookstore will trade 2 of its books for 3 of yours. If Val brings in 18 books to trade, How many books can she get from t

dolphi86 [110]

Answer:

She will get 12 books from the store

Step-by-step explanation:

We can use ratio's to solve

2 books out x books out

------------------- =-----------------------------

3 books in 18 books in from Val

Using cross products

2 * 18 = 3 *x

Divide each side by 3

2*18 /3 = 3x/3

2*6 = x

12 =x

She will get 12 books from the store

8 0

3 years ago

Read 2 more answers

Three times a number x is at least -18

Ksivusya [100]

3x is greater than or equal to -18. You would divide each side by 3 to get x alone. Then You will get what x stands for. (x= -6)

4 0

3 years ago