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3 years ago

If A=(-1,-3) and B=(11,-8) what is the length of AB

2 answers:

8 0

Distance formula = sqrt (x2 - x1)^2 + (y2 - y1)^2
(-1,-3)...x1 = -1 and y1 = -3
(11,-8)...x2 = 11 and y2 = -8
now we sub
d = sqrt (11 - (-1)^2 + (-8 - (-3)^2
d = sqrt (12^2) + (-5^2)
d = sqrt (144 + 25)
d = sqrt 169
d = 13 <=====length of AB

scZoUnD [109]3 years ago

4 0

The answer is 13 units

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Find the zeroes of the quadratic polynomial 4x²-4x+1 and verify the relation between its zeroes and coefficients

FromTheMoon [43]

Answer:

A) zeros are x = ½ or x = ½

B) >> sum of zeros = (-Coefficient of x)/(Coefficient of x²)

>> Product of the zeros = Constant term/Coefficient of x²

Step-by-step explanation:

To find the zeros, we will equate the polynomial to zero.

Thus;

4x² - 4x + 1 = 0

Using quadratic equation, we can find the zeros.

x = [-(-4) ± √((-4)² - (4 × 4 × 1))]/(2 × 4)

x = (4 ± 0)/8

x = 4/8 and x = 4/8

Thus, zeros are x = ½ or x = ½

Now, to find the relationships between its zeroes and coefficients;

Sum of zeroes = ½ + ½ = 1

This is equal to -b/a = -(-4)/4 = 1.

Thus;

sum of zeros = (-Coefficient of x)/(Coefficient of x²)

Product of zeros = ½ × ½ = ¼

c/a = 1/4

This is equal to the product of the zeros.

Thus;

Product of the zeros = Constant term/Coefficient of x²

6 0

3 years ago

The sum of three consecutive odd numbers is 123.

guajiro [1.7K]

39.

123/3=41

41-2=39
41+2=43

39+41+43=123

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1 year ago

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ArbitrLikvidat [17]

The answer is C.......

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2 years ago

19. Sally is a boss and Susie is a boss. Both are offering you a job. Sally says she will pay you $2 for the first hour you

madam [21]

Answer:

Sally

Step-by-step explanation:

Because you may work 8-10 hours and make $16-20 instead of 10 for the day

3 0

3 years ago

Find the work done by the force field f(x, y, z) = y + z, x + z, x + y on a particle that moves along the line segment from (1,

vivado [14]

Note that the vector field is irrotational, since

$\nabla\times\mathbf f(x,y,z)=\mathbf 0$

which means $\mathbf f$ is conservative. This means there is some scalar potential function $f(x,y,z)$ such that $\nabla f(x,y,z)=\mathbf f(x,y,z)$ . If we can find such a function, then we only need to evaluate the difference of $f(5,3,2)$ and $f(1,0,0)$ (because the gradient theorem holds in this case).

We're looking for a function $f(x,y,z)$ that satisfies

$\dfrac{\partial f}{\partial x}=y+z$
$\dfrac{\partial f}{\partial y}=x+z$
$\dfrac{\partial f}{\partial z}=x+y$

Integrate the first equation with respect to $x$ to get

$f(x,y,z)=xy+xz+g(y,z)$

Differentiate with respect to $y$ , then we must have

$\dfrac{\partial f}{\partial y}=x+z=x+\dfrac{\partial g}{\partial y}$
$\implies\dfrac{\partial g}{\partial y}=z$
$\implies g(y,z)=yz+h(z)$
$\implies f(x,y,z)=xy+xz+yz+h(z)$

Differentiate with respect to $z$ , and we have to have

$\dfrac{\partial f}{\partial z}=x+y=x+y+\dfrac{\mathrm dh}{\mathrm dz}$
$\implies\dfrac{\mathrm dh}{\mathrm dz}=0$
$\implies h(z)=C$
$\implies f(x,y,z)=xy+xz+yz+C$

Now, by the gradient theorem, we have

$\text{work}=\displaystyle\int_{\mathcal C}\mathbf f\cdot\mathrm d\mathbf r=f(5,3,2)-f(1,0,0)=31$

where $\mathcal C$ is the line segment.

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3 years ago