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svlad2 [7]
3 years ago
6

The point (7, 4) lies on a circle centered at the origin. Write the equation of the circle and state the radius.

Mathematics
1 answer:
k0ka [10]3 years ago
7 0

Given:

The point (7, 4) lies on a circle centered at the origin.

To find:

The equation of the circle and the radius of the circle.

Solution:

Distance formula:

d=\sqrt{(x_2-x_1)^2+(y_2-y_1)^2}

The point (7, 4) lies on a circle centered at the origin. So, the distance between the points (7,4) and (0,0) is equal to the radius of the circle.

r=\sqrt{(0-7)^2+(0-4)^2}

r=\sqrt{(-7)^2+(-4)^2}

r=\sqrt{49+16}

r=\sqrt{65}

The standard form of the circle is

(x-h)^2+(y-k)^2=r^2            ...(i)

Where, (h,k) is the center of the circle and r is the radius of the circle.

Putting h=0, k=0 and r=\sqrt{65} in (ii), we get

(x-0)^2+(y-0)^2=(\sqrt{65})^2

x^2+y^2=65

Therefore, the equation of the circle is x^2+y^2=65 and its radius is r=\sqrt{65}.

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Nirmala graphed the relationship between the duration (in hours) of using an oil lamp and the volume (in milliliters) of oil rem
mariarad [96]

Answer:

Nirmala can use the lamp for 31.66 hours before it runs out of oil.

Step-by-step explanation:

From the graph,

Take any two points, let say

(15, 25)

(25, 10)

\mathrm{Slope\:between\:two\:points}:\quad \mathrm{Slope}=\frac{y_2-y_1}{x_2-x_1}

\left(x_1,\:y_1\right)=\left(15,\:25\right),\:\left(x_2,\:y_2\right)=\left(25,\:10\right)

m=\frac{10-25}{25-15}

m=-\frac{3}{2}

The equation of line in slope-intercept form

y = mx + b

Putting m=-\frac{3}{2}  and any point, let say (25, 10), to find the y-intercept 'b'

10=-\frac{3}{2}\left(25\right)+b

-\frac{3}{2}\left(25\right)+b=10

-\frac{75}{2}+b=10

\mathrm{Add\:}\frac{75}{2}\mathrm{\:to\:both\:sides}

-\frac{75}{2}+b+\frac{75}{2}=10+\frac{75}{2}

b=\frac{95}{2}

b=47.5

So the equation of line will be:

y = mx + b

y=-\frac{3}{2}x+47.5

In order to find how long Nirmala can use the lamp before it runs out of oil, we need to find x-intercept which can be obtained by putting y = 0, and solve for x, as duration lies on x-axis.

so

y=-\frac{3}{2}x+47.5

Putting y = 0

0=-\frac{3}{2}x+47.5

-\frac{3}{2}x+47.5=0

-\frac{3}{2}x=-47.5

\mathrm{Multiply\:both\:sides\:by\:}2

2\left(-\frac{3}{2}x\right)=2\left(-47.5\right)

-3x=-95

\mathrm{Divide\:both\:sides\:by\:}-3

\frac{-3x}{-3}=\frac{-95}{-3}

x=\frac{95}{3}

x=31.66

Therefore, Nirmala can use the lamp for 31.66 hours before it runs out of oil.

4 0
3 years ago
Read 2 more answers
What is the degree of this polynomial? x ^ 3 + xy + x * y ^ 2 + 5y + 3
ludmilkaskok [199]

Answer:

The degree of the given polynomial is 3.

Hope it will help :)

6 0
3 years ago
What is the value of x? x−2/5=7 Enter your answer in the box in simplest form. x =
fenix001 [56]

Answer:

Your answer is 17.5

Step-by-step explanation:

Turn your fraction into a decimal

2/5 = 0.4

Next multiply my given answer by 0.4

17.5 x 0.4 = 7

Therefore 17.5 is your final answer

3 0
3 years ago
What’s the sum of interior angles of a 45-gon?
Mashutka [201]

Answer:

Step-by-step explanation:

As each exterior angle is 45o , number of angles or sides of the polygon is 360o45o=8 . Further as each exterior angle is 45o , each interior angle is 180o−45o=135o .

7 0
3 years ago
Don't just answer for point plz
Hunter-Best [27]

Answer:

Step-by-step explanation:

The area of a triangle is

A=bh/2 where b=base dimension and h=height

1) 10(12)/2=60mm^2

2) 14(34)/2=238in^2

3) 9.5(19.25)/2=91.4375yd^2

4) 4.9(23.7)/2=232.26m^2

5) 285=15b/2, 15b=578, b=38ft

6) 17h/2=18.7, 17h=37.4, h=2.2cm

7) 12.25b/2=128.625, 12.25b=257.25, b=21in

4 0
3 years ago
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