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Kitty [74]
3 years ago
8

Find the arc length function for the curve with starting point (0,1). y=sin−1x+√1−x2

Mathematics
1 answer:
Ilya [14]3 years ago
8 0

dy/dx = 1/√(1 - x^2) - x/√(1 - x^2) = (1 - x)/√(1 - x^2) 

1 + (dy/dx)^2 = 1 + (1 - x)^2/(1 - x^2) = [(1 - x^2) + (1 - x)^2]/(1 - x^2) = (1 - x^2 + 1 - 2x + x^2)/(1 - x^2) = (2 - 2x)/(1 - x^2) = 2(1 - x)/[(1 + x)(1 - x)] = 2/(1 + x) 

ds = √(1 + (dy/dx)^2 = √(2/(1 + x)) = √2/√(1 + x) dx 

<span>L = √2 ∫ dx/√(1 + x) {0, 1} = √2 ∫ (1 + x)^(-1/2) dx = 2√2 √(1 + x) {0, 1} = 2√2 (√2 - 1) = 4 - 2√2 ≈ 1.1716

The arc length would be </span><span>1.1716 units.</span><span>

I hope my answer has come to your help. Thank you for posting your question here in Brainly.
</span>
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Answer:

5

Step-by-step explanation:

3(14+x) = 57

42 +3x = 57

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6 0
3 years ago
Nora got an allowance of 50¢ each weekday and 75¢ each weekend altogether how much do they get in:
Furkat [3]
A) > since it is 50c per weekday and 75c each weekend assuming it allows for the 2 days each saturday/sunday.
50c * 5 = $2.50 since there are 5 days in weekdays
75c * 2 = $1.50 since there are 2 days in the weekend
Add $2.50 and $1.50 to get $4.00

b) For 3 school days we know it is a weekday on the school week.
So perform 50c * 3 which gives us <span>$1.50

</span>c) 12 days off from school is 10 weekdays and 1 weekend or 2 days of 75c
So now just do 50c * 10 which is $5.00 and 75c * 2 which is $1.50
Add $5.00 and $1.50 and we get $6.50

d) 4 weeks = 20 weekdays since 5 *4 = 20 and 8 days in each weekend since 2 * 4 = 8
Now that we have the amount of weekdays and weekend days we can multiply.
50c * 20 = $10.00
75c * 4 = $3.00
Add $10.00 and $3.00 to get $13.00 for 4 weeks.

e) We have 1 day of the weekend and 2 weekdays here.
50c * 2 = $1.00
75c * 1 = 75c
<span>$1.00 + 75c = $1.75 in those 3 days listed.
</span>
Add all these together to get your total value.
$4.00 + $1.50 + $6.50 + $13.00 + $1.75 = $26.75

7 0
3 years ago
Help please!! (attachment below)
Aleksandr-060686 [28]

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3 years ago
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Which of these is equivalent to 1 over x to the power of 5 ? 1 fifth x negative x to the power of 5 x to the power of 5 x to the
Kisachek [45]

Answer:

x^-5 = x to the power of negative 5

Step-by-step explanation:

Which of these is equivalent to 1 over x to the power of 5 ?

Mathematically this is expressed as

(1/x)⁵

We have a rule when it comes to expressing power

(1/a)^b = a^-b

Hence, applying this rule to our question

(1/x)⁵ = (1/x)^5

= x^-5

This is written in words as:

x to the power of negative 5

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