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3 years ago

13

Write inequalites to describe the region. The solid cylinder that lies on or below the z=8 and or above the disk in the xy-plane

with center the origin and radius 2

1 answer:

Vladimir79 [104]3 years ago

8 0

Answer:

x^2 + y^2 <= 4, 0 <= z <= 8

Step-by-step explanation:

Region that lies on/below the plane means Z<=8
Region that lies on/above the xy plane means Z>=0.

Combining 1 and 2, we get

0<=Z<=8

If we want disk of radius 2 in x-y plane to be centered at origin the inequality becomes:

x^2 + y^2 <= 4

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What's the answer to this question

frutty [35]

Step-by-step explanation:

there are several things to be considered to solve this.

the strategy is to caucuses the volume of the full "box", and then to deduct the 3-dimensional triangle that is "cut off" from the oil.

then we know the volume of the pool.

next step is to calculate the volume of a "box" with the same layout but is only 20 cm deep.

then we know how much volume can be pumped out in 30 minutes.

and then we divide the whole volume by that small volume to see how many 30-minues units are needed to empty the whole pool.

and then we transform the 30- minutes units into actual minutes or hours.

so, let's begin :

the whole box's volume is

2×1×1.4 = 2.8 m³

the volume of the 3-D triangle we need to subtract is the area of the triangle × width of the pool (this pool width is the height of the 3-D triangle).

2×(1.4 - 0.6) × 1 / 2 = 2×0.8 × 1 / 2 = 1.6/2 = 0.8 m³

so, the volume of the pool is

2.8 - 0.8 = 2 m³

now, how much volume can the pump eliminate in 30 minutes ?

the content of a box

1×2×0.2 = 0.4 m³

as 20 cm = 0.2 m

so, the pump pumps out 0.4 m³ in 30 minutes.

and we need to empty 2 m³.

that means we need

2 / 0.4 = 5

30-minues units = 5×30 = 150 minutes = 2.5 hours.

Colin has to wait 2.5 hours (150 minutes) to empty the complete pool.

6 0

3 years ago

3/8×1/3×3/4=? <br> What is is the answer???

Leno4ka [110]

The exact form is: 3/32

And the decimal form is: 0.09375

4 0

2 years ago

This is confusing me to death

Yuri [45]

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4 0

3 years ago

Shelly has a roll of fabric and decides to make some scarves for her friend the roll contains 6 2/3 yards of fabric she needs 5/

ivann1987 [24]

Answer:

8

Step-by-step explanation:

Total length of the fabric is $6\dfrac{2}{3}=\dfrac{20}{3}\ \text{yards}$

We need to find the number of scarves can she make if she needs 5/6 of a yard for each scarf.

Let she needs x scarves. So, ATQ

$x\times \dfrac{5}{6}=\dfrac{20}{3}\\\\x=\dfrac{20}{3}\cdot\dfrac{6}{5}\\\\x=8$

Hence, she can make 8 scarves.

8 0

3 years ago

Suppose that 5 J of work is needed to stretch a spring from its natural length of 30 cm to a length of 39 cm.

vesna_86 [32]

Answer

given,

work = 5 J

spring stretch form 30 cm to 39 cm

$W = \dfrac{1}{2}kx^2$

x = 0.39 - 0.30 = 0.09 m

$5 = \dfrac{1}{2}k\times 0.09^2$

$k = \dfrac{5\times 2}{0.09^2}$

k = 1234.568 N/m

a) work when spring is stretched from 32 cm to 34 cm

x₂= 0.34 -0.30 = 0.04 m

x₁ = 0.32 - 0.30 = 0.02

$W = \dfrac{1}{2}k(x_2^2-x_1^2)^2$

$W = \dfrac{1}{2}\times 1234.568 \times (0.04^2-0.02^2)^2$

W = 0.741 J

b) F = k x

25 = 1234.568 × x

x = 0.0205 m

x = 2.05 cm

3 0

4 years ago