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2 years ago

10 Find the standard equation of the circle having the given center and radius.

Mathematics

1 answer:

xz_007 [3.2K]2 years ago

8 0

the standard equation of the circle having the given center and radius is $(x-9)^2+(y-2)^2=\frac{9}{25}$ .

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Special Triangles

Ugo [173]

Answer:

see explanation

Step-by-step explanation:

Using the cosine and tangent trigonometric ratios and the exact values

cos30° = $\frac{\sqrt{3} }{2}$ and tan30° = $\frac{1}{\sqrt{3} }$ , then

cos30° = $\frac{adjacent}{hypotenuse}$ = $\frac{6}{m}$ = $\frac{\sqrt{3} }{2}$ ( cross- multiply )

$\sqrt{3}$ × m = 12 ( divide both sides by $\sqrt{3}$ )

m = $\frac{12}{\sqrt{3} }$ ← rationalise by multiplying numerator/ denominator by $\sqrt{3}$ )

m = $\frac{12}{\sqrt{3} }$ × $\frac{\sqrt{3} }{\sqrt{3} }$ = $\frac{12\sqrt{3} }{3}$ = 4 $\sqrt{3}$

-------------------------------------------------------------------------------

tan30° = $\frac{opposite}{adjacent}$ = $\frac{n}{6}$ = $\frac{1}{\sqrt{3} }$ ( cross- multiply )

$\sqrt{3}$ × n = 6 ( divide both sides by $\sqrt{3}$ )

n = $\frac{6}{\sqrt{3} }$ ← rationalise the denominator

n = $\frac{6}{\sqrt{3} }$ × $\frac{\sqrt{3} }{\sqrt{3} }$ = $\frac{6\sqrt{3} }{3}$ = 2 $\sqrt{3}$

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7 0

3 years ago

Find the area of the shape shown below.

maw [93]

Answer:

The area is 28.

Step-by-step explanation:

Visualize the rectangle as 2 split squares.

The top square is easily 4x4, so the area of that part is 16.

Now visualize the bottom square as two rectangles.

To find the area of the dented side, you would use the equation of finding the area of a triangle, a=(w x h) $\frac{1}{2}$ because the dented side is actually just one half of the rectangle on the other side.

Since it is the same height as the top square, but is 2 in width, it would be written as a=(2 x 4) $\frac{1}{2}$ . So the area of that part is 4, and the area of the other rectangle would be just 2 x 4 so it is 8.

Totaling these numbers, you get the area of the full rectangle.

8 0

4 years ago

Read 2 more answers

On Heiki's trip, the ratio of distance traveled to time is 112 km to 3 h.

allsm [11]

336

112x = 336

112
x3
=336

37.3
x3
= 112

37.3
x9
=336

6 0

3 years ago

Find the volume of the composite solid. Round your answer to the nearest tenth.

alexira [117]

We need a picture of the shape.