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4 years ago

In order to increase the circumference of a circle from 12π cm to 18π cm, by how much must the diameter increase?

Mathematics

2 answers:

Vadim26 [7]4 years ago

8 0

Answer:

Step-by-step explanation:

It's actually 6 cm. This is because the diameter of the smaller circle is 12pi/pi which is 12, and the diameter of the bigger one is 18pi/pi which is 18. 12 + 6 = 18, so the diameter increases by 6.

kow [346]4 years ago

8 0

Answer: The increase in the diameter is 6 cm.

Step-by-step explanation:

The circumference of a circle with diameter 'd' is given by :

Circumference= $\pi d$

Given: The circumference is increased from $12\pi\ cm\ to\ 18\pi\ cm$

It implies the increase in the circumference= $\pi d_2-\pi d_1=18\pi-12\pi$ , where $d_1$ is the previous diameter and $d_2$

is the new diameter.

$\Rightarrow\pi(d_2-d_1)=\pi(18-12)\\\Rightarrow(d_2-d_1)=6$

Hence, the increase in the diameter= 6 cm

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Free_Kalibri [48]

Answer:

(a) 1,902,231,808,400

(b) 84

Step-by-step explanation:

In mathematics, the procedure to select k items from n distinct items, without replacement, is known as combinations.

The formula to compute the combinations of k items from n is given by the formula:

${n\choose k}=\frac{n!}{k!\cdot(n-k)!}$

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${100\choose 9}=\frac{100!}{9!\cdot(100-9)!}$

$=\frac{100!}{9!\times 91!}\\\\=\frac{100\times 99\times 98\times 97\times 96\times 95\times 94\times 93\times 92\times 91!}{9!\times 91!}\\\\=\frac{100\times 99\times 98\times 97\times 96\times 95\times 94\times 93\times 92}{9!}\\\\=1902231808400$

(b)

Compute the number of ways to select 6 people from 9 as follows:

${9\choose 6}=\frac{9!}{6!\cdot(9-6)!}$

$=\frac{9!}{6!\times 3!}\\\\=\frac{9\times 8\times 7\times 6!}{6!\times 3!}\\\\=\frac{9\times 8\times 7}{3!}\\\\=84$

(c)

Compute the number of ways to select top 3 candidates from 6 as follows:

${6\choose 3}=\frac{6!}{3!\cdot(6-3)!}$

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3 years ago

I need help with 6,7,8,9

algol [13]

Hi there!

6. x² + 6x = 27
subtract 27 on both sides to make the equation equal to 0.
x² + 6x - 27 = 0
(x - 3)(x + 9) = 0
x - 3 = 0 x + 9 = 0
x = 3 x = -9

7. k² - 13k + 36 = 0
(k - 9)(k - 4) = 0
k - 9 = 0 k - 4 = 0
k = 9 k = 4

8. g(x) is translated up 5 from f(x).

9. g(x) is reflected by x-axis, then translated 3 down from f(x).

Hope this helped! :)

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3 years ago

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