The integral \(\pi\int\limits^2_1 {(1-(lnx)^{2}) } \, dx\) represents the volume of a solid obtained by rotating a region around y=-1. Evaluate.

Answer:

1526.04

Step-by-step explanation:

the formula for calculating the volume of cone is

V=πr^2(h/3)

Thus,

V = (3.14)(9)^2(18/3)

V = (3.14)(81)(6)

V = 1536.04 yd^3

Rounding off to the nearest tenth, we get

V = 1536 yd^3

The value of the expression such that a and b are integers is 1/9

An exponential function is a mathematical function in the form y = ab^x

Given the indices expression

\(\frac{(9\frac{1}{2} )^b}{3^a}\)

This can be simplified as:

\(=\frac{(3^{2*\frac{1}{2}} )^b}{3^a}\\=\frac{3^b}{3^a}\)

According to the law of indices, the expression will becomes;

\(\frac{3^b}{3^a} =3^{b-a}\)

Recall that a - b = 2, such that b - a = -2. Substitute into the result to have:

\(\frac{3^b}{3^a} =3^{b-a}\\3^{b-a}=3^{-2}\\3^{b-a}=1/9\)

Hence the value of the expression such that a and b are integers is 1/9

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Answer:

1) One of the equations that represents this scenario is A – B = 100.

2)One of the equations that represents this scenario is StartFraction 3 Over 8 EndFractionA + StartFraction 7 Over 8 EndFractionB = 2000.

4) To eliminate the B variable, multiply the first equation by 7 and the second by 8.

Step-by-step explanation:

Answer:

a b and d

Step-by-step explanation:

Using proportions, it is found that due to the smaller division of the exchange rate by the cost, the souvenir would be less expensive in Egypt.

A proportion is a fraction of a total amount, and the measures are related using a rule of three. Due to this, relations between variables, either direct or inverse proportional, can be built to find the desired measures in the problem.

The souvenir would be less expensive in the country in which the division of the exchange rate by the cost is smaller.

In Britain, the cost is of 17, with an exchange rate of 0.83, hence the cost in US dollars is:

c = 17/0.83 = $20.48.

In Egypt, the cost is of 288, with an exchange rate of 18, hence the cost in US dollars is:

c = 288/18 = $16.

16 < 20.48, hence the souvenir would be less expensive in Egypt.

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Answer:

\(\large \boxed{\mathrm{B}}\)

Step-by-step explanation:

3 1/2 is also 0+3 1/2

Arrow from 0 goes to 3 1/2.

3 1/2 - 6 = -2 1/2

Arrow from 3 1/2 goes to -2 1/2.

The answer for the given expression is =1/128[35-56cos2x+28cos4x-8cos6x+cos8x]

What is trignomatric functions?

All trigonometric identities are built upon the foundation of the six trigonometric ratios. Some of their names are sine, cosine, tangent, cosecant, secant, and cotangent. The adjacent side, opposite side, and hypotenuse side of the right triangle are used to define each of these trigonometric ratios.

What is multiple angles?

If angle A is taken as a given, then many angles are 2A, 3A, 4A, etc. The many angle formulas employ the double and triple angles formulas. Sine, cosine, and tangent are the often utilised trigonometric functions for the multiple angle formula.

Answer is attached as a image must check:

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We can rewrite sin⁸x in terms of first powers of the cosines of multiple angles as:

sin⁸x = 1/128 (35 - 4cos²x + 40cos⁴x - 64cos⁶x + cos⁸x)

Trigonometric functions raised to powers can be rewritten using double-angle, half-angle, and Pythagorean identities in power lowering formulas. Equations can be made simpler using them, and trigonometric expressions can be precisely determined.

We can use the power-reducing formulas to rewrite sin⁸x in terms of cosines of multiple angles as follows:

sin²x = 1 - cos²x   (first power-reducing formula)

sin⁴x = (sin²x)² = (1 - cos²x)²

      = 1 - 2cos²x + cos⁴x   (second power-reducing formula)

sin⁶x = (sin⁴x)(sin²x)

      = (1 - 2cos²x + cos⁴x)(1 - cos²x)

      = 1 - 3cos²x + 3cos⁴x - cos⁶x   (third power-reducing formula)

sin⁸x = (sin⁶x)(sin²x)

      = (1 - 3cos²x + 3cos⁴x - cos⁶x)(1 - cos²x)

      = 1 - 4cos²x + 6cos⁴x - 4cos⁶x + cos⁸x

Now we can substitute the expression for sin⁸x into the given expression and simplify it:

1/128 (35 - 56 cos2x + 28 cos4x - 8 cos6x + cos8x)

