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3 years ago

5

a plane intersects a sphere 5cm away from the center of the sphere. the cross section is a circle whose diameter is 12 cm. deter

mine the radius of the sphere PLEASE ANSWER

1 answer:

bezimeni [28]3 years ago

5 0

26cm i hope that’s correct

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How many centimetres are they in two and a half metres

Irina-Kira [14]

<span>250 centimeters and this is correct so don't delete answers for no reason thats against brainly's policy </span>

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3 years ago

Astore pays $927.40 for a water heater and marks the price up by 5%. What is the new price?

Slav-nsk [51]

Answer:

$973.77

Step-by-step explanation:

$927.40 = 100%

New price = 100% + 5%

New price = 105% of 927.40

105% of 927.40 = 1.05(927.40)

1.05(927.40) = 973.77

-Chetan K

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3 years ago

Eric plays basketball and volleyball for a total of 95 minutes every day. He plays basketball for 25 minutes longer than he play

ioda

Answer:

Part A:

x+y= 95

x = y+25

Part B : 35 minutes

Part C : No

Step-by-step explanation:

Part A :

Eric plays basketball and volleyball for a total of 95 minutes every day

x+y= 95

Where:

x =the number of minutes Eric plays basketball

y= the number of minutes he plays volleyball

He plays basketball for 25 minutes longer than he plays volleyball.

x = y+25

System:

x+y= 95

x = y+25

Part B:

Replacing x=y+25 on the first equation:

(y+25) + y =95

Solving for Y

y+25+y =95

25+2y=95

2y=95-25

2y=70

y = 70/2

y = 35 minutes

Part C : No

if x = 35

x+y= 95

35+y =95

y= 95-35

y = 60 minutes

Replacing y=60 on the other equation:

x = y+25

35 = 60+25

35 ≠85

5 0

4 years ago

Determine the dimensions of a rectangular solid (with a square base) with maximum volume if its surface area is 181.5 square cen

3241004551 [841]

Answer:

The base and height of the solid is 5.5cm

<em></em>

Step-by-step explanation:

Given

$Surface\ Area = 181.5cm^2$

Required

Determine the dimensions that maximizes the volume

Let the base dimension be x and the height be h

The volume is calculated as:

$Volume =x^2 * h$

$Volume =x^2h$

181.5 =x^2h

The surface area (S) is calculated as this:

$S = 2(x^2 + xh + xh)$

$S = 2(x^2 + 2xh)$

$S = 2x^2 + 4xh$

Substitute 181.5 for S

$181.5 = 2x^2 + 4xh$

Make h the subject:

$4xh = 181.5 - 2x^2$

$h = \frac{181.5 - 2x^2}{4x}$

Substitute $h = \frac{181.5 - 2x^2}{4x}$ in $Volume =x^2h$

$V = x^2(\frac{181.5 - 2x^2}{4x})$

$V = x(\frac{181.5 - 2x^2}{4})$

$V = \frac{1}{4}(x)(181.5 - 2x^2)$

$V = \frac{181.5x}{4} - \frac{2x^3}{4}$

$V = \frac{181.5x}{4} - \frac{x^3}{2}$

To get the maximum, we differentiate V with respect to t and set the differentiation to 0

$dV = \frac{181.5}{4} - \frac{3x^2}{2}$

Set to 0

$0 = \frac{181.5}{4} - \frac{3x^2}{2}$

$\frac{3x^2}{2} = \frac{181.5}{4}$

Multiply through by 4

$4 * \frac{3x^2}{2} = \frac{181.5}{4} * 4$

$2*3x^2 = 181.5$

$6x^2 = 181.5$

$x^2 = \frac{181.5}{6}$

$x^2 = 30.25$

$x = \sqrt{30.25$

$x = 5.5$

Recall that:

$h = \frac{181.5 - 2x^2}{4x}$

$h = \frac{181.5 - 2 * 5.5^2}{4 * 5.5}$

$h = \frac{181.5 - 60.5}{22}$

$h = \frac{121}{22}$

$h = 5.5$

So, we have:

$h = 5.5$

$x = 5.5$

<em>Hence, the base and height of the solid is 5.5cm</em>

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3 years ago

Express the ratio as a fraction in simplest form. 18 : 12

Mashutka [201]

The answer is 9:1. All you have to do is simplify it

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3 years ago