Pls I need help with this one

Substitute [tex]x\mapsto\sqrt{1-x^2}[/tex], which transforms the integral to

[tex]\displaystyle \int_0^1 \ln^{2k} \left(\frac{\ln\left(\frac{1-\sqrt{1-x^2}}x\right)}{\ln\left(\frac{1-\sqrt{1-x^2}}x\right)}\right) \, dx = \int_0^1 \ln^{2k}\left(\frac{\ln\left(\frac{1-x}{\sqrt{1-x^2}}\right)}{\ln\left(\frac{1+x}{\sqrt{1-x^2}}\right)}\right) \frac{x}{\sqrt{1-x^2}} \, dx[/tex]

and factoring [tex]\sqrt{1-x^2}=\sqrt{(1-x)(1+x)}[/tex] reduces this to

[tex]\displaystyle = \int_0^1 \ln^{2k}\left(\frac{\ln\left(\sqrt{\frac{1-x}{1+x}}\right)}{\ln\left(\sqrt{\frac{1+x}{1-x}}\right)}\right) \frac x{\sqrt{1-x^2}} \, dx[/tex]

The inner logarithms differ only by a sign, so that

[tex]\displaystyle = \int_0^1 \ln^{2k}(-1) \frac x{\sqrt{1-x^2}} \, dx[/tex]

Using the principal branch of the complex logarithm, we have

[tex]\ln(-1) = \ln|-1| + i\arg(-1) = i\pi[/tex]

and hence

[tex]\displaystyle \int_0^1 \ln^{2k} \left(\frac{\ln\left(\frac{1-\sqrt{1-x^2}}x\right)}{\ln\left(\frac{1-\sqrt{1-x^2}}x\right)}\right) \, dx = (i\pi)^{2k} \underbrace{\int_0^1 \frac x{\sqrt{1-x^2}} \, dx}_{=1} = \boxed{(-\pi^2)^k}[/tex]

where I assume k is an integer.

The answer is [tex] {2}^{5} [/tex] or 32.

The best way to represent this is with a binary tree. Each split represents a choice, and each line represents a possible outcome. Choice #1 at the top of the tree has 2 possible outcomes. The second level repeats that process with 2 possible choices and 4 possible outcomes, this repeats for all 5 levels giving us 32 possible outcomes at the bottom.

There will be eight outcomes.

Sample space : {HHH,HHT,HTH,HTT,THH,THT,TTH,TTT}

Answer:

$77

Step-by-step explanation:

The answer is $77 because first you need to find how much money was discounted by doing 70-49 to get 21. Then you need to find how much percent 21 is of 70 by doing 21/70, then you would get 0.3 which is 30% since you have to multiply it by 100. This means that there is a 30% discount. Then you would do 0.3*110=33. This means that the 30% discount takes away $33. So 110-33=77. The answer is $77.

She invested $11,250 in the stock, $3,750 in the CD and $12,000 in the bond fund.

Given that Sylvia invested a total of $27,000, and she invested part of the money in a certificate of deposit (CD) that earns 3% simple interest per year, she invested in a stock that returns the equivalent of 7% simple interest, and she invested in a bond fund that returns 2%, and she invested three times as much in the stock as she did in the CD, and earned a total of $1140 at the end of 1 yr, to determine how much principal did she put in each investment, the following calculation must be made:

Therefore, she invested $11,250 in the stock, $3,750 in the CD and $12,000 in the bond fund.

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Answer:

The length of the arc is 8*pi cm. An arc that subtends a central angle of 120 degrees has a length of 120/360 = 1/3 the length of the total circumference of the circle. We know the entire circumference of the circle is 2πr, which in this case is 2π*12 = 24π.

Step-by-step explanation:

sorry I only have the 8

Answer:

8x^{12}yx^{3}  

Step-by-step explanation:

Simplify the expression.

