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3 years ago

A. Find and explain the error in the work shown.

Mathematics

1 answer:

Marizza181 [45]3 years ago

5 0

The error is that they had placed the numbers in the wrong placeholder. Remember that the Distance formula is $D=\sqrt{(x_2-x_1)^2+(y_2-y_1)^2}$ .

Correct Work:

$D=\sqrt{(5-(-1))^2+(16-15)^2}\\D=\sqrt{6^2+1^2}\\D=\sqrt{36+1}\\D=\sqrt{37}\ \approx 6.08$

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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

What is the solution set for the given inequality if the replacement set for r is {5, 6, 7, 8, 9, 10}?

tangare [24]

Answer:

{6,7,8,9,10}

Step-by-step explanation:

Solve the inequality using inverse operations.

$3r\leq 4r-6\\3r-4r\leq -6\\-r\leq -6\\r\geq 6$

This solution means values equal to or larger than 6 from the set are solutions. This means 6, 7, 8, 9, and 10 are the solution set.

8 0

2 years ago

Aight man can someone help me lol

uranmaximum [27]

Answer: 11/24

Step-by-step explanation:

whenever u see this — (

it means the opposite of. so the opposite of -5/8 is +5/8.

-1/6 + 5/8 = 11/24

4 0

3 years ago

a game is played by drawing 4 cards from a standard playing deck and replacing each card after it is drawn. find the probability

natima [27]

It is a 1 in 13 chance of drawing at least 1 ace.

8 0

3 years ago

What is the best estimate for the number of people in line at 7.A.M

Keith_Richards [23]

We have been given the equation

$y=-5.131x^2+31.821x-3.333$

It represents the number of people standing to catch a commuter train x hours after 5 A.M.

Now, in order to find the number of people in line at 7 a.m. , we need to substitute x= 2 in the above equation.

$y(2)=-5.131(2)^2+31.821(2x)-3.333\\y(2)= 39.785 \approx 40$

Therefore, the number of people in the line at 7 a.m. is 40

D id the correct option.

5 0

3 years ago