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3 years ago

Find the length of the diameter of a sphere with a surface area of 50.27 ft^2.

1 answer:

6 0

Sphere Surface Area = 4 • π • r²

50.27 = 4 * PI * r^2

50.27 / (4 * PI) = r^2

 4.0003594946 = r^2

r = sq root ( 4.0003594946)

radius = 2.0000898716 

So the diameter = 4.0001797433 

or it is roughly 4 feet

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Solve the differential. This was in the 2016 VCE Specialist Maths Paper 1 and i'm a bit stuck

Nimfa-mama [501]

$\sqrt{2 - x^{2}} \cdot \frac{dy}{dx} = \frac{1}{2 - y}$
$\frac{dy}{dx} = \frac{1}{(2 - y)\sqrt{2 - x^{2}}}$

Now, isolate the variables, so you can integrate.
$(2 - y)dy = \frac{dx}{\sqrt{2 - x^{2}}}$
$\int (2 - y)\,dy = \int\frac{dx}{\sqrt{2 - x^{2}}}$
$2y - \frac{y^{2}}{2} = sin^{-1}\frac{x}{\sqrt{2}} + \frac{1}{2}C$

$4y - y^{2} = 2sin^{-1}\frac{x}{\sqrt{2}} + C$
$y^{2} - 4y = -2sin^{-1}\frac{x}{\sqrt{2}} - C$
$(y - 2)^{2} - 4 = -2sin^{-1}\frac{x}{\sqrt{2}} - C$
$(y - 2)^{2} = 4 - 2sin^{-1}\frac{x}{\sqrt{2}} - C$

$y - 2 = \pm\sqrt{4 - 2sin^{-1}\frac{x}{\sqrt{2}} - C}$
$y = 2 \pm\sqrt{4 - 2sin^{-1}\frac{x}{\sqrt{2}} - C}$

At x = 1, y = 0.
$0 = 2 \pm\sqrt{4 - 2sin^{-1}\frac{1}{\sqrt{2}} - C}$
$-2 = \pm\sqrt{4 - 2sin^{-1}\frac{1}{\sqrt{2}} - C}$

$4 - 2sin^{-1}\frac{1}{\sqrt{2}} - C > 0$
$\therefore 2 = \sqrt{4 - 2sin^{-1}\frac{1}{\sqrt{2}} - C}$

$4 = 4 - 2sin^{-1}\frac{1}{\sqrt{2}} - C$
$0 = -2sin^{-1}\frac{1}{\sqrt{2}} - C$
$C = -2sin^{-1}\frac{1}{\sqrt{2}} = -2\frac{\pi}{4}$
$C = -\frac{\pi}{2}$

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3 years ago

Help helpp pleaseee

Len [333]

Answer:

3 is the right I think idonk

8 0

3 years ago

Solve for x. 2=4x-6

77julia77 [94]

Answer:

x = 2

Step-by-step explanation:

Rewrite the equation as 4x - 6 = 2

Move all terms not containing x to the right side of the equation:

Add 6 to both sides of the equation.

4x = 2 + 6

Add 2 and 6.

4x = 8

Divide each term by 4 and simplify.

Divide each term in 4x = 8 by 4.

$\frac{4x}{4} =\frac{8}{4}$

Reduce the expression by cancelling the common factors.

$x=\frac{8}{4}$

Divide 8 by 4.

x = 2

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3 years ago

What is the equation of the circle with center (-3.2, -2.1) and radius 4.3?

Ilya [14]

The equation of the circle is : $x^{2}$ + $y^{2}$ + 6.4 $x$ + 4.2 $y$ = 3.84

<h3>Meaning of a Circle</h3>

A circle is a loci or a continuous line that equidistant from the center to any point on the line. it drawn starting from a point and ending on that same point.

The equation of a circle is an equation used to find points on a circle so the circle can be drawn with accurate measurement. it can also be used to find the missing points.

In conclusion, The equation of the circle is : $x^{2}$ + $y^{2}$ + 6.4 $x$ + 4.2 $y$ = 3.84

Learn more about equation of a circle: brainly.com/question/1506955

#SPJ1

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2 years ago

Geometry question any help is appreciated!!

sladkih [1.3K]

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Equation of the circle , where (h, k) coordinates of the center of the radius.
(h,k)=(5,-7)
(x-h)² +(y-k)² = r²
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(x-5)² +(y+7)² = 100

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3 years ago