Hopefully this helps you

- Matthew

Answer:

0.05km

Step-by-step explanation:

There are 1000 meters in a single kilometer. Using some dimensional analysis, we get set up the following expression:

[tex]\frac{50}{1} \frac{meters}{1}\frac{1}{1000} \frac{kilometers}{meters}[/tex]

The meters will cancel leaving the units of kilometers:

[tex]\frac{50}{1000} km=0.05km[/tex]

Answer:

0.825 bags of oranges

Step-by-step explanation:

1/3 is 0.33 and 2/5 is 0.4 so 0.33/0.4 is 0.825

Answer:

the question can be understand but the question is not telling what to find

it is comfugen to answe're the question

Answer:

10 and 30

Step-by-step explanation:

The sum of 10 and 30 is 40.

30 is three times ten (10 x 3 = 30).

hope this helps!

The answer is 10 and 30

10 times 3 is 30, meaning 10 will be the number times 3 they wanted. 10 + 30 is 40, therefore the answer is 10 and 30

Answer:

Equation:

C = 1.75x + 5 25

A 22-mile ride costs $43.75.

Step-by-step explanation:

Because there is a flat fee of 5.25, only the first two equations could possibly be correct.

Then check with the examples given. If a 7 mile ride costs 17.50, the second equation cannot possibly be right. 7 miles times over $5 per mile will cost more than $35 not even including the flat fee.

Check:

1.75(7) + 5.25 = 17.50

and

12(1.75) + 5.25 = 26.25

So, the correct equation is

C = 1.75x + 5.25

Next use this equation to find the cost of the 22 mile ride.

1.75(22) + 5.25

= 43.75

Use logarithms to solve for a.

[tex]3^a = 2 \implies \log_3(3^a) = a\log_3(3) = \log_3(2) \implies a = \log_3(2)[/tex]

Similarly, for b and x.

[tex]3^b = 5 \implies b = \log_3(5)[/tex]

[tex]3^x = 150 \implies x = \log_3(150)[/tex]

Factorize 150:

150 = 2 • 3 • 5²

Then we can expand log₃(150) using the product-to-sum and exponent property,

[tex]\log_3(150) = \log_3(2\times3\times5^2) = \log_3(2) + \log_3(3) + \log_3(5^2)[/tex]

[tex]\implies \log_3(15) = \log_3(2) + 1 + 2 \log_3(5) \iff \boxed{x = 1 + a + 2b}[/tex]

The linear function that gives the candle's height, y, after x hours, is defined by:

y = -0.25x + 11.

A linear function is modeled by:

y = mx + b

In which:

In this problem, in 12 hours, the height decayed 3 inches, hence the slope is given by:

m = -3/12 = -0.25.

So:

y = -0.25x + b.

After 4 hours, the height was of 10 inches, hence we use this to find b:

10 = -0.25(4) + b

b = 11

Thus the equation is given by:

y = -0.25x + 11.

More can be learned about linear functions at https://brainly.com/question/24808124

#SPJ1

Answer: 3

Step-by-step explanation:

3x8 = 24

24x2= 48!

8x12= 96!

Answers must be divisible by both numbers, and achievable by both inputs.

Hope This Helped

Answer:

$3096

Step-by-step explanation:

There are 12 months in 1 year.

3 × 12 = 36

There are 36 months in 3 years.

$86 × 36 = $3096

Answer:

3096

Step-by-step explanation:

I just completed the quiz.

Answer:

r = 50 degrees.

Step-by-step explanation:

r = 50 degrees ( vertical angles are congruent).

Answer:

Step-by-step explanation:

x 1= 3 x 2=−4

Answer:

$18.60

Step-by-step explanation:

The total amount spent is $372, and this can be divided by 20. Each costume would cost $18.60.

Answer:

  30 mL

Step-by-step explanation:

You are being asked to solve the given equation for the value of x.

__

  0.10x +0.15(50 -x) = 0.12(50) . . . . given

  -0.05x = -0.03(50) . . . . . subtract 0.15(50), combine terms

  x = 30 . . . . . . . . . . . divide by -0.05

Bruce should use 30 mL of the 10% alcohol solution.

Answer:

6 hours

Step-by-step explanation:

2 2/3 +3 1/3= 5+1=6

Answer:

2 2/3+ 3 1/3 = 6. Multiply 6 by 4 weeks. 24 as your whole number.

