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3 years ago

A manager must select 5 delivery locations from 9 that are available. Find the number of

Mathematics

1 answer:

Dmitry_Shevchenko [17]3 years ago

6 0

$C^9_5=\dfrac{9!}{5!4!}=\dfrac{6\cdot7\cdot8\cdot9}{2\cdot3\cdot4}=2\cdot7\cdot9=126$

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Assume that the radius r of a sphere is expanding at a rate of 40 cm/min. The volume of a sphere is V = 4 3 πr3 and its surface

Scrat [10]

Answer:

The rate of change in surface area when r = 20 cm is 20,106.19 cm²/min.

Step-by-step explanation:

The area of a sphere is given by the following formula:

$A = 4\pi r^{2}$

In which A is the area, measured in cm², and r is the radius, measured in cm.

Assume that the radius r of a sphere is expanding at a rate of 40 cm/min.

This means that $\frac{dr}{dt} = 40$

Determine the rate of change in surface area when r = 20 cm.

This is $\frac{dA}{dt}$ when $r = 20$ . So

$A = 4\pi r^{2}$

Applying implicit differentiation.

We have two variables, A and r, so:

$\frac{dA}{dt} = 8r\pi \frac{dr}{dt}$

$\frac{dA}{dt} = 8*20\pi*40$

$\frac{dA}{dt} = 20106.19$

The rate of change in surface area when r = 20 cm is 20,106.19 cm²/min.

6 0

3 years ago

If the length of line segment AB is 9 inches, the total number of point 4 inches from Point A and 6 inches from Point B is

brilliants [131]

9514 1404 393

Answer:

B. Two

Step-by-step explanation:

There are two points that are 4 inches from A and 6 inches from B.

<em>Additional comment</em>

They are at the intersection points of circle A with radius 4 inches and circle B with radius 6 inches.

4 0

2 years ago

I have to estimate 9,105-4031 and im soo confused! Help me plss

balandron [24]

9105-4031= 5074

Step-by-step explanation:

please mark me as branliest

7 0

3 years ago

Read 2 more answers

4 The ratio of corresponding dimensions of two similar solids is 3/4. The surface

White raven [17]

4.

The ratio is 3/4 for corresponding dimensions, the ratio of their surface areas is equal to the square of this ratio:

$\sf (\dfrac{3}{4})^2=\dfrac{S}{96}$

Simplify the exponent:

$\sf \dfrac{9}{16}=\dfrac{96}{S}$

Cross multiply:

$\sf 9S=1536$

Divide 9 to both sides:

$\sf S\approx 170.7~m^2$

So the surface area of the second solid is 54 square meters.

The ratio is 3/4 for corresponding dimensions, the ratio of their volumes is equal to the cube of this ratio:

$\sf (\dfrac{3}{4})^3=\dfrac{720}{V}$

Simplify the exponent:

$\sf \dfrac{27}{64}=\dfrac{720}{V}$

Cross multiply:

$\sf 27V=46080$

Divide 64 to both sides:

$\sf V\approx 1706.7~m^3$

5.

A globe is a sphere, use the formula for the volume of a sphere:

$\sf V=\dfrac{4}{3}\pi r^3$

The radius is half of the diameter, so the radius here is 40/2 = 20. Plug it in the formula, use 3.14 to approximate for Pi:

$\sf V=\dfrac{4}{3}(3.14)(20)^3$

Simplify the exponent:

$\sf V=\dfrac{4}{3}(3.14)(8000)$

Multiply:

$\sf V\approx \boxed{\sf 33,493~in^3}$

6 0

3 years ago

Read 2 more answers

Please help with this question

mojhsa [17]

Equation a and equation c

8 0

3 years ago