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2 years ago

Find the nth term of the geometric sequence whose initial term is a1

Mathematics

1 answer:

Alborosie2 years ago

6 0

Answer:

Step-by-step explanation:

geometric progresion formula:

$a_n=a_1*r^{n-1}\\a_1=0.5\\r=10\\a_n=0.5*10^{n-1}$

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An open-top box with a square base is to have a volume of 4 cubic feet. Find the dimensions of the box (in ft) that can be made

Lemur [1.5K]

Answer:

The dimension of box= $2ft\times 2ft\times 1ft$

Step-by-step explanation:

We are given that

Volume of box=4 cubic feet

Let x be the side of square base and h be the height of box

Volume of box= $lbh=x^2h$

$4=x^2h$

$h=\frac{4}{x^2}$

Now, surface area of box,A= $x^2+4xh$

$A=x^2+4x(\frac{4}{x^2})=x^2+\frac{16}{x}$

$\frac{dA}{dx}=2x-\frac{16}{x^2}$

$\frac{dA}{dx}=0$

$2x-\frac{16}{x^2}=0$

$2x=\frac{16}{x^2}$

$x^3=8$

$x=2$

$\frac{d^2A}{dx^2}=2+\frac{32}{x^3}$

Substitute x=2

$\frac{d^2A}{dx^2}=2+\frac{32}{2^3}=2+4=6>0$

Hence, the area of box is minimum at x=2

Therefore, side of square base,x=2 ft

Height of box,h= $\frac{4}{2^2}=1 ft$

Hence, the dimension of box= $2ft\times 2ft\times 1ft$

5 0

2 years ago

Which is an equation in point-slope form for the given point and slope point (8 -4) slope 5/6

Alina [70]

If you want to say thank you, click the "Thanks" button and select the answer "The Brainliest!" We appreciate it!

Step-by-step explanation:

Point slope form: (y−y1) = m (x−x1), where (x1,y1) is the point, and m is the slope.

(y- (-4)) = (5/6)*(x - 8)

(y + 4) = (5/6)*(x - 8)

If you want in standard form

(y + 4) = (5/6)*x - (5/6)*8

y = (5/6) x - (5/6)*8 - 4

y = (5/6)x - (16/6)

Answer:

(y + 4) = (5/6)*(x - 8)

4 0

2 years ago

A scientist has 100 milligrams of a radioactive element. The amount of radioactive element remaining after t days can be determi

grandymaker [24]

The mass of the first shipment at time t is
$m_{1}=100( \frac{1}{2} )^{ \frac{t}{10}}$

The mass of the second shipment at time t is
$m_{2}=100( \frac{1}{2} )^{ \frac{t-3}{10} }$

At time t, the ratio of m₁ to m₂ is
$\frac{m_{1}}{m_{2}} = \frac{100}{100}. \frac{(1/2)^{t/10}}{(1/2)^{(t-3)/10}} \\ = \frac{(1/2)^{t/10}}{(1/2)^{t/10}}. \frac{1}{(1/2)^{-3/10}} \\ = (1/2)^{3/10} \\ = 0.8123$

Therefore as a percentage,
$\frac{m_{1}}{m_{2}} =100*0.8123 = 81.23 \%$

Answer: B. 81.2%

4 0

3 years ago

Represent the following expression algebredically: a number, x, decreased by 5

PIT_PIT [208]

X-5 is your answer. hope that helps

5 0

3 years ago

Find the sum of the linear expressions<br> (8x - 16) + (-12x - 2)

Allushta [10]

Answer:

-4x-18

Step-by-step explanation:

pickle

4 0

3 years ago

Read 2 more answers