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3 years ago

What is the equation of the circle in general form

Mathematics

1 answer:

Anni [7]3 years ago

3 0

Answer:

(x - 3)^2 + (y - 5)^2 = (√89)^2

Step-by-step explanation:

Well if you estimate, you can see that the circle touches one point at (-5, 0) and the center is at about (3, 5).

The standard equation for the circle is (x - h)^2 + (y - k)^2 = r^2 where (h, k) is the center.

So, you can start by plugging in the center. (x - 3)^2 + (y - 5)^2 = r^2

Now, all you have to do is find the radius.

You can do this by connecting the point (-5, 0) to the center.

You will have to use the distance formula:

√(-5 - 3)^2 + (0 - 5)^2 = √64 + 25 = √89

The final equation will be (x - 3)^2 + (y - 5)^2 = (√89)^2

This is the general idea, but my answer may not be correct, so check my steps.

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The Blue Jays’ soccer field has 53 bleachers that can each seat exactly 12 people. The Tigers’ soccer field has 48 bleachers tha

andriy [413]

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3 years ago

Read 2 more answers

PLEASE HELP ASAP!!! CORRECT ANSWER ONLY PLEASE!!!

Alborosie

Answer: $tan(V)=2.92$

Step-by-step explanation:

For this exercise you need to remember the following Trigonometric Identity:

$tan\alpha =\frac{opposite}{adjacent}$

You must observe the figure given in the exercise.

You can notice that the given triangle UVW is a Right triangle (because it has an angle that measures 90 degrees).

So, you can identify in the figure that:

$\alpha =V\\\\opposite=UW=35\\\\adjacent=VW=12$

Knowing these values, you can substitute them into $tan\alpha =\frac{opposite}{adjacent}$ :

$tan(V)=\frac{35}{12}$

Now you must evaluate:

$tan(V)=2.916$

Finally, rounding to the nearest hundreth, you get:

$tan(V)=2.92$

7 0

3 years ago

Santa Claus is assigning elves to work an eight-hour shift making toy trucks. Apprentice earn five candy canes per hour but can

dimaraw [331]

Answer:

(a) 5 senior, 4 apprentice

(b) 368 per shift

Step-by-step explanation:

The problem can be described by two inequalities. On describes the limit on the number of elves in the shop; the other describes the limit on the total payroll. Let x and y represent the number of apprentice and senior elves, respectively. Then the inequalities for the first scenario are ...

x + y ≤ 9 . . . . . . . . . . . . total number of elves in the shop

5x +8y ≤ 480/8 . . . . . . candy canes per hour paid to elves

These two inequalities are graphed in the first attachment. They describe a solution space with vertices at ...

(x, y) = (0, 7.5), (4, 5), (9, 0)

(a) Santa wants to maximize the output of trucks, so wants to maximize the function t = 4x +6y.

At the vertices of the solution space, the values of this function are ...

t(0, 7.5) = 45

t(4, 5) = 46

t(9, 0) = 36

Output of trucks is maximized by a workforce of 4 apprentice elves and 5 senior elves.

(b) The above calculations show 46 trucks per hour can be made, so ...

46×8 = 368 . . . trucks in an 8-hour shift

(c) The new demands change the inequalities to ...

x + y ≤ 8 . . . . . . number of workers

7x +8y ≤ 60 . . . total wages (per hour)

The vertices of the feasible region for these condtions are ...

(x, y) = (0, 7.5), (4, 4), (8, 0)

From above, we know the truck output will be maximized at the vertex (x, y) = (0, 7.5). However, we know we cannot have 7.5 senior elves working in the shop. We can have 7 or 8 elves working.

If the workforce must remain constant, truck output is maximized by a workforce of 7 senior elves.

If the workforce can vary through the shift, truck output is maximized by adding one more senior elf in the shop for half a shift.

Santa should assign 7 senior elves for the entire shift, and 8 senior elves (one more) for half a shift.

_____

<em>Comment on apprentice elf wages</em>

At 5 candy canes for 4 trucks, apprentice elves produced trucks for a cost of 1.25 candy canes per truck. At 8 candy canes for 6 trucks, senior elves produced trucks for a cost of about 1.33 candy canes per truck. The reason for employing senior elves in the first scenario is that their productivity is 1.5 times that of apprentice elves while their cost per truck is about 1.07 times that of apprentice elves.

After the apprentice elves wages were increased, their cost per truck is 1.75 candy canes per truck, but their productivity hasn't changed. They have essentially priced themselves out of a job, because they are not competitive with senior elves.

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3 years ago

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Answer:

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Step-by-step explanation:

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