Find the surface area. Round your answer to the nearest hundredths, if necessary. Leave your answer in terms of for answers that contain .

[tex]\frac{dy}{dy}=1[/tex], so I assume you mean "find [tex]\frac{dy}{dx}[/tex]".

We can rewrite this as an implicit equation to avoid using too much of the chain rule, namely

[tex]y = \sqrt[3]{\dfrac{e^x (x+1)}{x^2+1}} \implies (x^2+1) y^3 = e^x (x+1)[/tex]

Differentiate both sides with respect to [tex]x[/tex] using the product and chain rules.

[tex]2x y^3 + 3(x^2+1) y^2 \dfrac{dy}{dx} = e^x(x+1) + e^x[/tex]

[tex]\implies 3(x^2+1) y^2 \dfrac{dy}{dx} = e^x (x+2) - 2x y^3[/tex]

[tex]\implies \dfrac{dy}{dx} = \dfrac{e^x (x+2) - 2x y^3}{3(x^2+1) y^2}[/tex]

Now substitute the original expression for [tex]y[/tex].

[tex]\dfrac{dy}{dx} = \dfrac{e^x (x+2) - 2x \left(\sqrt[3]{\frac{e^x(x+1)}{x^2+1}}\right)^3}{3(x^2+1) \left(\sqrt[3]{\frac{e^x(x+1)}{x^2+1}}\right)^2}[/tex]

[tex]\implies \dfrac{dy}{dx} = \dfrac{e^x (x+2) - \frac{2e^x(x^2+x)}{x^2+1}}{3(x^2+1) \left(\frac{e^x(x+1)}{x^2+1}\right)^{2/3}}[/tex]

[tex]\implies \dfrac{dy}{dx} = e^x \dfrac{x^3-x+2}{3(x^2+1)^2 \frac{e^{2x/3}(x+1)^{2/3}}{(x^2+1)^{2/3}}}}[/tex]

[tex]\implies \dfrac{dy}{dx} = e^{x/3} \dfrac{x^3-x+2}{3(x^2+1)^{4/3} (x+1)^{2/3}}[/tex]

Now, since

[tex]y = \sqrt[3]{\dfrac{e^x (x+1)}{x^2+1}} = \dfrac{e^{x/3} (x+1)^{1/3}}{(x^2+1)^{1/3}}[/tex]

we can write

[tex]\dfrac{dy}{dx} = e^{x/3} \dfrac{x^3-x+2}{3(x^2+1)^{4/3} (x+1)^{2/3}} = \dfrac{e^{x/3} (x+1)^{1/3}}{(x^2+1)^{1/3}} \times \dfrac{x^3-x+2}{3(x^2+1)^{3/3} (x+1)^{3/3}}[/tex]

[tex]\implies \dfrac{dy}{dx} = y \dfrac{x^3-x+2}{3(x^2+1)(x+1)}[/tex]

Focusing on the rational expression in [tex]x[/tex], we have the partial fraction expansion

[tex]\dfrac{x^3 - x + 2}{(x^2 + 1) (x+1)} = a + \dfrac{bx+c}{x^2+1} + \dfrac d{x+1}[/tex]

where we have the constant term on the right side because both the numerator and denominator have degree 3.

Writing everything with a common denominator and equating the numerators leads to

[tex]x^3 - x + 2 = a (x^2+1) (x+1) + (bx+c)(x+1) + d(x^2+1) \\\\ = ax^3 + (a+b+d)x^2 + (a+b+c)x + a+c+d[/tex]

[tex]\implies \begin{cases} a = 1 \\ a+b+d=0 \\ a+b+c = -1 \\ a+c+d=2 \end{cases}[/tex]

[tex]\implies a=1, b=-2, c=0, d=1[/tex]

[tex]\implies \dfrac{x^3 - x + 2}{(x^2 + 1) (x+1)} = 1 - \dfrac{2x}{x^2+1} + \dfrac 1{x+1}[/tex]

and it follows that

[tex]\boxed{\dfrac{dy}{dx} = \dfrac y3 \left(1 - \dfrac{2x}{x^2+1} + \dfrac1{x+1}\right)}[/tex]

Hello and Good Morning/Afternoon

Let's take this problem step-by-step:

To find the solution to a system of equation

  ⇒ must set the equations equal to each other

     ⇒ and solve

Let's put that into action

  [tex]x^2-2x+3 = -2x + 12\\x^2-2x+2x+3-12=0\\x^2-9=0\\(x+3)(x-3)=0[/tex]

          ⇒ either 'x+3' or 'x-3' equals zero

              ⇒ must find 'x' that satisify either equation

                    [tex]x-3=0\\x=3\\\\x+3=0\\x=-3[/tex]

Let's find the corresponding f(x) to each x-value

  [tex]f(3) = -2(3)+12=-6+12 = 6\\\\f(-3) = -2(-3) + 12=6+12=18[/tex]

Therefore the solutions are (3,6) and (-3,18)

Answer: (3,6), (-3,18)

Hope that helps!

