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3 years ago

Help pls someone?!? )):

Mathematics

1 answer:

matrenka [14]3 years ago

7 0

Answer:

Step-by-step explanation:

a(n) = n² - 3n - a(n-1) and a(1) = 4

We have a(1) = 4 and want a(2) (for which n = 2).

a(2) = 2² - 3(2) - a(2-1) → a(2) = 4 - 6 - 4 = -6 = a(2)

a(3) = 3² - 3(3) - (-6) = 9 - 9 + 6 = 6 = a(3)

a(4) = 4² - 3(4) - 6 = 16 - 12 - 6 = -2 = a(4)

a(5) = 5² - 3(5) + 2 = 12 = a(5)

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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

1 year ago

Read 2 more answers

3 ½ times as many guests arrived as were expected. If 105 guests were unexpected, how many guests were expected ?

lara [203]

Let x be the expected number Number arriving = 3•5 x Unexpected number 2•5 x 2•5 x = 105 10x = 420 x = 42______Option D

8 0

2 years ago

What is the common ratio between successive terms in the sequence?

GrogVix [38]

Answer:

It's 1/3.

Step-by-step explanation:

Common ratio = 9/27 = 1/3.

3 / 9 = 1/3

1 / 3 = 1/3 and so on.

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2 years ago

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Which of the following is a rule for the geometric sequence 1,3,9,27...

antoniya [11.8K]

The rule would be : 3^x, where x starts at 0.

3^0 is 1,

3^1 is 3, because 3 one time is 3.

3^2 is 9, because 3x3 is 9.

3^3 is 27, because 3x3x3 is 27

Answer: 3^x

5 0

2 years ago

I'll give 100 brainly points, i just need help...plz

Solnce55 [7]

Answer:

A. $(x^{2/7})(y^{-3/5})$

Step-by-step explanation:

The numerator is:

$\sqrt[7]{x^2} = (x^2)^{1/7} = x^{2/7}\\$

The denominator is:

$\sqrt[5]{y^3} = (y^3)^{1/5} = y^{3/5}$

The fraction is equivalent to:

$\frac{x^{2/7}}{y^{3/5}} =$
$(x^{2/7})(y^{-3/5})$

Correct choice is A

4 0

2 years ago