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3 years ago

The largest ball of yarn ever created has a radius of 6 feet. It took 30 years to create.

Mathematics

2 answers:

ch4aika [34]3 years ago

6 0

Answer:

904.32 cubic ft

Step-by-step explanation:

To find the volume of a sphere, the formula is $4\pi\frac{r^3}{3}$

First, 3.14 * 4 for 12.56.

The radius is 6, and that cubed is 216.

After that, divide 216 by 3 for 72

Then, 12.56 times 72, which gets you the final answer of 904.32 cubic ft.

(10 * 72) + (2 * 72) + (0.5 * 72) + (0.06 * 72)

720 + 144 = 864

864 + 36 = 900

900 + 4.32 = 904.32

Tju [1.3M]3 years ago

3 0

Your answer is D, I took the test.

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F(x) = lnx/x

My name is Ann [436]

$f(x) = \frac{lnx}{x}$

(a) $f'(x) = \frac{d}{dx}[\frac{lnx}{x}]$
Using the quotient rule:
$f'(x) = \frac{\frac{1}{x} \cdot x - lnx}{x^{2}}$
$f'(x) = \frac{1 - lnx}{x^{2}}$

For maximum, f'(x) = 0;
$\frac{1 - lnx}{x} = 0$
$lnx = 1, x = e$

(b) <em>Deduce:
</em> $e^{x} \geq x^{e}, x > 0$
<em>
Soln:</em> Since x = e is the greatest value, then f(e) ≥ f(x) > f(0)
$\frac{ln(e)}{e} \geq \frac{lnx}{x}$
$\frac{1}{e} \geq \frac{lnx}{x}$ , since ln(e) is simply equal to 1

Now, since x > 0, then we don't have to worry about flipping the signs when multiplying by x.
$\frac{x}{e} \geq lnx$
$x \geq elnx$
$x \geq ln(x^{e})$

Taking the exponential to both sides will cancel with the natural logarithmic function in the right hand side to produce:
$e^{x} \geq e^{ln(x^{e}})$
$e^{x} \geq x^{e}$ , as required.

3 0

3 years ago

For a triangle list the respective names of the points of concurrency of medians

devlian [24]

Centroid, orthocenter, circumcenter, and incenter are the four locations that commonly concur.

<h3>Explain about the concurrency of medians?</h3>

A segment whose ends are the triangle's vertex and the middle of the other side is called a median of a triangle. A triangle's three medians are parallel to one another. The centroid, also known as the point of concurrency, is always located inside the triangle.

The incenter of a triangle is the location where the three angle bisectors meet. The only point that can be inscribed into the triangle is the center of the circle, which is thus equally distant from each of the triangle's three sides.

Draw the medians BE, CF, and their intersection at point G in the triangle ABC. Create a line from points A through G that crosses BC at point D. We must demonstrate that AD is a median and that medians are contemporaneous at G since AD bisects BC (the centroid)

To learn more about concurrency of medians refer to:

brainly.com/question/14364873

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4 0

1 year ago

Two experiments are defined below. An event is defined for each of the experiments. Experiment I: Corrine rolls a standard six-s

-BARSIC- [3]

Answer: The correct answer is option C: Both events are equally likely to occur

Step-by-step explanation: For the first experiment, Corrine has a six-sided die, which means there is a total of six possible outcomes altogether. In her experiment, Corrine rolls a number greater than three. The number of events that satisfies this condition in her experiment are the numbers four, five and six (that is, 3 events). Hence the probability can be calculated as follows;

P(>3) = Number of required outcomes/Number of possible outcomes

P(>3) = 3/6

P(>3) = 1/2 or 0.5

Therefore the probability of rolling a number greater than three is 0.5 or 50%.

For the second experiment, Pablo notes heads on the first flip of a coin and then tails on the second flip. for a coin there are two outcomes in total, so the probability of the coin landing on a head is equal to the probability of the coin landing on a tail. Hence the probability can be calculated as follows;

P(Head) = Number of required outcomes/Number of all possible outcomes

P(Head) = 1/2

P(Head) = 0.5

Therefore the probability of landing on a head is 0.5 or 50%. (Note that the probability of landing on a tail is equally 0.5 or 50%)

From these results we can conclude that in both experiments , both events are equally likely to occur.

3 0

3 years ago

The ratio of two numbers is 4 to 3. The sum of the numbers is 49. What are the two numbers?

Irina-Kira [14]

Answer:

28/21

Step-by-step explanation: