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3 years ago

The diameter of a sphere is 21.6 cm. What is the sphere's volume? Round to the nearest tenth, if necessary.

1 answer:

5 0

By definition, the volume of a sphere is:
$V = \frac{4}{3} (\pi) (r ^ 3)
$
Where,
r: sphere radio
Substituting values we have:
$V = \frac{4}{3}(3.14)(( \frac{21.6}{2} ) ^ 3)
$
$V = 5273.99424
$ Rounding the result to the nearest tenth:
$V = 5274.0 cm ^ 3
$ Answer:
the sphere's volume is:
$V = 5274.0 cm ^ 3$

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A garden contains several different types of flowers. In the garden, 2/3 of the flowers are roses. Of the roses, 1/5 of the flow

andreyandreev [35.5K]

Answer:

D. 8/15

Step-by-step explanation:

4/5 = 2/3 +1/3

We need to multiply by 6 to find answer as 3 is a divider of 6

4 x 6 =24

5 x 6 =30

24/30

Then we find 1/2 of 30 and add this to make 3/3

Just like 1/2 of 2 = 1 and 2+1 = 3

30 / 2 = 15

15 + 30 =45

The answer is 24/45

We then reduce this fraction by 3 as 6 + 8 do not divide into 45

24/45 = 8/15

The answer is 8/15

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3 years ago

What is the exponential form of the expanded form below? 3 times 3 times 3 times 3 times 3 times 3 times 3 3 times 7 3 superscri

svetlana [45]

Answer:

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Step-by-step explanation:

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3 years ago

Read 2 more answers

Find an example for each of vectors x, y ∈ V in R.

rjkz [21]

(a) Both conditions are satisfied with x = (1, 0) for $\mathbb R^2$ and x = (1, 0, 0) for $\mathbb R^3$ :

||(1, 0)|| = √(1² + 0²) = 1

max{1, 0} = 1

||(1, 0, 0)|| = √(1² + 0² + 0²) = 1

max{1, 0, 0} = 1

(b) This is the well-known triangle inequality. Equality holds if one of x or y is the zero vector, or if x = y. For example, in $\mathbb R^2$ , take x = (0, 0) and y = (1, 1). Then

||x + y|| = ||(0, 0) + (1, 1)|| = ||(1, 1)|| = √(1² + 1²) = √2

||x|| + ||y|| = ||(0, 0)|| + ||(1, 1)|| = √(0² + 0²) + √(1² + 1²) = √2

The left side is strictly smaller if both vectors are non-zero and not equal. For example, if x = (1, 0) and y = (0, 1), then

||x + y|| = ||(1, 0) + (0, 1)|| = ||(1, 1)|| = √(1² + 1²) = √2

||x|| + ||y|| = ||(1, 0)|| + ||(0, 1)|| = √(1² + 0²) + √(0² + 1²) = 2

and of course √2 < 2.

Similarly, in $\mathbb R^3$ you can use x = (0, 0, 0) and y = (1, 1, 1) for the equality, and x = (1, 0, 0) and y = (0, 1, 0) for the inequality.

x • y = ||x|| ||y|| cos(θ),

where θ is the angle between the vectors x and y. Both sides are scalar, so taking the norm gives

||x • y|| = ||(||x|| ||y|| cos(θ)|| = ||x|| ||y|| |cos(θ)|

Suppose x = (0, 0) and y = (1, 1). Then

||x • y|| = |(0, 0) • (1, 1)| = 0

||x|| • ||y|| = ||(0, 0)|| • ||(1, 1)|| = 0 • √2 = 0

For the inequality, recall that cos(θ) is bounded between -1 and 1, so 0 ≤ |cos(θ)| ≤ 1, with |cos(θ)| = 0 if x and y are perpendicular to one another, and |cos(θ)| = 1 if x and y are (anti-)parallel. You get everything in between for any acute angle θ. So take x = (1, 0) and y = (1, 1). Then

||x • y|| = |(1, 0) • (1, 1)| = |1| = 1

||x|| • ||y|| = ||(1, 0)|| • ||(1, 1)|| = 1 • √2 = √2

In $\mathbb R^3$ , you can use the vectors x = (1, 0, 0) and y = (1, 1, 1).

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3 years ago

Sarah's favorite candy consists of sour patch kids and M&Ms. She has 17 total packages of sour patch kids and M&Ms. She

faltersainse [42]

Answer:

Sarah has 11 packages of sour patch kids and 6 packages of M&Ms

Step-by-step explanation:

11 + 6 = 17, and 11 is five more than 6, fulfilling the needs of the problem

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3 years ago

Explain how you know that the sum of 12.6,3.1, and 5.4 is greater than 20

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By just looking at ur whole numbers...12 + 3 + 5 = 20...and thats not even counting ur decimals..so by adding ur decimals, u know that it will be over 20.

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3 years ago