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1 year ago

Find the 12th term of the geometric sequence 4, 8, 16, ...

Mathematics

1 answer:

sweet [91]1 year ago

7 0

Answer:

8192

Step-by-step explanation:

The pattern is mulitply by 2 to get the next term

4*2=8

8*2=16

So: 4,8,16,32,64,128,256,512,1024,2048,4096,8192

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Answer:

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Step-by-step explanation:

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2 years ago

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I guess I'm lacking in differential equations. I couldn't solve this question. Can you help me?

Sonja [21]

Answer:

See Explanation.

General Formulas and Concepts:

Pre-Algebra

Equality Properties

Reciprocals

Algebra II

Log/Ln Property: $ln(\frac{a}{b} ) = ln(a) - ln(b)$

Calculus

Derivatives

Basic Power Rule:

f(x) = cxⁿ
f’(x) = c·nxⁿ⁻¹

Chain Rule: $\frac{d}{dx}[f(g(x))] =f'(g(x)) \cdot g'(x)$

Derivative of Ln: $\frac{d}{dx} [ln(u)] = \frac{u'}{u}$

Step-by-step explanation:

Step 1: Define

$ln(\frac{2x-1}{x-1} )=t$

Step 2: Differentiate

Rewrite: $t = ln(\frac{2x-1}{x-1})$
Rewrite [Ln Properties]: $t = ln(2x-1) - ln(x - 1)$
Differentiate [Ln/Chain Rule/Basic Power Rule]: $\frac{dt}{dx} = \frac{1}{2x-1} \cdot 2 - \frac{1}{x-1} \cdot 1$
Simplify: $\frac{dt}{dx} = \frac{2}{2x-1} - \frac{1}{x-1}$
Rewrite: $\frac{dt}{dx} = \frac{2(x-1)}{(2x-1)(x-1)} - \frac{2x-1}{(2x-1)(x-1)}$
Combine: $\frac{dt}{dx} = \frac{-1}{(2x-1)(x-1)}$
Reciprocate: $\frac{dx}{dt} = -(2x-1)(x-1)$
Distribute: $\frac{dx}{dt} = (1-2x)(x-1)$

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2 years ago

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The points J (-13,10) and K(-1,-6) are endpoints of a diameter of circle G. What is the equation of circle G?

In-s [12.5K]

The correct answer is D

The equation of a circle is (x-h)^2 + (y-k)^2 = r^2

to find (h,k), you find the middle of the circle, in this scenario you do so by finding the middle of the diameter, a line that goes through the center of the circle.

To find the X value of the midpoint, add both x values together and divide by 2 and repeat for y

-13 + -1 = -14
-14/2 =-7

10+ -6 = 4
4/2 = 2

therefore (h,k) = ( -7, 2 )

Next plug these values in the equation of a circle

(x-h)^2 + (y-k)^2 = r^2

becomes

(x- (-7)) ^2 + (y-(2)) ^2 = r^2

to find r, use the distance formula to find the length of the diameter, 20, and divide by 2

plug 10 in for r and you get 100

(x+7)^2 + (y-2)^2 = 100

sorry for the late response

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3 years ago

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What is 18,307 in expanded form?

olga_2 [115]

Answer:

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Step-by-step explanation:

18,307

= 10000 + 8000 + 300 + 7

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2 years ago

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never [62]

I think its C but not sure

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2 years ago