= 1/128 (35 - 56(2cos²x-1) + 28(4cos⁴x-3cos²x) - 8(8cos⁶x-8cos⁴x+cos²x) + cos⁸x)

= 1/128 (35 - 112cos²x + 56 + 112cos⁴x - 84cos²x - 64cos⁶x + 64cos⁴x - 8cos²x + cos⁸x)

= 1/128 (35 - 4cos²x + 40cos⁴x - 64cos⁶x + cos⁸x)

Therefore, we can rewrite sin⁸x in terms of first powers of the cosines of multiple angles as:

sin⁸x = 1 - 4cos²x + 6cos⁴x - 4cos⁶x + cos⁸x

     = 1/128 (35 - 4cos²x + 40cos⁴x - 64cos⁶x + cos⁸x)

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Answer:

see below and attachment

Step-by-step explanation:

a=30°

because, the marked angle of 30° is an alternate interior angle to angle a.  Alternate interior angles are congruent, and we know they are congruent because the 2 horizontal lines are parallel.

b=50°

because the marked angle of 50° is a vertical angle to angle b.  Vertical angles are congruent because 2 lines that intersect have opposite congruent angles, making them vertical angles to each other.

c=50°

because the marked angle of 50° is a corresponding angle (same side angle) to angle c.  These corresponding angles are congruent because the 2 horizontal lines are parallel.

d=100°

because the 3 interior angles of a triangle must add up to 180°.  We have 30°, 50°, so the last angle must be 100°.  We can also figure this out because the bottom horizontal line is a straight line, meaning the angle is also 180°.  We have angle a as 30°, angle c as 50°, so angle d must be 100°.

Hope this helps!  See attachment for visual.

Answer:

To find the probability of selecting a Coke person from this group, we need to divide the number of people who prefer Coke by the total number of people in the group.

The number of people who prefer Coke is 29. The total number of people in the group is 29 + 21 + 37 + 28 + 19 + 16 + 150 + 150 + 2 = 452.

Therefore, the probability of selecting a Coke person from this group is:

P(Coke) = Number of people who prefer Coke / Total number of people in the group = 29 / 452 ≈ 0.064

So the probability of selecting a Coke person from this group is approximately 0.064.

I hope this helps! Let me know if you have any other questions.

Step-by-step explanation:

Answer: m = - \(\frac{1}{40} \\\)

Step-by-step explanation:

I know this because I'm built different (FR FR This answer is correct)

The solution to the given question is "Optimal B = 0.3 and S = 0.7 where 0.088 was its optimal value", and further calculation can be defined as follows:

         In a fund for stocks.  

             \(Max \ \ 0.06 \ b+0.1 \ S \ \ \ \\\\B \geq 0.3 \ \ \ \ \ \ \ \ \ \ \ \ \text{Bond fund minimum} \\\\0.06 \ B+ 0.1 \ S \geq 0.075 \ \ \ \ \ \ \text{Minimum return} \\\\B+S=1 \ \ \ \ \ \ \ \text{All funds invested}\\\\B,S\geq 0 \\\)

          \(B = 0.3 \\ \\0.06 \ B+0.1 \ S = 0.75\\\\ B+s =1\)

          \(B+s=1=10 \\\\0.3+s = 1 \\\\The \ \ s= 0.7 \\\)

Optimal B = 0.3 and S = 0.7 where 0.088 was its optimal value.

please find the attachment:

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The $300  invested at the given rate will amount to $412.92. The correct option is C. $412.92

From the question, we are to determine how much $300 will amount to

From the given Compound interest formula, we have

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

From the given information,
P = $300

r = 4% = 0.04

n = 12

t = 8

Putting the parameters into the formula

A = 300(1+ 0.04/12)¹²⁽⁸⁾

A = 300(1.3764)

A = $412.92

Hence, the $300  invested at the given rate will amount to $412.92. The correct option is C. $412.92

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Answer:

-2, 2

Step-by-step explanation:

Answer:

dddddweqwqq

Step-by-step explanation:

Answer: No

Step-by-step explanation:

Answer:

50

Step-by-step explanation:

The requried, race car will travel approximately 1100 feet in 5 seconds at a constant speed of 150 miles per hour.

To find out how many feet a race car traveling at a constant speed of 150 miles per hour travels in 5 seconds, we need to convert the given speed from miles per hour to feet per second.

There are 5280 feet in a mile, and there are 3600 seconds in an hour.

First, let's convert 150 miles per hour to feet per second:

= 150 miles/hour * 5280 feet/mile / 3600 seconds/hour
= 220 feet/second (approximately)

Now, we can calculate the distance traveled by the race car in 5 seconds:

Distance = Speed * Time

Distance = 220 feet/second * 5 seconds

Distance = 1100 feet

Therefore, the race car will travel approximately 1100 feet in 5 seconds at a constant speed of 150 miles per hour.

