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3 years ago

Evaluate the expression for the given values of the variables. x2 + 4(x − y) ÷ z2, for x = 8, y = 5, and z = 2

Mathematics

1 answer:

prisoha [69]3 years ago

7 0

(8)(2)+4(8)(-5)(2)(2)

The answer is -624

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Three cell phones towers can be modeled by the points X(6,0), Y(8,4), and Z(3,9). Determine the location of another cell phone t

Marat540 [252]

Answer:

The location of the new cell phone tower is $(h,k) = (3,4)$ , and the equation of the circle is $x^{2}+y^{2} -6\cdot x - 8\cdot y = 0$ .

Step-by-step explanation:

The location of the cell phone tower coincides with the location of a circunference passing through the three cell phone towers. By Analytical Geometry, the equation of the circle is represented by the following general formula:

$x^{2} + y^{2}+A\cdot x + B\cdot y +C = 0$ (1)

Where:

$x$ - Independent variable.

$y$ - Dependent variable.

$A$ , $B$ , $C$ - Circunference constants.

Given the number of variable, we need the location of three distinct points:

$(x_{1},y_{1}) = (6,0)$

$36 +6\cdot A + C = 0$

$(x_{2},y_{2}) = (8,4)$

$80 + 8\cdot A + 4\cdot B + C = 0$

$(x_{3},y_{3}) = (3,9)$

$90 + 3\cdot A + 9\cdot B + C = 0$

Then, we have the following system of linear equations:

$6\cdot A + C = -36$ (2)

$8\cdot A +4\cdot B + C = -80$ (3)

$3\cdot A + 9\cdot B + C = -90$ (4)

The solution of this system is:

$A = -6$ , $B = -8$ , $C = 0$

By comparing the general form with the standard form of the equation of the circunference is:

$A = -2\cdot h$ (5)

$B = -2\cdot k$ (6)

$C = h^{2}+k^{2}-r^{2}$ (7)

Where:

$h$ , $k$ - Coordinates of the center of the circle.

$r$ - Radius of the circle.

If we know that $A = -6$ , $B = -8$ and $C = 0$ , then coordinates of the center of the circle and its radius are, respectively:

$h = -\frac{A}{2}$

$k = -\frac{B}{2}$

$r = \sqrt{h^{2}+k^{2}-C}$

$h = 3$ , $k = 4$ , $r = 5$

The location of the new cell phone tower is $(h,k) = (3,4)$ , and the equation of the circle is $x^{2}+y^{2} -6\cdot x - 8\cdot y = 0$ .

3 0

2 years ago

Multiply and simplify. 3xy4z2⋅5x2yx

Olenka [21]

I think the answer is 15x^4y^5z^2

4 0

4 years ago

Read 2 more answers

The volume of a cube is 441cm3.<br> Work out the length of its side rounded to 1 DP.

Rainbow [258]

Answer:

volume of cube=441cm³

l³=441cm³

$\sqrt[3]{441}$

length=7.6cm

3 0

3 years ago

-13=r/9+8<br> what is r equal to?

AURORKA [14]

Answer: r=(-189)

first you subtract both sides by 8 and get -21=r/9

then you multiply 9 with each side and get -189 = r

you can check by rewriting the problem with -189 as r and solving the equation

7 0

3 years ago

What is the distance between (-5, -6) and (-3,-8)?

Mashcka [7]

Answer:-2 and 2

Step-by-step explanation:

3 0

3 years ago