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3 years ago

Which formula can be used to find the nth term of a geometric sequence where the fifth term is 1/16 and the common ratio is 1/4?

Mathematics

2 answers:

Flauer [41]3 years ago

7 0

Answer:

Step-by-step explanation:

E2020

ale4655 [162]3 years ago

3 0

Any geometric sequence can be expressed as:

a(n)=ar^(n-1), a=initial term, r=common ratio, n=term number

We are given that a(5)=1/16 and r=1/4 so we can say:

1/16=a(1/4)^(5-1)

1/16=a(1/4)^4

1/16=a/256

256/16=a

16=a

So the initial term is 16 so our formula is:

a(n)=16(1/4)^(n-1)

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Find exact value for cos(pi/16)

stellarik [79]

The exact value for cos(pi/16) would be :

cos (pi/16) = +/- √1+cosa/2

cos (pi/4) = sqrt2/2

Hope this helps

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3 years ago

Ella has gold,silver,and copper wire for stringing beads.she has1 1\2ft.of gold wire,2 1\3ft.of silver wire,and3 3\4ft.of copper

Oksana_A [137]

Ella would have 65/8ft wire all together.

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2 years ago

Ellie buys a mobile phone in spain for €352.50. Her brother jack buys an identical phone from japan for ¥39856. Using exchange r

Nonamiya [84]

Answer:

The answer to your question is: Japan

Step-by-step explanation:

Mobile cost in Spain = € 352.5

Mobile cost in Japan = ¥39856

Exchange rate = £1 = €1.41

£1 = ¥188

Cost of mobile in pounds

£ 1 ------------------ € 1.41

x ----------------- €352.5

x = (352.5 x 1) / 1.41

x= £250

£1 ------------------ ¥188

x ----------------- -¥ 39856

x = (39856 x 1) / 188

x = £212

Then, it was cheaper in Japan

8 0

2 years ago

Read 2 more answers

What two numbers add up to -27 and multiply to 72?

leonid [27]

-3-24=-27, -3x-24=72
Answer is -3 and -24

5 0

2 years ago

Find the absolute extrema for f(x,y)=4-x^2-y^4+1/2y^2 over the closed disk D:x^2+y^2 is less than or equal to 1

algol [13]

Find the critical points of $f(x,y)$ :

$\dfrac{\partial f}{\partial x}=-2x=0\implies x=0$

$\dfrac{\partial f}{\partial y}=y-4y^3=y(1-4y^2)=0\implies y=0\text{ or }y=\pm\dfrac12$

All three points lie within $D$ , and $f$ takes on values of

$\begin{cases}f(0,0)=4\\f\left(0,-\frac12\right)=\frac{65}{16}\\f\left(0,\frac12\right)=\frac{65}{16}\end{cases}$

Now check for extrema on the boundary of $D$ . Convert to polar coordinates:

$f(x,y)=f(\cos t,\sin t)=g(t)=4-\cos^2-\sin^4t+\dfrac12\sin^2t=3+\dfrac32\sin^2t-\sin^4t$

Find the critical points of $g(t)$ :

$\dfrac{\mathrm dg}{\mathrm dt}=3\sin t\cos t-4\sin^3t\cos t=\sin t\cos t(3-4\sin^2t)=0$

$\implies\sin t=0\text{ or }\cos t=0\text{ or }\sin t=\pm\dfrac{\sqrt3}2$

$\implies t=n\pi\text{ or }t=\dfrac{(2n+1)\pi}2\text{ or }\pm\dfrac\pi3+2n\pi$

where $n$ is any integer. There are some redundant critical points, so we'll just consider $0\le t< 2\pi$ , which gives

$t=0\text{ or }t=\dfrac\pi3\text{ or }t=\dfrac\pi2\text{ or }t=\pi\text{ or }t=\dfrac{3\pi}2\text{ or }t=\dfrac{5\pi}3$

which gives values of

$\begin{cases}g(0)=3\\g\left(\frac\pi3\right)=\frac{57}{16}\\g\left(\frac\pi2\right)=\frac72\\g(\pi)=3\\g\left(\frac{3\pi}2\right)=\frac72\\g\left(\frac{5\pi}3\right)=\frac{57}{16}\end{cases}$

So altogether, $f(x,y)$ has an absolute maximum of 65/16 at the points (0, -1/2) and (0, 1/2), and an absolute minimum of 3 at (-1, 0).

5 0

2 years ago