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zavuch27 [327]
2 years ago
14

You are a laboratory technician. You are filling spherical flasks with a salt solution and then putting them into boxes. Each fl

ask has a volume of 113.04 cubic inches.
Rounded to the nearest tenth of an inch, what is the radius of one flask?

3.0
3.6
5.2
6.4
6.9
Mathematics
1 answer:
Jobisdone [24]2 years ago
7 0

Answer:

3.0 inches

Step-by-step explanation:

The formula for the volume of a sphere is

V = 4/3 × π × r³

V = 113.04 cubic inches

To find r

r = (3V/4π)⅓

r = (3 × 113.04/4 × π )⅓

r = 3.0 inches

The radius of one flask = 3.0 inches

Option A is correct

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Evaluate the line integral, where c is the given curve. c y3 ds,
postnew [5]
Parameterizing \mathcal C by

\mathbf r(t)=(t^3,t)

with 0\le t\le2, we have

\mathrm ds=\|\mathbf r'(t)\|\,\mathrm dt=\sqrt{(3t^2)^2+1^2}\,\mathrm dt=\sqrt{9t^4+1}\,\mathrm dt

So

\displaystyle\int_{\mathcal C}y^3\,\mathrm ds=\int_{t=0}^{t=2}t^3\sqrt{9t^4+1}\,\mathrm dt
=\displaystyle\frac1{36}\int_0^236t^3\sqrt{9t^4+1}\,\mathrm dt
=\displaystyle\frac1{36}\int_{u=1}^{u=145}\sqrt u\,\mathrm du
=\dfrac{145^{3/2}-1}{54}
5 0
3 years ago
Describe lengths of three segments that could not be used to form a triangle. Segments with lengths of 5 in., 5 in., and ______
Vesna [10]

Answer:

c = 11

Step-by-step explanation:

Given

Let the three sides be a, b and c

Such that:

a = b= 5

Required

Find c such that a, b and c do not form a triangle

To do this, we make use of the following triangle inequality theorem

a + b > c

a + c > b

b + c > a

To get a valid triangle, the above inequalities must be true.

To get an invalid triangle, at least one must not be true.

Substitute: a = b= 5

5 + 5 > c ===> 10 > c

5 + c > 5  ===> c > 5 - 5 ===> c > 0

5 + c > 5  ===> c > 5 - 5 ===> c > 0

The results of the inequality is: 10 > c and c > 0

Rewrite as: c > 0 and c < 10

0 < c < 10

This means that, the values of c that make a valid triangle are 1 to 9 (inclusive)

Any value outside this range, cannot form a triangle

So, we can say:

c = 11, since no options are given

8 0
2 years ago
Can I have help with 42?
Sphinxa [80]
#42.
14n - 32 = 22
add 32 to both sides
14n - 32 + 32 = 22 + 32
simplify
14n = 54
divide both sides by 14
14n/14 = 54/14
simplify
n = 3 12/14
n = 3 6/7 or n = 3.857


8 0
3 years ago
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3. The ratio of blue marbles to white
SSSSS [86.1K]

Answer:

C 40

Step-by-step explanation:

1 blue : 2 white

multiply both sides of the proportion by 20 to reach 20 blue marbles

20 blue: 40 white

7 0
3 years ago
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27 divided by 52,758
marta [7]

Answer:

511

Step-by-step explanation:

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3 0
3 years ago
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