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3 years ago

A=4pi r^{2} solve for r

1 answer:

5 0

A = 4πr² Divide both sides by 4π
A / 4π = r² Find the square root of both sides
√(A / 4π) = √(r²) Cancel out the square with the square root
√(A / 4π) = r Switch the sides to make it easier to read
r = √(A / 4π)

You might be interested in

Researchers at a pharmaceutical company have found that the effective time duration of a safe dosage of pain relief drug is norm

FrozenT [24]

Answer:

a) $P(1$

b) $P(X$

Step-by-step explanation:

1) Previous concepts

Normal distribution, is a "probability distribution that is symmetric about the mean, showing that data near the mean are more frequent in occurrence than data far from the mean".

The Z-score is "a numerical measurement used in statistics of a value's relationship to the mean (average) of a group of values, measured in terms of standard deviations from the mean".

2) Part a

Let X the random variable that represent the duration of a safe dosage of pain relief drug, and for this case we know the distribution for X is given by:

$X \sim N(1.5,0.8)$

Where $\mu=1.5$ and $\sigma=0.8$

We are interested on this probability

$P(1$

And the best way to solve this problem is using the normal standard distribution and the z score given by:

$z=\frac{x-\mu}{\sigma}$

If we apply this formula to our probability we got this:

$P(1$

And we can find this probability on this way:

$P(-0.625$

And in order to find these probabilities we can find tables for the normal standard distribution, excel or a calculator.

$P(-0.625$

3) Part b

We are interested on this probability

$P(X$

And the best way to solve this problem is using the normal standard distribution and the z score given by:

$z=\frac{x-\mu}{\sigma}$

If we apply this formula to our probability we got this:

$P(X$

And we can find this probability on this way:

$P(z$

6 0

3 years ago

What's the hight of a million pennies

TiliK225 [7]

The thickness of a brand new US penny that hasn't been
worn down is 1.52 millimeters.

If you have a million pennies, there are many ways to arrange them.
You can pile them all in one pile, or shovel them into many piles, or
stack them up in any number of stacks up to a half-million stacks
with two pennies in each stack, or try somehow to stack them all up
in one stack that's a million thicknesses high.

Any stack with 'n' pennies in the stack is 1.52n millimeters high.

If you somehow succeed in stacking all million of them in one stack,
then the height of that stack would be . . .

   (1,000,000) x (1.52 mm) = 1,520,000 millimeters
   152,000 centimeters
   1,520 meters
   1.52 kilometers

(about 59,842.5 inches
4,986.9 feet
   1,662.3 yards
   7.56 furlongs
0.944 mile
      all rounded)

3 0

3 years ago

I can't seem to find the answer for this I'm pretty sure it's non linear

Nata [24]

Answer:

(d) No. Slope is not constant.

Step-by-step explanation:

You want to know if the given graph shows a linear function.

<h3>Linear function</h3>

The graph of a linear function is a straight line. The points on the graph shown do not form a straight line, so the function is nonlinear.

<h3>Rate of change</h3>

The rate of change of a function is the ratio of "rise" to "run" between two points in the graph. This ratio is also called the "slope." For a straight line, the rate of change (slope) is constant. That is, a linear function has a constant rate of change.

If the function is nonlinear, its rate of change is not constant. The converse is also true: if the slope is not constant, the function is nonlinear.

6 0

1 year ago

Find the value of x.

drek231 [11]

Answer:

x= 13 degrees

Step-by-step explanation:

This is a 90 degree angle. We can create an equation to find x

68+x+9= 90

77+x= 90

-77 -77

x= 13 degrees

Hope this helps!

6 0

3 years ago

Let f be a differentiable function such that f(0) = -5 and f'(x) is less than or equal to 3 for all x. Of the following, which i

stepladder [879]

E) 2
Remember that the first derivative of a function is the slope of the function at any specified point. We've been told that f(0) = -5 and that f'(x) is always less than or equal to 3. So let's look at the available options and see what the average slope would have to be in order to get the specified value of f(2).
A) -10: (-10 - -5)/(2 - 0) = -5/2 = -2.5
B) -5: (-5 - -5)/(2 - 0) = 0/2 = 0
C) 0: (0 - -5)/(2 - 0) = 5/2 = 2.5
D) 1: (1 - -5)/(2 - 0) = 6/2 = 3
E) 2: (2 - -5)/(2 - 0) = 7/2 = 3.5
Now taking into consideration the mean value theorem, the value of the function f'(x) has to have the value equal to the average slope between the two points at at least one point between the two given values. For options A, B, C, and D it's possible for f'(x) to return values that make that slope possible. However, for option E, the mean value theorem indicates that f'(x) has to have the value of 3.5 for at least 1 point between x=0 and x=2. And since we've been told that f'(x) is less than or equal to 3 for all possible values of x, that is in conflict and f(2) can not have the value of 2.

3 0

3 years ago