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Len [333]
3 years ago
8

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

l=

\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
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