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Answer:

1413.7

Step-by-step explanation:

A(sphere) = 4 * π * r².

You can think about it like two times the cap surface area of a hemisphere. Therefore, the hemisphere cap area equals:

Ac = A(sphere) / 2,

Ac = 2 * π * r².

Answer:

-10u^3 - 4

Step-by-step explanation:

-3u^3-7u^3 = -10u^3

then -4

Here ABC is a right angle triangle because 1 angle is 90°

BY ASP,

90+56+ angle CAB=180

angle CAB=34°

rounded to nearest = 30°

sin A =opp/hyp

sin 30 = 7/x

1/2=7/x

x=14

rounding to nearest 10

14 =10

AB=10

By Pythagoras Theorem,

AB²=BC²+AC²

AC²=AB²-BC²=10² - 7²

100- 49 = 51

AC=root 51

An expression is defined as a set of numbers, variables, and mathematical operations. The value of (3√x + 7), when the value of x is 25 is 22.

In mathematics, an expression is defined as a set of numbers, variables, and mathematical operations formed according to rules dependent on the context.

The value of (3√x + 7), when the value of x is 25 is,

3√x + 7

= 3√25 + 7

= 3(5) + 7

= 22

Hence, The value of (3√x + 7), when the value of x is 25 is 22.

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The perimeter of the rectangular rose garden distance outside the path is 57.6m.

Two equal lengths and two equal widths make up a rectangle. We must sum up the lengths of the rectangle's four sides in order to get its perimeter.

Since there are two of each side length, it is easy to accomplish this by simply adding the length and width and multiplying the result by two.

Perimeter = 2(length + breadth)

Calculation for the outside of the path.

Th initial length of park is 15m.

The increment of the length after the width of path is included is;

= 15 + 1.2 + 1.2 (for both side)

= 17.4m

Similarly, the initial width of the park is 9m.

After the increment of the path the width becomes,

= 9 + 1.2 + 1.2 (both side included)

= 11.4m

The perimeter of the rose garden is ;

P = 2( 17.4 + 11.4)

  = 2×28.8

  = 57.6m

Therefore, the rectangular rose garden has the perimeter of 57.6m.

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Answer:

113.1 m

Step-by-step explanation:

Answer:

0.98 km/h

Step-by-step explanation:

Converting mi to km: 66*1.6 = 105.6 miles

Imani's average: 105.6 miles/ 90 min = 1.73 km/h

Abedi's average: 56 miles/ 75 min = 0.7466 ≈ 0.75 km/h

Difference: 1.73-0.75 = 0.98 km/h

Answer:

x ≈ 14.4

Step-by-step explanation:

using the cosine ratio in the right triangle

cos59° = [tex]\frac{adjacent}{hypotenuse}[/tex] = [tex]\frac{x}{28}[/tex] ( multiply both sides by 28 )

28 × cos59° , then

x ≈ 14.4 ( to the nearest tenth )

Answer:

$183.7

Step-by-step explanation:

To find the deposited amount you need to....

[tex]$532.20-$348.50=$183.70[/tex]

Hello!

Subtract the old balance from new balance to find deposit amount.

⇒ Deposit = $532.20 - $348.50

⇒ Deposit = $183.70

[tex]\Huge\boxed{\textsf{A. Exactly one solution}}[/tex]

We have the following system:

[tex]\begin{cases}4x-2y&=8\\2x+y&=2\end{cases}[/tex]

Here, a simple solution to find the answer is to graph the two lines and see how many times they intersect.

I've attached a graph, with [tex]4x-2y=8[/tex] in red and the other equation in blue.

See that the lines only intersect once, at [tex](1.5,-1)[/tex]. This means the system only has one solution.

Answer: No Solution

Let's bring both equations to slope-intercept form. Then we can think about the slopes and the y-intercepts of the lines represented by each equation.

The slope-intercept form of the first equation 2y=4x+62y=4x+62, y, equals, 4, x, plus, 6 is y=2x+3y=2x+3y, equals, 2, x, plus, 3. The second equation y = 2x+6y=2x+6y, equals, 2, x, plus, 6 is already in slope-intercept form.

Hint #22 / 3

The first equation is y = 2x+3y=2x+3y, equals, 2, x, plus, 3, so the slope of its line is 222 and the yyy-intercept is (0,3)(0,3)left parenthesis, 0, comma, 3, right parenthesis.

