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2 years ago

Solve for b. Put your answer in simplest radical form. Show Steps plz! A = 4πbc + πb^2

Mathematics

1 answer:

sladkih [1.3K]2 years ago

4 0

Answer:

b = -2c ± [√(4π²c² + πA)]/π

Step-by-step explanation:

A = 4πbc + πb^2

A = 4πbc + πb²

πb² + 4πbc - A = 0

Using the quadratic formula to solve this quadratic equation.

The quadratic formula for the quadratic equation, pb² + qb + r = 0, is given as

b = [-q ± √(q² - 4pr)] ÷ 2p

Comparing

πb² + 4πbc - A = 0 with pb² + qb + r = 0,

p = π

q = 4πc

r = -A

b = [-q ± √(q² - 4pr)] ÷ 2p

b = {-4πc ± √[(4πc)² - 4(π)(-A)]} ÷ 2π

b = {-4πc ± √[16π²c² + 4πA]} ÷ 2π

b = (-4πc/2π) ± {√[16π²c² + 4πA] ÷ 2π}

b = -2c ± [√(4π²c² + πA)]/π

Hope this Helps!!!

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3 years ago

the 11th term in a geometric sequence is 48 and the common ratio is 4. the 12th term is 192 and the 10th term is what?

Soloha48 [4]

Given:

The 11th term in a geometric sequence is 48.

The 12th term in the sequence is 192.

The common ratio is 4.

We need to determine the 10th term of the sequence.

General term:

The general term of the geometric sequence is given by

$a_n=a(r)^{n-1}$

where a is the first term and r is the common ratio.

The 11th term is given is

$a_{11}=a(4)^{11-1}$

$48=a(4)^{10}$ ------- (1)

The 12th term is given by

$192=a(4)^{11}$ ------- (2)

Value of a:

The value of a can be determined by solving any one of the two equations.

Hence, let us solve the equation (1) to determine the value of a.

Thus, we have;

$48=a(1048576)$

Dividing both sides by 1048576, we get;

$\frac{3}{65536}=a$

Thus, the value of a is $\frac{3}{65536}$

Value of the 10th term:

The 10th term of the sequence can be determined by substituting the values a and the common ratio r in the general term $a_n=a(r)^{n-1}$ , we get;

$a_{10}=\frac{3}{65536}(4)^{10-1}$

$a_{10}=\frac{3}{65536}(4)^{9}$

$a_{10}=\frac{3}{65536}(262144)$

$a_{10}=\frac{786432}{65536}$

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Answer:

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Step-by-step explanation:

I hope I explained well, please give me brainliest

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