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3 years ago

Solve for π: V= 2πr^2 + 2πrh

Mathematics

1 answer:

crimeas [40]3 years ago

3 0

Answer:

π = V/(2r²+2rh)

Step-by-step explanation:

"Solving" for something means to isolate it on one side of an equation. Because both terms on the right side of the equation have π in common, we can factor it out. Then from there, you just divide the rest of it on both sides to isolate π. It should look like this:

V=2πr^2 + 2πrh

V=π(2r² + 2rh)

V/(2r² + 2rh)=π

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Consider a bell-shaped symmetric distribution with mean of 16 and standard deviation of 1.5. Approximately what percentage of da

fredd [130]

Answer: 95.45 %

Step-by-step explanation:

Given : The distribution is bell shaped , then the distribution must be normal distribution.

Mean : $\mu=\ 16$

Standard deviation : $\sigma= 1.5$

The formula to calculate the z-score :-

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

For x = 13

$z=\dfrac{13-16}{1.5}=-2$

For x = 19

$z=\dfrac{19-16}{1.5}=2$

The p-value = $P(-2$

$0.9772498-0.0227501=0.9544997\approx0.9545$

In percent, $0.9545\times100=95.45\%$

Hence, the percentage of data lie between 13 and 19 = 95.45 %

6 0

2 years ago

A candle in the shape of a circular cone has a base of radius r and a height of h that is the same length as the radius. which e

ladessa [460]

Answer:

$\frac{r(1-\sqrt{2})}{-3}$

Step-by-step explanation:

Volume of cone = $\frac{1}{3} \pi r^{2} h$

Since we are given that a circular cone has a base of radius r and a height of h that is the same length as the radius

= $\frac{1}{3} \pi r^{2} \times r$

= $\frac{1}{3} \pi r^{3}$

Surface area of cone including 1 base = $\pi r^{2} +\pi\times r \times \sqrt{r^2+h^2}$

Since r = h

So, area = $\pi r^{2} +\pi\times r \times \sqrt{r^2+r^2}$

= $\pi r^{2} +\pi\times r \times \sqrt{2r^2}$

= $\pi r^{2} +\pi\times r^2 \times \sqrt{2}$

Ratio of volume of cone to its surface area including base :

$\frac{\frac{1}{3} \pi r^{3}}{\pi r^{2} +\pi\times r^2 \times \sqrt{2}}$

$\frac{\frac{1}{3}r}{1+\sqrt{2}}$

$\frac{r}{3(1+\sqrt{2})}$

Rationalizing

$\frac{r}{3(1+\sqrt{2})} \times \frac{1-\sqrt{2}}{1-\sqrt{2}}$

$\frac{r(1-\sqrt{2})}{-3}$

Hence the ratio the ratio of the volume of the candle to its surface area(including the base) is $\frac{r(1-\sqrt{2})}{-3}$

8 0

3 years ago

Read 2 more answers

Which two transformations are applied to pentagon ABCDE to create A'B'C'D'E'?

vekshin1

The answer is C. I need a total of 20 characters so heres a smiley face:)

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3 years ago

Simplify (6²)4. how to get the answer

Anna71 [15]

Answer:

144

Step-by-step explanation:

6^2 = 6x6 = 36

36 x 4 = 144

7 0

2 years ago

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Algebra 1 : ordered pairs kinda dont get it

lesantik [10]

Answer:

Option C; 3x - y = -27 and x + 2y = 16

Step-by-step explanation:

1. Let us consider the equation 21x - y = 9. In this case it would be best to keep the equation in this form, in order to find the x and y intercept. Let us first find to y - intercept, for the simplicity ⇒ 21 * ( 0 ) - y = 9 ⇒ y = - 9 when x = 0. Now if we take a look at the first plot of line q, we can see that the x value is -9 rather than the y value, so this equation doesn't match that of line q. This would eliminate the first two options being a possibility.

2. Now let us consider the equation 3x - y = -27. Let us consider the x-intercept in this case. That being said, ⇒ 3x - ( 0 ) = -27 ⇒ 3x = -27 ⇒ x = -9 when y = 0. As we can see, this coordinate matches with one of the coordinates of line q, which might mean that the second equation could match with the equation for line v.

3. To see whether Option 3 is applicable, we must take a look at the 2nd equation x + 2y = 16. Let us calculate the y - intercept here: ( 0 ) + 2y = 16 ⇒ 2y = 16 ⇒ y = 8 when x = 0. Here we can see that this coordinate matches with that of the second coordinate provided as one of the points in line v. That means that ~ Answer: Option C

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2 years ago