Ask question

Ask question

All categories

Dmitry_Shevchenko [17]

3 years ago

15

General terms of a sequence

1 answer:

MatroZZZ [7]3 years ago

5 0

(2n-1) /(n+9)
hope it can help u

You might be interested in

If $5,500 is invested in an account that pays 3% interest compounded annually, how much money will be in the account at the end

Citrus2011 [14]

He would have 7150 in his account

3 0

3 years ago

A right circular cylinder is inscribed in a sphere with diameter 4cm as shown. If the cylinder is open at both ends, find the la

SOVA2 [1]

Answer:

$8\pi\text{ square cm}$

Step-by-step explanation:

Since, we know that,

The surface area of a cylinder having both ends in both sides,

$S=2\pi rh$

Where,

r = radius,

h = height,

Given,

Diameter of the sphere = 4 cm,

So, by using Pythagoras theorem,

$4^2 = (2r)^2 + h^2$ ( see in the below diagram ),

$16 = 4r^2 + h^2$

$16 - 4r^2 = h^2$

$\implies h=\sqrt{16-4r^2}$

Thus, the surface area of the cylinder,

$S=2\pi r(\sqrt{16-4r^2})$

Differentiating with respect to r,

$\frac{dS}{dr}=2\pi(r\times \frac{1}{2\sqrt{16-4r^2}}\times -8r + \sqrt{16-4r^2})$

$=2\pi(\frac{-4r^2+16-4r^2}{\sqrt{16-4r^2}})$

$=2\pi(\frac{-8r^2+16}{\sqrt{16-4r^2}})$

Again differentiating with respect to r,

$\frac{d^2S}{dt^2}=2\pi(\frac{\sqrt{16-4r^2}\times -16r + (-8r^2+16)\times \frac{1}{2\sqrt{16-4r^2}}\times -8r}{16-4r^2})$

For maximum or minimum,

$\frac{dS}{dt}=0$

$2\pi(\frac{-8r^2+16}{\sqrt{16-4r^2}})=0$

$-8r^2 + 16 = 0$

$8r^2 = 16$

$r^2 = 2$

$\implies r = \sqrt{2}$

Since, for r = √2,

$\frac{d^2S}{dt^2}=negative$

Hence, the surface area is maximum if r = √2,

And, maximum surface area,

$S = 2\pi (\sqrt{2})(\sqrt{16-8})$

$=2\pi (\sqrt{2})(\sqrt{8})$

$=2\pi \sqrt{16}$

$=8\pi\text{ square cm}$

4 0

3 years ago

Simplify the expression: (4p-8/p^3-2p^2-q+2/q^3+2q^2) x p/2q-p

Effectus [21]

+1 • (2p5q3x + 4p4q3x + 2p3q5x + p3q4x + 2p3q2 + 2p3x + 8q3x)

I would explain how to get it but it’s like 20 steps into getting this
Good luck though please tell me if I did any part of this problem wrong it might be some typos

5 0

2 years ago

the point slope form of the equation of a line that passes through (8,4) and (0,2) is y-4=1/4(×-8) what is the slope intercept f

marissa [1.9K]

Answer:

$\large\boxed{y=\dfrac{1}{4}x+2}$

Step-by-step explanation:

The slope-intercept form of the equation of a line:

$y=mx+b$

m - slope

b - y-intercept → (0, b)

The point-slope form of the equation of a line:

$y-y_1=m(x-x_1)$

m - slope

(x₁, y₁) - point

We have the equation of a line:

$y-4=\dfrac{1}{4}(x-8)\to m=\dfrac{1}{4}$

and the point (0, 2) → b = 2.

Substitute:

$y=\dfrac{1}{4}x+2$

7 0

3 years ago

Read 2 more answers

What is $5,158 round to the nearest percent

Gemiola [76]

I think it 5,158.00 round to the nearest percent

7 0

3 years ago