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3 years ago

Find the radius of the circle with a diameter of 3 yards. radius: yd

Mathematics

1 answer:

coldgirl [10]3 years ago

7 0

Answer:

1.5

Step-by-step explanation:

radius is half of the diameter of a circle

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If S_1=1,S_2=8 and S_n=S_n-1+2S_n-2 whenever n≥2. Show that S_n=3⋅2n−1+2(−1)n for all n≥1.

Snezhnost [94]

You can try to show this by induction:

• According to the given closed form, we have $S_1=3\times2^{1-1}+2(-1)^1=3-2=1$ , which agrees with the initial value S₁ = 1.

• Assume the closed form is correct for all n up to n = k. In particular, we assume

$S_{k-1}=3\times2^{(k-1)-1}+2(-1)^{k-1}=3\times2^{k-2}+2(-1)^{k-1}$

and

$S_k=3\times2^{k-1}+2(-1)^k$

We want to then use this assumption to show the closed form is correct for n = k + 1, or

$S_{k+1}=3\times2^{(k+1)-1}+2(-1)^{k+1}=3\times2^k+2(-1)^{k+1}$

From the given recurrence, we know

$S_{k+1}=S_k+2S_{k-1}$

so that

$S_{k+1}=3\times2^{k-1}+2(-1)^k + 2\left(3\times2^{k-2}+2(-1)^{k-1}\right)$

$S_{k+1}=3\times2^{k-1}+2(-1)^k + 3\times2^{k-1}+4(-1)^{k-1}$

$S_{k+1}=2\times3\times2^{k-1}+(-1)^k\left(2+4(-1)^{-1}\right)$

$S_{k+1}=3\times2^k-2(-1)^k$

$S_{k+1}=3\times2^k+2(-1)(-1)^k$

$\boxed{S_{k+1}=3\times2^k+2(-1)^{k+1}}$

which is what we needed. QED

6 0

2 years ago

Find the measures of the missing angles g, h, k, and m

Darina [25.2K]

Answer:

Angle g = 29 degrees

Angle h = 180-29 = 151 degrees

Angle k = 61 degrees

Angle m = 180 - 61 = 119 degrees

Step-by-step explanation:

6 0

2 years ago

A student graduated from a 4-year college with an outstanding loan of

melamori03 [73]

Answer:

University student has more debt

Step-by-step explanation:

9650-8455/1865 =0.64 College student

12360-10326/2143 =0.95 University student

Hopefully this helps

3 0

2 years ago

Find the equation of the line that passes through the points : (4 , -1 ) and (0 , -3)

Sergio [31]

Answer:

B. y= 1/2 x - 3

Step-by-step explanation:

base equation: y= mx+ b

slope(m) equation: $\frac{y_{2}-y_{2} }{x_{2} -x_{1} }$

y2= -1 y1= -3

x2= 4 x1= 0

$\frac{-1 - (-3)}{4-0} =\frac{2}{4} = \frac{1}{2}$

y- intercept: -3

found by taking the y from (0,-3)

3 0

2 years ago

Suppose that to make the golf team you need to score no more than 74 on average over 5 games. If you scored 77, 71, 77, and 67 i

vivado [14]

No more than 74 on average of 5 games means no more than 370 shots on total. If you add all of the numbers up you will get 292, so he can still shoot 370-292=78 in the last round, which is answer choice B.

5 0

3 years ago

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