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4 years ago

What is the easiest way to find a geometric mean?

Mathematics

1 answer:

zubka84 [21]4 years ago

6 0

GM= ( II i = 1 xi) 1/N
for example, {3,4,2,6}.
GM = (3*4*2*6) 1/4
GM = 144*1/4
GM ~ 3.464

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Find the length of the curve. R(t) = cos(8t) i + sin(8t) j + 8 ln cos t k, 0 ≤ t ≤ π/4

arsen [322]

we are given

$R(t)=cos(8t)i+sin(8t)j+8ln(cos(t))k$

now, we can find x , y and z components

$x=cos(8t),y=sin(8t),z=8ln(cos(t))$

Arc length calculation:

we can use formula

$L=\int\limits^a_b {\sqrt{(x')^2+(y')^2+(z')^2} } \, dt$

$x'=-8sin(8t),y=8cos(8t),z=-8tan(t)$

now, we can plug these values

$L=\int _0^{\frac{\pi }{4}}\sqrt{(-8sin(8t))^2+(8cos(8t))^2+(-8tan(t))^2} dt$

now, we can simplify it

$L=\int _0^{\frac{\pi }{4}}\sqrt{64+64tan^2(t)} dt$

$L=\int _0^{\frac{\pi }{4}}8\sqrt{1+tan^2(t)} dt$

$L=\int _0^{\frac{\pi }{4}}8\sqrt{sec^2(t)} dt$

$L=\int _0^{\frac{\pi }{4}}8sec(t) dt$

now, we can solve integral

$\int \:8\sec \left(t\right)dt$

$=8\ln \left|\tan \left(t\right)+\sec \left(t\right)\right|$

now, we can plug bounds

and we get

$=8\ln \left(\sqrt{2}+1\right)-0$

so,

$L=8\ln \left(1+\sqrt{2}\right)$ ..............Answer

5 0

3 years ago

Jessica has 84.5 of fabric to make curtain

qaws [65]

Answer:

$10.8\ yd$

Step-by-step explanation:

<u><em>The complete question is</em></u>

Jessica has 84.5 yards of fabric to make curtains. She makes 6 identical curtains and has 19.7 of fabric remaining. How many yards of fabric does Jessica use per curtain?

Let

x-------> amount of yards of fabric that Jessica used per curtain

we know that

The length of 6 identical curtains plus the length of the fabric remaining, must be equal to the total yards of fabric'

The linear equation that represent this situation is

Solve for x

$6x=84.5-19.7\\6x=64.8\\x=10.8\ yd$

3 0

3 years ago

conner has $25,000 in his bank account. Every month he spends $1,500 and does not add any money to the account how much will he

QveST [7]

Answer:

13000

Step-by-step explanation:

m= 1500(8)+25000

M= 12000+25000

$13000

6 0

3 years ago

Read 2 more answers

The net shown folds to form a right rectangular prism. Determine the surface area of the prism.

Alexeev081 [22]

find the area of all single figure and add.

Use Pemdas

2 * 3 + 2 * 3 + 2 * 4 + 2 * 4 + 3 * 4 + 3 * 4 =

6 + 6 + 8 + 8 + 12 + 12 =

52 cm² is your answer

8 0

3 years ago

16. Which of the following situations is represented by the graph?

Stells [14]

Answer:

B. conversion of feet to inches

Step-by-step explanation:

there are 12 inches in one foot.

7 0

3 years ago