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3 years ago

What is the answer for 3x×5y

Mathematics

1 answer:

lukranit [14]3 years ago

5 0

3x×5y = 15xy

hope it helps

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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

Read 2 more answers

element x is a radioactive isotope such that every 32 years, its mass decreases by half. given that the initial mass of the samp

VashaNatasha [74]

Answer:

the answer is 31.9 years

Step-by-step explanation:

initial mass, $M_{0}$ = 150 gram

half life, $t_{half\hspace{0.1cm}life}$ = 32 years

new mass = half of initial mass = M = 0.5 $M_{0}$

formula , M = $M_{0}$ $e^{\frac{\ln\frac{1}{2}}{t_{half} }\times x }$ where x is the number of years required.

therefore 0.5 $M_{0}$ = $M_{0}$ $e^{\frac{\ln\frac{1}{2}}{t_{half} }\times x } = M_{0} e^{-0.0217x}$

therefore -0.0217 x = $\ln{0.5} = -0.693$

therefore x = $\frac{-0.693}{-0.0217}$ = 31.942

8 0

3 years ago

If the graph of function g is 6 units below the graph of function f, which could be function g? f(x) = -2x + 7

Otrada [13]

It will help you...

Thank you...

4 0

3 years ago

NO LINKS!!!!!!!!! please solve it and explain it.

Usimov [2.4K]

Answer:

Linear: y = 2x-1

Step-by-step explanation:

slope 1 = (5 - -9)/(3 - -4) = 14/7 = 2

slope 2 = (19-5)/(10-3) = 14/7 = 2

equation: y = mx + b b = y-mx = 19 - 2*10 = -1

y = 2x - 1

3 0

3 years ago

There are 645 students at Tech Middle School, and

forsale [732]

Answer:

.20

Step-by-step explanation:

The word percent literally means "Out of 100". With that being said, 20% can be written as a fraction, mixed number or whole number as follows: 1/5 (fraction), 20/100 (mixed number) or .20 (whole number).

3 0

3 years ago