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2 years ago

13

The volume of a cylinder is 768 N in³. Find the radius of the cylinder (in inches) if the height is 3 in

1 answer:

yarga [219]2 years ago

6 0

To find the volume of the cylinder we multiply the area of the face by the height of the cylinder. Area pi*r^2
First find area
768in^3/3in = 256in^2
Pi*r^2 = 256
r^2 = 256 / pi
radius = root of 256/pi
Hence radius = 9.027033337 in
To check answer
Pi*9.027033337^2 * 3in = 768in^3

Finalized answer to 2 d.p
Radius = 9.03 in

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Answer:

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3 years ago

54 out of the 60 magazines at the bookstore are women's magazines. What percentage of the magazines at the bookstore are women's

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90

Step-by-step explanation:

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$\frac{54}{60}$ ×100

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3 years ago

Simplify the following

den301095 [7]

Answer:

1) 11 $\sqrt{3}$

2) 2 $\sqrt{2}$

3) $20\sqrt{3} + 15\sqrt{2}$

4) $53 + 12\sqrt{10}$

5) -2

6) $7\sqrt{2} - 5\sqrt{3}$

Step-by-step explanation:

1) 2 $\sqrt{12}$ + 3 $\sqrt{48}$ - $\sqrt{75}$

=(2 × 2 $\sqrt{3}$ )+ (3 × 4 $\sqrt{3}$ ) - 5 $\sqrt{3}$

= 4 $\sqrt{3}$ + 12 $\sqrt{3}$ - 5 $\sqrt{3}$

= 11 $\sqrt{3}$

2) 4 $\sqrt{8}$ -2 $\sqrt{98}$ + $\sqrt{128}$

= (4 × 2 $\sqrt{2}$ ) - (2 × 7 $\sqrt{2}$ ) + 8 $\sqrt{2}$

= 8 $\sqrt{2}$ - 14 $\sqrt{2}$ +8 $\sqrt{2}$

= 2 $\sqrt{2}$

3) 5 $\sqrt{12\\}$ - 3 $\sqrt{18} + 4 \sqrt{72} +2\sqrt{75}$

= 5× $2\sqrt{3}$ - 3× $3\sqrt{2}$ + 4× $6\sqrt{2}$ + 2× $5\sqrt{3}$

= $10\sqrt{3} - 9\sqrt{2} +24\sqrt{2} +10\sqrt{3}$

= $20\sqrt{3} + 15\sqrt{2}$

4) $(2\sqrt{2} + 3\sqrt{5} )^{2}$

= $8 + 12\sqrt{10} + 45$

= $53 + 12\sqrt{10}$

5) $(1+\sqrt{3} ) (1-\sqrt{3} )$

= $1 - 3$

= -2

6) $(2\sqrt{6} -1) (\sqrt{3} -\sqrt{2} )$

= $2\sqrt{18}-2\sqrt{12} -\sqrt{3} +\sqrt{2}$

= 2× $3\sqrt{2}$ - 2× $2\sqrt{3}$ - $\sqrt{3} + \sqrt{2}$

= $6\sqrt{2} - 4\sqrt{3} -\sqrt{3} +\sqrt{2}$

= $7\sqrt{2} - 5\sqrt{3}$

Hope the working out is clear and will help you. :)

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2 years ago

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Q5: Identify the graph of the equation and write an equation of the translated or rotated graph in general form.

MAVERICK [17]

Answer:

$d.\:ellipse;\:3x^2+y^2+6x-6y+3=0$ .

Step-by-step explanation:

The given conic has equation;

$3x^2+y^2=9$

Divide through by 9.

$\Rightarrow \frac{3x^2}{9}+\frac{y^2}{9}=\frac{9}{9}$

$\Rightarrow \frac{x^2}{3}+\frac{y^2}{9}=1$ .

This is an ellipse centered at the origin;

This ellipse has been translated so that the center is now at;

$(-1,3)$

The translated ellipse has equation;

$\frac{(x+1)^2}{3}+\frac{(y-3)^2}{9}=1$ .

Clear the fraction;

$3(x+1)^2+(y-3)^2=9$ .

Expand;

$3(x^2+2x+1)+(y^2-6y+9)=9$ .

$3x^2+6x+3+y^2-6y+9=9$ .

Write in general form;

$3x^2+y^2+6x-6y+9-9+3=0$ .

$3x^2+y^2+6x-6y+3=0$ .

The correct choice is D

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3 years ago

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An observer is standing in a lighthouse 96 feet above the level of the water. The angle of depression of a buoy is 22. What is t

lorasvet [3.4K]

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3 years ago

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