The second equation is y = 2x+6y=2x+6y, equals, 2, x, plus, 6, so the slope of its line is 222 and the yyy-intercept is (0,6)(0,6)left parenthesis, 0, comma, 6, right parenthesis.

Since both lines have the same slopes but different yyy-intercepts, they are distinct parallel lines.

Hint #33 / 3

Since distinct parallel lines don't intersect, we conclude that the system has no solutions.

A true statement about this transformation is: C. It can be a rigid or a nonrigid transformation depending on whether the corresponding side lengths have the same measures.

In Geometry, a transformation can be defined as the movement of a point from its initial position to a new location. Hence, when an object is transformed, all of the points would also be transformed.

In this scenario, we can logically deduce that triangle J'K'L' can either be a rigid or a nonrigid transformation based on the magnitude of the corresponding side lengths in both triangles, considering that their angles are equal in magnitude.

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Complete Question:

Triangle JKL is transformed to create triangle J'K'L'. The angles in both triangles are shown.

J = 90° J' = 90°

K = 65° K' = 65°

L = 25° L' = 25°

Which statement is true about this transformation?

A. It is a rigid transformation because the pre-image and image have the same corresponding angle measures.

B. It is not a rigid transformation because the corresponding side lengths are not equal.

C. It can be a rigid or a nonrigid transformation depending on whether the corresponding side lengths have the same measures.

D. It can be a rigid or a nonrigid transformation because a pair of corresponding angles measures 90°.

It is a rigid transformation because the pre-image and image have the same corresponding angle measures.

The complete question is added as an attachment

From the image and the preimage triangles, we have that:

The corresponding sides of both triangles are equal

This is identified by the marks I, II and III on the side lengths

Equal corresponding sides represent a rigid transformation

Hence, the true statement about the dilation is (a)

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The statement that is true about line segment P'S' is (c) Segment P'S' s 4 units long and lies on a different segment

The complete question is in the attached image

From the image, we have:

PS = 8 units

This means that:

P'S' = 1/2 * PS

So, we have:

P'S' = 1/2 * 8

Evaluate

P'S' = 4

Also, the segment PS and P'S' do not lie on the same segment

Hence, the true statement is (c)

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Answer: 27:1

Step-by-step explanation:

The ratio of the volumes is equal to the cube of the ratio of the altitudes.

fraction 2/9 is twice the value of fraction 1/9.

What are mathematics operations?

• A mathematical operation is a function that converts a set of zero or more input values (also called "b" or "arguments") into a defined output value. The number of operands determines the operation's arity. Most commonly studied operations are binary operations (i.e., operations of arity 2), such as addition and multiplication, and unary operations (i.e., operations of arity 1), such as additive and multiplicative inverses.

• Zero-arity operations, or nullary operations, are constants, and mixed products are arity three operations, or ternary operations.

Here, the given fractions are :

1/9 and 2/9

clearly 2/9 is twice the value of fraction 1/9.

And, there decimal form​ will be :

1/9 = 0.11

2/9 = 0.22

Here, both are multiple of 11.

Therefore, fraction 2/9 is twice the value of fraction 1/9.

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The order of the side lengths from least to greatest is; GH< IH< FG< GI< FH.

As with other closed geometric figures, the shortest side length is opposite the smallest angle measure while the longest side length, is opposite the greatest angle measure.

Hence, it follows from the statement above that the order of side lengths is; GH< IH< FG< GI< FH.

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Answer:

Who is the youngest in your family?

The statement "If ∠1 and ∠2 form a linear pair; ∠1 and ∠3 are supplementary, then ∠2 = ∠3" is proved.

If the sum of two angles is 180 then they are called supplmentary angles of each other.

If one straight line meets another straight line at a point, then two adjoint angles at that point on that line is called Linear angles to each other.

Here given that ∠1 and ∠2 are linear to each other.

From property of the linear angles we know that the sum of linear angles is 180.

Therefore, ∠1 + ∠2 = 180

So, ∠2 = 180 - ∠1 .........(1)

Also it is given that, ∠1 and ∠3 are supplementary angles.

So, ∠1 + ∠3 = 180

Therefore, ∠3 = 180 - ∠1.....(2)

Comparing (1) and (2) we get,

∠2 = ∠3 = 180 - ∠1

Therefore, ∠2 = ∠3, proved

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Ethnographic research is the type of sample is specifically used for gathering information about clandestine or difficult-to-identify groups.