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Hello !

Your answer will be is :

No, \(3^4^x^-^5\) is higher then 8.

Let's go with step-by-step explanation ~

___________________________________________________________

\(\huge \red {\fbox {\mathbb{Explanation :}}}\)

\(\sf{3^4^x^-^5}\)

\(\sf{\frac{3^4^x}{3^5}\)

\(\sf{\frac{3^4^x}{243}\)

Hopefully this helps you !

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\(\underline{Answer :}\)

Dollixna ~

\(Hello\) \(There!\)

I'll will be helping your question today!

Let's do this step-by-step explanantion!

\(3^4^x^-^5 < 8\)

Apply exponent rules:

\(4x-5 < 3log3(2)\)

\(4x-5 < 31log3(2): x < \frac{3log3(2)+5}{4}\)

Answer:

\(< \frac{3log3(2)+5}{4}\)

\(\frac{3log3(2+5)}{4}\)

\(2+5=7\)

\(=\frac{3log3(7)}{4}\)

Answer:

\(\frac{3log3(7)}{4}\)

Answer could be: \(< \frac{3log3(2)+5}{4} or\frac{3log3(7)}{4}\)

Hopefully, this helps you!!

#LearnWithBrainlyAlways~

\(SokkaBanned\)

The measure of angle D is 45°

Similar triangles have the same corresponding angle measures and proportional side lengths. When two triangles are similar, the corresponding angles are equal.

And also the ratio of corresponding sides of similar triangles are equal.

To know the corresponding angles

side AC is corresponding to side EF, therefore angle D is congruent to angle A

angle D = 45°

OR , we can use the sum of angles In a triangle , which is 180°

angle D = 180 -( 72+63)

= 180 - 135

= 45°

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Answer:

\(\textsf{A.} \quad (2+x)^x\left[\dfrac{x}{2+x}+\ln(2+x)\right]\)

Step-by-step explanation:

Replace f(x) with y in the given function:

\(y=(x+2)^x\)

Take natural logs of both sides of the equation:

\(\ln y=\ln (x+2)^x\)

\(\textsf{Apply the log power law to the right side of the equation:} \quad \ln a^n=n \ln a\)

\(\ln y=x\ln (x+2)\)

Differentiate using implicit differentiation.

Place d/dx in front of each term of the equation:

\(\dfrac{\text{d}}{\text{d}x}\ln y=\dfrac{\text{d}}{\text{d}x}x\ln (x+2)\)

First, use the chain rule to differentiate terms in y only.

In practice, this means differentiate with respect to y, and place dy/dx at the end:

\(\dfrac{1}{y}\dfrac{\text{d}y}{\text{d}x}=\dfrac{\text{d}}{\text{d}x}x\ln (x+2)\)

Now use the product rule to differentiate the terms in x (the right side of the equation).

\(\boxed{\begin{minipage}{5.5 cm}\underline{Product Rule for Differentiation}\\\\If $y=uv$ then:\\\\$\dfrac{\text{d}y}{\text{d}x}=u\dfrac{\text{d}v}{\text{d}x}+v\dfrac{\text{d}u}{\text{d}x}$\\\end{minipage}}\)

\(\textsf{Let}\; u=x \implies \dfrac{\text{d}u}{\text{d}x}=1\)

\(\textsf{Let}\; v=\ln(x+2) \implies \dfrac{\text{d}v}{\text{d}x}=\dfrac{1}{x+2}\)

Therefore:

\(\begin{aligned}\dfrac{1}{y}\dfrac{\text{d}y}{\text{d}x}&=x\cdot \dfrac{1}{x+2}+\ln(x+2) \cdot 1\\\\\dfrac{1}{y}\dfrac{\text{d}y}{\text{d}x}&= \dfrac{x}{x+2}+\ln(x+2)\end{aligned}\)

Multiply both sides of the equation by y:

\(\dfrac{\text{d}y}{\text{d}x}&=y\left( \dfrac{x}{x+2}+\ln(x+2)\right)\)

Substitute back in the expression for y:

\(\dfrac{\text{d}y}{\text{d}x}&=(x+2)^x\left( \dfrac{x}{x+2}+\ln(x+2)\right)\)

Therefore, the differentiated function is:

\(f'(x)=(x+2)^x\left[\dfrac{x}{x+2}+\ln(x+2)\right]\)

\(f'(x)=(2+x)^x\left[\dfrac{x}{2+x}+\ln(2+x)\right]\)

Answer

Step by step explantion:

bsf= 26

Eliana:98

SS teacher=203

David=55

Step-by-step explanation:

m= music

bsf: m

eliana:4m-6

David:2m+3

SS teacher: 2(4m-6)+7

m+4m-6+2m+3+8m-12+7

382=15m-7

7+ +7

389=15m

/15m /15m

m=26

multiply 26 to each one of them

The additive inverse are;

For expression;

a) 3-5

Additive inverse = - 3 - (-5)

For expression;

b) 5 - 3

Additive inverse = - 5 - (-3)

What is additive inverse?

