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liubo4ka [24]
3 years ago
6

A gardener purchases a ceramic planter, in the shape of a hemisphere, for a small batch of leftover annuals. The volume of a hem

isphere is modeled by the function V = πr3. Write a model for the radius as a function of the volume. The label on the planter says that it holds approximately 134 cubic inches of potting soil. What is the radius of the planter, rounded to the nearest inch? Use 3.14 for π.
Mathematics
1 answer:
musickatia [10]3 years ago
5 0
A gardener purchases a ceramic planter, in the shape of a hemisphere, for a small batch of leftover annuals. The volume of a hemisphere is modeled by the function V = 2/3πr 3 


<span>A. Write a model for the radius as a function of the volume. </span>
<span>B. The label on the planter says that it holds approximately 134 cubic inches of potting soil. What is the radius of the planter, rounded to the nearest inch? Use 3.14 for π </span>


<span>r = ∛[(3/2)V) / π] </span>


<span>134 = (2/3) (3/14) r^3 </span>

<span>r = ∛[(3/2) (134) / 3.14] ≈ 4.00 inches </span>
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x^3 is strictly increasing on [0, 5], so

\max\{x^3 \mid 0\le x\le5\} = 5^3 = 125

and

\min\{x^3 \mid 0 \le x\le5\} = 0^3 = 0

so the integral is bounded between

\displaystyle \boxed{0} \le \int_0^5x^3\,dx \le \boxed{125}

8 0
1 year ago
In how many ways can six people sit in a six-passenger car?
nekit [7.7K]

Answer:

number of ways = 720

Step-by-step explanation:

The number of ways  six people sit in a six-passenger car is given by the number of permutations of 6 elements in 6 different positions ( seats), then

number of ways = number of permutations of 6 elements = 6! = 6 * 5 * 4 *3 * 2 * 1 = 720

Since the first person that sits can be on any of the seats , but then the second person that sits can choose any of 5 seats (since the first person had already occupied one) , the third can choose 4 ... and so on.

5 0
3 years ago
Find the selling price for a case of Newman's Own® special blend coffee that costs the retailer $35.87 if the markup is 22% of t
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Answer:

The selling price is $46 approx.

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The cost price is = $35.87

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So, solution is = 35.87/0.78=45.98 ≈ $46.

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2 years ago
PLEASE ANSWER! Given the functions f(x) = x2 + 6x - 1, g(x) = -x2 + 2, and h(x) = 2x2 - 4x + 3, rank them from least to greatest
Ratling [72]

Answer:

<em>he rank from least to great based on their axis of symmetry: </em>

0, 1, -3 ⇒ g(x), h(x), f(x)

So, <em>option C</em> is correct.

Step-by-step explanation:

A quadratic equation is given by:

ax^2+bx+c =0

Here, a, b and c are termed as coefficients and x being the variable.

<em>Axis of symmetry can be obtained using the formula</em>

x = \frac{-b}{2a}

Identification of a, b and c in f(x), g(x) and h(x) can be obtained as follows:

f(x) = x^2 + 6x - 1

⇒ a = 1, b = 6 and c = -1

g(x) = -x^2 + 2

⇒ a = -1, b = 0 and c = 2

h(x) = 2^2 - 4x + 3

⇒ a = 2, b = -4 and c = 3

So, axis of symmetry in f(x) = x^2 + 6x - 1 will be:

x = \frac{-b}{2a}

x = -6/2(1) = -3

and axis of symmetry in g(x) = -x^2 + 2 will be:

x = \frac{-b}{2a}

x = -(0)/2(-1) = 0

and axis of symmetry in h(x) = 2^2 - 4x + 3 will be:

x = \frac{-b}{2a}

x = -(-4)/2(2) = 1

<em>So, the rank from least to great based on their axis of symmetry: </em>

0, 1, -3 ⇒ g(x), h(x), f(x)

So, <em>option C</em> is correct.

<em>Keywords: axis of symmetry, functions</em>

<em>Learn more about axis of symmetry from brainly.com/question/11800108</em>

<em>#learnwithBrainly</em>

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