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Ksju [112]
3 years ago
15

What is the circumference of the circle?

Mathematics
1 answer:
oksian1 [2.3K]3 years ago
3 0

Answer:

20π ft

Step-by-step explanation:

Formula: C=2πr, where C is the circumference and r is the radius.

r=10 ft.

C=2*π*10

=20π ft.

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Anybody help please hm​
77julia77 [94]

Answer:

1

Step-by-step explanation:

if you use a calculator, it will come up as 1. I don't know why, but it does.

Hope this helps!

5 0
2 years ago
<img src="https://tex.z-dn.net/?f=%24a%2Ba%20r%2Ba%20r%5E%7B2%7D%2B%5Cldots%20%5Cinfty%3D15%24%24a%5E%7B2%7D%2B%28a%20r%29%5E%7B
riadik2000 [5.3K]

Let

S_n = \displaystyle \sum_{k=0}^n r^k = 1 + r + r^2 + \cdots + r^n

where we assume |r| < 1. Multiplying on both sides by r gives

r S_n = \displaystyle \sum_{k=0}^n r^{k+1} = r + r^2 + r^3 + \cdots + r^{n+1}

and subtracting this from S_n gives

(1 - r) S_n = 1 - r^{n+1} \implies S_n = \dfrac{1 - r^{n+1}}{1 - r}

As n → ∞, the exponential term will converge to 0, and the partial sums S_n will converge to

\displaystyle \lim_{n\to\infty} S_n = \dfrac1{1-r}

Now, we're given

a + ar + ar^2 + \cdots = 15 \implies 1 + r + r^2 + \cdots = \dfrac{15}a

a^2 + a^2r^2 + a^2r^4 + \cdots = 150 \implies 1 + r^2 + r^4 + \cdots = \dfrac{150}{a^2}

We must have |r| < 1 since both sums converge, so

\dfrac{15}a = \dfrac1{1-r}

\dfrac{150}{a^2} = \dfrac1{1-r^2}

Solving for r by substitution, we have

\dfrac{15}a = \dfrac1{1-r} \implies a = 15(1-r)

\dfrac{150}{225(1-r)^2} = \dfrac1{1-r^2}

Recalling the difference of squares identity, we have

\dfrac2{3(1-r)^2} = \dfrac1{(1-r)(1+r)}

We've already confirmed r ≠ 1, so we can simplify this to

\dfrac2{3(1-r)} = \dfrac1{1+r} \implies \dfrac{1-r}{1+r} = \dfrac23 \implies r = \dfrac15

It follows that

\dfrac a{1-r} = \dfrac a{1-\frac15} = 15 \implies a = 12

and so the sum we want is

ar^3 + ar^4 + ar^6 + \cdots = 15 - a - ar - ar^2 = \boxed{\dfrac3{25}}

which doesn't appear to be either of the given answer choices. Are you sure there isn't a typo somewhere?

7 0
2 years ago
Mary leaves her house to take a walk. The graph shows the distance, d, in feet from her house that Mary is at any given time, t,
Mkey [24]

Answer:

It would be option A. 10 Minutes.

Step-by-step explanation:

If you look at the graph, the farthest point, and the time of 10 minutes meet at the point (10, 2,500)

(Really hoping this helps <3)

7 0
3 years ago
The following items are in the shape of a square. How many squares are
kramer
A because I have done this before
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3 years ago
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Solve for x in the equation 4x-3(4x-5)=3
lubasha [3.4K]

Answer: x=3/2

Step-by-step explanation:

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2 years ago
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