Can you find 10/21 of 3/ 10

Hello people ~

Luden [163]

Cone details:

height: h cm

radius: r cm

Sphere details:

radius: 10 cm

================

From the endpoints (EO, UO) of the circle to the center of the circle (O), the radius is will be always the same.

Using Pythagoras Theorem

(a)

TO² + TU² = OU²

(h-10)² + r² = 10² [insert values]

r² = 10² - (h-10)² [change sides]

r² = 100 - (h² -20h + 100) [expand]

r² = 100 - h² + 20h -100 [simplify]

r² = 20h - h² [shown]

r = √20h - h² ["r" in terms of "h"]

(b)

volume of cone = 1/3 * π * r² * h

===========================

$\longrightarrow \sf V = \dfrac{1}{3} * \pi * (\sqrt{20h - h^2})^2 \ ( h)$

$\longrightarrow \sf V = \dfrac{1}{3} * \pi * (20h - h^2) (h)$

$\longrightarrow \sf V = \dfrac{1}{3} * \pi * (20 - h) (h) ( h)$

$\longrightarrow \sf V = \dfrac{1}{3} \pi h^2(20-h)$

To find maximum/minimum, we have to find first derivative.

(c)

First derivative

$\Longrightarrow \sf V' =\dfrac{d}{dx} ( \dfrac{1}{3} \pi h^2(20-h) )$

apply chain rule

$\sf \Longrightarrow V'=\dfrac{\pi \left(40h-3h^2\right)}{3}$

Equate the first derivative to zero, that is V'(x) = 0

$\Longrightarrow \sf \dfrac{\pi \left(40h-3h^2\right)}{3}=0$

$\Longrightarrow \sf 40h-3h^2=0$

$\Longrightarrow \sf h(40-3h)=0$

$\Longrightarrow \sf h=0, \ 40-3h=0$

$\Longrightarrow \sf h=0,\:h=\dfrac{40}{3}$

maximum volume: when h = 40/3

$\sf \Longrightarrow max= \dfrac{1}{3} \pi (\dfrac{40}{3} )^2(20-\dfrac{40}{3} )$

$\sf \Longrightarrow maximum= 1241.123 \ cm^3$

minimum volume: when h = 0

$\sf \Longrightarrow min= \dfrac{1}{3} \pi (0)^2(20-0)$

$\sf \Longrightarrow minimum=0 \ cm^3$

6 0

2 years ago

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In 2010, the population of a town was 8500. The population decreased by 4.5% each year.

Soloha48 [4]

Answer:

This is a problem in exponential decay.

a) If a town's population decreases by 4.5% every year that also means that the town's population decreases by a factor of .955 each year. (1 - .045 = .955)

So, after 5 years, the town's population is:

8,500 * .955^5 which equals 6,752.

So, basically, after t years, the town's population equals

8,500 * .955^t where t is the number of years that have passed since the year 2010.

b) population = 8,500 * .955 ^ (number of years since 2010)

7,000 / 8,500 = .955 ^ (number of years since 2010)

0.8235294118 = .955 ^ (number of years since 2010)

To solve for (number of years since 2010) we take logs of both sides

log (0.8235294118 ) = number of years since 2010 * log(.955)

-0.0843208857 = number of years since 2010 * -0.0199966284

-0.0843208857 / -0.0199966284 = number of years since 2010

4.2167551422 = number of years since 2010

So, population = 7,000 when the year is 2014.2167551422

Or about 2.6 months into 2014

(YES, it's just that "easy") LOL

Step-by-step explanation:

6 0

3 years ago

You are planning a survey of starting salaries for recent business major graduates from your college. From a pilot study you est

xxTIMURxx [149]

Answer:

1245

Step-by-step explanation:

-Given the standard deviation is $9000 and the margin of error is $500.

-the minimum sample size at a 95% confidence level can be calculated using the formula:

$n\geq( \frac{z\sigma}{MOE})^2\\\\\\\geq (\frac{1.96\times 9000}{500})^2\\\\\\\geq 1244.6784\approx 1245$

Hence, the minimum sample size is 1245

*Since there's no data fromw which we are drawing our variables, we can manually input our parameters in excel and calculate as attached.

5 0

3 years ago

Guys please help! In triangle CDE, the measure of angle C is 90 degrees, side CD is 15 and DE is 3 more than CE. Find the length

AURORKA [14]

You can calculate it using the law of cosines: c^2=a^2+b^2-2*a*b*cos(C)

your triangle is
CD=15=a
CE=?=b
DE=CE+3=b+3=c
and C=90°

-> insert those values, with c substituted with b+3 to remove c

c^2=a^2+b^2-2*a*b*cos(C)
(b+3)^2=15^2+b^2-2*15*b*cos(90)
cos(90)=0->
(b+3)^2=15^2+b^2
b^2+2*3*b+3^2=225+b^2
6b+9=225
6b=216
b=36=CE

DE=CE+3=36+3=39

4 0

3 years ago

20 At Honey Beepot, the bulk price for honey is $2.50 per pound, with a minimum purchase of 20 pounds. If Bobby paid $80 for som

Pachacha [2.7K]

Answer:
12 pounds (B)
Explanation:
80/2.5 = 32
32-20 = 12
I don’t know if this is right but I’m pretty sure it is.

7 0

3 years ago

Read 2 more answers