I need the answer to this plzzzz

The circumference of the ellipse approximate. Which equation is the result of solving the formula of the circumference for b?

Serhud [2]

Answer:

$b = \sqrt{\frac{C^{2} }{2(\pi )^{2} } - a^{2}}$

Step-by-step explanation:

Given - The circumference of the ellipse approximated by $C = 2\pi \sqrt{\frac{a^{2} + b^{2} }{2} }$ where 2a and 2b are the lengths of 2 the axes of the ellipse.

To find - Which equation is the result of solving the formula of the circumference for b ?

Solution -

$C = 2\pi \sqrt{\frac{a^{2} + b^{2} }{2} }\\\frac{C}{2\pi } = \sqrt{\frac{a^{2} + b^{2} }{2} }$

Squaring Both sides, we get

$[\frac{C}{2\pi }]^{2} = [\sqrt{\frac{a^{2} + b^{2} }{2} }]^{2} \\\frac{C^{2} }{(2\pi)^{2} } = {\frac{a^{2} + b^{2} }{2} }\\2\frac{C^{2} }{4(\pi)^{2} } = {{a^{2} + b^{2} }$

$\frac{C^{2} }{2(\pi )^{2} } = a^{2} + b^{2} \\\frac{C^{2} }{2(\pi )^{2} } - a^{2} = b^{2} \\\sqrt{\frac{C^{2} }{2(\pi )^{2} } - a^{2}} = b$

∴ we get

$b = \sqrt{\frac{C^{2} }{2(\pi )^{2} } - a^{2}}$

8 0

3 years ago

Simplify: (8t4 + 6 )+(914 – 2ť + 6t? – 6 )

vekshin1

Answer:t

2⋅(17t 2 −2t+6)

Step-by-step explanation:

v(8•(t4))+6)+((((9•(t4))-(2•(t3)))+(2•3t2))-6)

STEP

2

:

Equation at the end of step

2

:

((8•(t4))+6)+((((9•(t4))-2t3)+(2•3t2))-6)

STEP

3

:

Equation at the end of step

3

:

((8•(t4))+6)+(((32t4-2t3)+(2•3t2))-6)

STEP

4

:

Equation at the end of step

4

:

(23t4 + 6) + (9t4 - 2t3 + 6t2 - 6)

STEP

5

:

STEP

6

:

Pulling out like terms

6.1 Pull out like factors :

17t4 - 2t3 + 6t2 = t2 • (17t2 - 2t + 6)

(8•(t4))+6)+((((9•(t4))-(2•(t3)))+(2•3t2))-6)

STEP

2

:

Equation at the end of step

2

:

((8•(t4))+6)+((((9•(t4))-2t3)+(2•3t2))-6)

STEP

3

:

Equation at the end of step

3

:

((8•(t4))+6)+(((32t4-2t3)+(2•3t2))-6)

STEP

4

:

Equation at the end of step

4

:

(23t4 + 6) + (9t4 - 2t3 + 6t2 - 6)

STEP

5

:

STEP

6

:

Pulling out like terms

6.1 Pull out like factors :

17t4 - 2t3 + 6t2 = t2 • (17t2 - 2t + 6)

(8•(t4))+6)+((((9•(t4))-(2•(t3)))+(2•3t2))-6)

STEP

2

:

Equation at the end of step

2

:

((8•(t4))+6)+((((9•(t4))-2t3)+(2•3t2))-6)

STEP

3

:

Equation at the end of step

3

:

((8•(t4))+6)+(((32t4-2t3)+(2•3t2))-6)

STEP

4

:

Equation at the end of step

4

:

(23t4 + 6) + (9t4 - 2t3 + 6t2 - 6)

STEP

5

:

STEP

6

:

Pulling out like terms

6.1 Pull out like factors :

17t4 - 2t3 + 6t2 = t2 • (17t2 - 2t + 6)

5 0

3 years ago

Type the correct answer in each box. Use numerals instead of words.<br> Consider function h.

Anika [276]

Answer:

10

16

Step-by-step explanation:

8 0

3 years ago

Chai Hu deposited $5500 in a savings account earning 6% interest compound quarterly if he makes no other deposits or withdrawals

Arada [10]

Answer:

5,477.63

Step-by-step explanation:

First, convert R percent to r a decimal

r = R/100

r = 6%/100

r = 0.06 per year,

Then, solve our equation for P

P = A / (1 + r/n)nt

P = 5,500.00 / (1 + 0.06/4)(4)(0.068448)

P = 5,500.00 / (1 + 0.015)(0.273792)

P = $ 5,477.63

Summary:

The principal investment required to get

a total amount of $ 5,500.00

from compound interest at a rate of 6% per year

compounded 4 times per year

over 0.068448 years

is $ 5,477.63.

** i got this from calculator soup

8 0

3 years ago

A manufacturing unit currently operates at 80 percent of its capacity. The profit function for the unit at the optimum output, x

emmasim [6.3K]

B.
I hope I helped!!!!!!!!!

7 0

4 years ago

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