Step-by-step explanation:

hope this helps

Answer: 640

Step-by-step explanation:

How many acres are there in 1 square mile? There are 640 acres in 1 square mile. To convert from square miles to acres, multiply your figure by 640 (or divide by 0.0015625) .

Answer:

640 acres²

Divide the area value by 68

[tex]43,560 / 68 = 640[/tex]

or

[tex]1~mile^2 * 640 = 640[/tex]

you multiply the area value by 640 for each square mile, since there is only one square mile, the answer is 640

Answer:

  $26.25

Step-by-step explanation:

To find the discounted price, subtract the discount amount from the original price. The amount of the discount is the product of the discount rate and the original price.

__

  discounted price = original price - (original price) × (discount rate)

You can calculate it this way, or you can factor out the original price:

  discounted price = (origina price) × (1 - discount rate)

  = $37.50 × (1 -0.30) = $37.50 × 0.70 = $26.25

The sale price of the sweater is $26.25.

__

Additional comment

The amount of the discount is ...

  $37.50 × 0.30 = $11.25

which makes the discounted price be ...

  $37.50 -11.25 = $26.25

Answer:

umm 9?

Step-by-step explanation:

Answer:

1. Triangle: B = 47.0° , C = 103.05° , c = 2.53 cm

2. Lake: c = 1105.31 ft

Step-by-step explanation:

Law of Sine Formula:[tex]\frac{sin(A)}{A} = \frac{sin(B)}{B} = \frac{sin(C)}{C}[/tex]

Given: A = 30° , a = 1.3 cm , b = 1.9 cm

[tex]\frac{sin(30)}{1.3} = \frac{sin(B)}{1.9} = \frac{sin(C)}{C}[/tex]

Solving for sin(B). Cross Multiply.

[tex]\frac{sin(30)}{1.3} = \frac{sin(B)}{1.9}\\1.3*sin(B)=1.9*sin(30)\\sin(B)=\frac{1.9*sin(30)}{1.3} \\[/tex]

B = sin^-1( [tex]\frac{1.9*sin(30)}{1.3}[/tex] )

B ≈ 46.9509202

B = 47.0°

Solve for C°

A° + B° + C° = 180°

30° + 46.95° + C° = 180°

C° = 180° - 30° - 46.95°

C° = 103.05°

Solve for sin(C)

[tex]\frac{sin(30)}{1.3} = \frac{sin(103.05)}{C}\\[/tex]

Cross Multiply

[tex]C*sin(30)=1.3*sin(103.05)\\C=\frac{1.3*sin(103.05)}{sin(30)}[/tex]

C ≈ 2.532850806

C = 2.53 cm

Law of Cosine Formula: [tex]c^2=a^2+b^2-2*a*b*cos(C)[/tex]

Given: a = 850 ft , b = 960 ft ,  C=75°

Solve for c.

[tex]c^2=a^2+b^2-2*a*b*cos(C)\\c^2=(850ft)^2+(960ft)^2-2*(850ft)*(960ft)*cos(75)\\\\c=\sqrt{(850ft)^2+(960ft)^2-2*(850ft)*(960ft)*cos(75)\\} \\[/tex]

c ≈ 1105.308698

c = 1105.31 ft

Answer:

3/4_2/3 find the LCM= 1/12

Answer:

y=6^x+0.612 - 4

Step-by-step explanation:

x = -4 ---> horizontal asymptote

m = 6 ---> use points (0, -1) and (1, 5)

Parent function of the graph: [tex]y=b^x[/tex]

Our equation: [tex]y=6^x[/tex]

Add alterations:

Final equation: y=6^x+0.612 - 4

Answer:

17.51

Step-by-step explanation:

this is a right triangle, so sohcahtoa applies

we want x

relative to the angle, x is opposite of it and 25 is adjacent to it (the hypotenuse is the other side)

the formula that combines opposite and adjacent is tan

tanθ = opposite/adjacent

tan(35°) = x/25

multiply both sides by 25 to isolate x

tan(35°) * 25 = x

x ≈ 17.51