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3 years ago

Give the equation of the circle centered at the origin and passing through the point , 0−9.

Mathematics

1 answer:

e-lub [12.9K]3 years ago

3 0

Answer:

$x^2+y^2=81$

Step-by-step explanation:

step 1

Find the radius of the circle

we know that

The radius of the circle is the distance between the center and any point on the circle

the formula to calculate the distance between two points is equal to

$d=\sqrt{(y2-y1)^{2}+(x2-x1)^{2}}$

we have the points

(0,0) and (0,-9)

substitute in the formula

$r=\sqrt{-9-0)^{2}+(0-0)^{2}}$

$r=\sqrt{-9)^{2}+(0)^{2}}$

$r=9/ units$

step 2

Find the equation of the circle

The equation of the circle in center radius form is equal to

$(x-h)^2+(y-k)^2=r^2$

we have

$(h,k)=(0,0)\\r=9\ units$

substitute

$(x-0)^2+(y-0)^2=9^2$

$x^2+y^2=81$

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Answer:

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Step-by-step explanation:

Simplify the following:

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Determine whether the system of linear equations has one and only one solution, infinitely many solutions, or no solution. 2x-y=

Bond [772]

Answer:

The system of linear equations has infinitely many solutions

Step-by-step explanation:

Let's modified the equations and find the answer.

Using the first equation:

$2x-y=5$ we can multiply by 2 in both sides, obtaining:

$2*(2x-y)=2*5$ which can by simplified as:

$4x-2y=10$ which is equal to:

$4x=2y+10$

Considering the second equation:

$=4x+ky=2$

Taking into account that from the first equation we know that: $4x=2y+10$ , we can express the second equation as:

$2y+10+ky=2$ , which can be simplified as:

$(2+k)y=2-10$

$(2+k)y=-8$

$y=-8/(2+k)$

Because (-8) is being divided by (2+k), then (2+k) can't be equal to 0, so:

$2+k=0$ if $k=-2$

This means that k can be any number different than -2, and for each of these solutions, there is a different solution for y, allowing also, different solutions for x.

For example, if k=0 then

$y=-8/(2+0)$ which give us y=-4, and, because:

$4x=2y+10$ if y=-4 then $x=(-8+10)/4=0.5$

Now let's try with k=-1, then:

$y=-8/(2-1)$ which give us y=-8, and, because:

$4x=2y+10$ if y=-8 then $x=(-16+10)/4=-1.5$ .

Then, the system of linear equations has infinitely many solutions

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3 years ago

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Step-by-step explanation:

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3 years ago

A company studied the number of lost-time accidents occurring at its Brownsville, Texas, plant. Historical records show that 20%

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Answer:

a. 5% of the employees will experience lost-time accidents in both years

b. 24% of the employees will suffer at least one lost-time accident over the two-year period

Step-by-step explanation:

a. What percentage of the employees will experience lost-time accidents in both years?

20% last year, of those who suffered last year, 25% during this year. So

$p = 0.2*0.25 = 0.05$

5% of the employees will experience lost-time accidents in both years.

b. What percentage of the employees will suffer at least one lost-time accident over the two-year period?

5% during the two years.

10% during the current year. 25% of employees who had lost-time accidents last year will experience a lost-time accident during the current year.

So the 10% is composed of 5% during both years(25% of 20%) and 5% of the 80% who did not suffer during the first year.

First year yes, not on the second.

75% of 20%. So, total:

$0.05 + 0.05*0.8 + 0.75*0.2 = 0.24$

24% of the employees will suffer at least one lost-time accident over the two-year period

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3 years ago