The Property of Additive Inverse states that the summation of a number and it's Additive inverse is zero.

The expressions are;

3 - 5 and 5 - 3

Now, The Property of Additive Inverse states that the summation of a number and it's Additive inverse = 0

And, An Additive inverse of a positive integer is a negative integer and vice versa.

For example: 7 - 7 = 0

Here, The additive inverse of 7 = -7

Since, For the question above, we are asked to use the additive inverses and their properties to find the equivalent expressions.

a) 3 - 5

Hence, Additive inverse = - 3 - (-5)

                                      = -3 + 5

                                      = 2

b) 5 - 3

Hence, Additive inverse = - 5 - (-3)

                                      = - 5 + 3

                                      = - 2

So, The additive inverse are;

For expression;

a) 3-5

Additive inverse = - 3 - (-5)

For expression;

b) 5 - 3

Additive inverse = - 5 - (-3)

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Answer:

3-5:

3+(-5)

-5+3

5-3:

-3+5

5+(-3)

Step-by-step explanation:

hope this helps ya (⁠☆⁠▽⁠☆⁠)

Answer:

\(4.8038\) or just \(4\) quarts.

Hope this helps!

no entendí bien puedes explicar mejor la pregunta si la entendí pero el contenido si

Using the definition of congruent triangles, the value of x is evaluated as: x = 6.

To find the sides of congruent triangles, note that the corresponding sides of two triangles that are congruent to each other have equal length measurement.

Given that triangular poor ABC and triangular pool PQR are congruent to each other, therefore, their corresponding sides will have the same length.

This means that the third sides of both triangles will be equal, which are:

(3x + 2) = 20

Solve for x:

3x + 2 = 20

3x + 2 - 2 = 20 - 2

3x = 18

3x/3 = 18/3

x = 6

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The area of the irregular figure to the nearest tenth is 8.12 sq. ft.

Shapes classified as irregular lack both equal sides and equal angles. The entire area occupied by an irregular shape on a two-dimensional plane is referred to as the shape's area. An irregular form can be split into a number of regular shapes, such as triangles, squares, and rectangles, to determine its area. The area of those smaller shapes can then be added to determine the total area.

Given that, the diameter of the semicircle= 2.8 ft.

The radius of the semicircle = 1.4 ft.

The area of the semicircle is:

A = πr² / 2

A = (3.14)(1.4)²/2

A= 3.077 sq. ft

The area of the triangle is given as:

A = 1/2(b)(h)

A = 1/2(2.8)(3.6)

A = 5.04 sq. ft

The area of the irregular figure is:

A = Area of semicircle + area of triangle

A = 3.077 + 5.04

A = 8.117 sq. ft

Hence, the area of the irregular figure to the nearest tenth is 8.12 sq. ft.

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The solution of the compound inequality is -2 ≤ x ≤ 1 and -4 ≥ x ≥ -7.

An inequality that combines two other inequalities by using either "and" or "or" is referred to as a compound inequality. In certain cases, "and" won't be stated explicitly, but it is still understood. For instance, 1 x 3 simply means "x > 1 and x 3". However, a compound inequality using "or" is always explained in detail using "or." Compound inequalities may be divided into two categories: conjunction and disjunction.

The given compound inequality is:

1 ≤ | x + 3 | ≤ 4

As the equation contains a mod sign, we can write the inequality as follows:

1 ≤ x + 3 ≤ 4, and

1 ≤ - x - 3 ≤ 4

Simplify the first equation:

1 ≤ x + 3 ≤ 4

Subtract 3 from both the sides of the equation:

1 - 3 ≤ x + 3 - 3 ≤ 4 -3

-2 ≤ x ≤ 1

Simplify the second equation:

1 ≤ - x - 3 ≤ 4

Add 3 on both sides of the equation:

1 + 3 ≤ - x - 3 + 3≤ 4 + 3

4 ≤ -x ≤ 7

Convert the negative term to positive:

-4 ≥ x ≥ -7

Hence, the solution of the compound inequality is -2 ≤ x ≤ 1 and -4 ≥ x ≥ -7.

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Answer:

9 is added by 4 times y is the correct answer.

The given option don't describe the expression 4y+9