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3 years ago

A circle has a diameter of 12 units, and its center lies on the x-axis. What could be the equation of the circle?

Mathematics

1 answer:

ycow [4]3 years ago

8 0

Answer:

$x^{2} +y^{2} =36$

Step-by-step explanation:

A circle centered at (0,0) with radius r is $x^{2} +y^{2} =r^{2}$

Since your circle has diameter of 12, then its radius is 6. Then $r^{2} =36$

So a possible answer is: $x^{2} +y^{2} =36$

If you want to move the location of the center, but keep it on the x-axis, then add or subtract a number to the x, such as this:

$(x+4)^{2} +y^{2} =36$

The center of this circle would be (-4, 0) which is still on the x-axis.

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What is the area of the figure below? Use 3.14 for pi. Round your answer to the nearest hundredth.

sammy [17]

Answer:

area of the figure ≈61.23 cm² to the nearest hundredth

Step-by-step explanation:

To find the area of the figure, we will follow the steps below;

Looking at the figure, we will see that the figure comprises of both semi-circle and a parallelogram

area of figure = area of semicircle + area of parallelogram

first, we will find the area of the semi-circle

area of a semi-circle = πr² /2

from the diagram given, diameter = 7cm

but diameter = 2r, this implies that radius r = d/2, hence radius r = 7/2 = 3.5 cm

π = 3.14

Lets insert the values into the formula

area of a semi-circle = πr² /2

=3.14×3.5² /2

=3.14×12.25 /2

=19.2325 cm²

Area of a parallelogram = b×h

where b = base and h = height

from the figure given, base b = 7cm and height h = 6 cm

Lets insert the values into the formula

Area of a parallelogram = b×h

= 7×6

=42 cm²

area of the figure = area of semicircle + area of parallelogram

=19.2325 cm² + 42 cm²

=61.2325 cm²

≈61.23 cm² to the nearest hundredth

area of the figure ≈61.23 cm² to the nearest hundredth

8 0

2 years ago

How can you tell if a number is rational and irrational??

kompoz [17]

All numbers that are not rational are considered irrational. An irrational number can be written as a decimal, but not as a fraction. An irrational number has endless non-repeating digits to the right of the decimal point.

4 0

3 years ago

Read 2 more answers

HELPPPPPP what is x minus 1 x-1

Evgesh-ka [11]

Answer:

-1

Step-by-step explanation:

x - 1x - 1

1x = x

x - x -1

x - x = 0

0 - 1 = -1

-1

3 0

3 years ago

A quadrilateral has vertices at $(0,1)$, $(3,4)$, $(4,3)$ and $(3,0)$. Its perimeter can be expressed in the form $a\sqrt2+b\sqr

seraphim [82]

Answer:

a + b = 12

Step-by-step explanation:

Given

Quadrilateral;

Vertices of (0,1), (3,4) (4,3) and (3,0)

$Perimeter = a\sqrt{2} + b\sqrt{10}$

Required

$a + b$

Let the vertices be represented with A,B,C,D such as

A = (0,1); B = (3,4); C = (4,3) and D = (3,0)

To calculate the actual perimeter, we need to first calculate the distance between the points;

Such that:

AB represents distance between point A and B

BC represents distance between point B and C

CD represents distance between point C and D

DA represents distance between point D and A

Calculating AB

Here, we consider A = (0,1); B = (3,4);

Distance is calculated as;

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

$(x_1,y_1) = A(0,1)$

$(x_2,y_2) = B(3,4)$

Substitute these values in the formula above

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

$AB = \sqrt{(0 - 3)^2 + (1 - 4)^2}$

$AB = \sqrt{( - 3)^2 + (-3)^2}$

$AB = \sqrt{9+ 9}$

$AB = \sqrt{18}$

$AB = \sqrt{9*2}$

$AB = \sqrt{9}*\sqrt{2}$

$AB = 3\sqrt{2}$

Calculating BC

Here, we consider B = (3,4); C = (4,3)

Here,

$(x_1,y_1) = B (3,4)$

$(x_2,y_2) = C(4,3)$

Substitute these values in the formula above

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

$BC = \sqrt{(3 - 4)^2 + (4 - 3)^2}$

$BC = \sqrt{(-1)^2 + (1)^2}$

$BC = \sqrt{1 + 1}$

$BC = \sqrt{2}$

Calculating CD

Here, we consider C = (4,3); D = (3,0)

Here,

$(x_1,y_1) = C(4,3)$

$(x_2,y_2) = D (3,0)$

Substitute these values in the formula above

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

$CD = \sqrt{(4 - 3)^2 + (3 - 0)^2}$

$CD = \sqrt{(1)^2 + (3)^2}$

$CD = \sqrt{1 + 9}$

$CD = \sqrt{10}$

Lastly;

Calculating DA

Here, we consider C = (4,3); D = (3,0)

Here,

$(x_1,y_1) = D (3,0)$

$(x_2,y_2) = A (0,1)$

Substitute these values in the formula above

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

$DA = \sqrt{(3 - 0)^2 + (0 - 1)^2}$

$DA = \sqrt{(3)^2 + (- 1)^2}$

$DA = \sqrt{9 + 1}$

$DA = \sqrt{10}$

The addition of the values of distances AB, BC, CD and DA gives the perimeter of the quadrilateral

$Perimeter = 3\sqrt{2} + \sqrt{2} + \sqrt{10} + \sqrt{10}$

$Perimeter = 4\sqrt{2} + 2\sqrt{10}$

Recall that

$Perimeter = a\sqrt{2} + b\sqrt{10}$

This implies that

$a\sqrt{2} + b\sqrt{10} = 4\sqrt{2} + 2\sqrt{10}$

By comparison

$a\sqrt{2} = 4\sqrt{2}$

Divide both sides by $\sqrt{2}$

$a = 4$

By comparison

$b\sqrt{10} = 2\sqrt{10}$

Divide both sides by $\sqrt{10}$

$b = 2$

Hence,

a + b = 2 + 10

a + b = 12

3 0

3 years ago

I need help on finding m

EastWind [94]

Answer:

39°

Step-by-step explanation:

$\angle RUS +\angle SUT = \angle RUT\\\\5x-4+3x+6 = 90\\\\8x+2=90\\\\8x=88\\\\x=11$

and now for SUT

$\angle SUT = 3(11)+6= 33+6 = 39$

4 0

2 years ago

Read 2 more answers