Cultures have a set of rules and beliefs about what is correct for that specific culture. Ethnocentrism is the measuring and judging of one culture by another culture. This can be either a positive or negative judgment about the difference between the beliefs of the two cultures. Ethnocentrism is also believing in the inferiority of other cultures compared to the superiority of one's own culture.

Additionally, ethnocentrism is defined by individualistic or collective cultures. Many Western cultures are individualistic; they tend to focus on what is best for the individual.

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Among the congruent quadrilaterals, the segment that must also measure 3 cm is: A. A F.

Congruent quadrilaterals have corresponding congruent angles and sides.

Given that, GHJK ≅ ASDF and GHJK ≅ VBNM, it means that all corresponding sides and angles are equal to each other.

MV corresponds to KG and A F. If MV = 3 cm, then one segment that must measure 3 cm is:

A. A F

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Answer: A. A F

same answer as the other person gave but you don't have to read a bunch

Using the definitions of local maximum and minimum, it is found that:

In this problem, we have that the function is as follows:

Hence:

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Answer:

-2,0  0,2

Step-by-step explanation:for anyone needing it in the future cause I couldn't find the answer

Answer:

The equation of the unknown line is [tex]$g(x)=-\frac{1}{3} x+6$[/tex].

Step-by-step explanation:

In the question, it is given that a line passes through (-2,-15) and (2,-3). Another line perpendicular to the first line passes through (6,4).

It is required to find the equation of the second line. of b and substitute all these values to find the equation of second line.

Step 1 of 2

Find the slope of first line.

[tex]$$\begin{aligned}&m_{1}=\frac{-3-(-15)}{2-(-2)} \\&m_{1}=\frac{12}{4} \\&m_{1}=3\end{aligned}$$[/tex]

Therefore, the slope of second line is [tex]$m_{2}$[/tex].

[tex]$$m_{2}=-\frac{1}{3}$$[/tex]

Step 2 of 2

Substitute the values of [tex]$m_{2}[/tex],x and g(x) to find the b.

[tex]$$\begin{aligned}&g(x)=m x+b \\&4=-\frac{1}{3}(6)+b \\&b=4+2 \\&b=6\end{aligned}$$[/tex]

Therefore, the equation of the unknown line is [tex]$g(x)=-\frac{1}{3} x+6$[/tex].

Step 1 of 2

Find the slope of first line.

[tex]$$\begin{aligned}&m_{1}=\frac{-3-(-15)}{2-(-2)} \\&m_{1}=\frac{12}{4} \\&m_{1}=3\end{aligned}$$[/tex]

Therefore, the slope of second line is [tex]$m_{2}$[/tex].

[tex]$$m_{2}=-\frac{1}{3}$$[/tex]

Step 2 of 2

Substitute the values of [tex]$m_{2}[/tex], x and g(x) to find the b.

[tex]$$\begin{aligned}&g(x)=m x+b \\&4=-\frac{1}{3}(6)+b \\&b=4+2 \\&b=6\end{aligned}$$[/tex]

Therefore, the equation of the unknown line is [tex]$g(x)=-\frac{1}{3} x+6$[/tex].

Answer:

Answers all found below.

Step-by-step explanation:

1) Given from diagram, RT = RS + RT

RT = 2cm + 2.5cm = 4.5cm

2) Given from diagram, AC = AB + BC

BC = AC - AB

= [tex]6 in-2\frac{3}{4} in\\=3\frac{1}{4} or 3.25in[/tex]

3)Given from diagram, XZ = XY + YZ

XZ = [tex]3\frac{1}{2} +\frac{3}{4} \\=4\frac{1}{4} or 4.25in[/tex]

4)Given from diagram, WX = XY and WY = 6cm

WX = WY / 2

= 6 / 2

= 3cm

For Questions 5,6 and 7, refer to the attached photos, apologies for the terrible drawing.

5) From the diagram,

RS + ST = RT

5x + 3x = 48

8x = 48

x = 48 / 8

= 6

6) From the diagram,

RS + ST = RT

2x + 5x+4 = 32

7x + 4 = 32

7x = 32 - 4

7x = 28

x = 28 / 7

= 4

7) From the diagram,

RS + ST = RT

6x + 12 = 72

6x = 72 - 12

6x = 60

x = 60 / 6

= 10

The proof is shown below:

A parallelogram is a quadrilateral with opposite sides parallel (and therefore opposite angles equal).

As,

<A= 104

<B= 76

As AB || CD,

<A + <D =180

104 + <D =180

<D = 76

and <B + <C =180

76 + <C = 180

<C = 104.

As, opposite angles are equals and  AB || CD.

Hence, ABCD is a parallelogram.

For 2 part,

Use m<A = 104° and m<B= 76° to show that <A and <B are same-side interior angles. Then, use AB || CD to show that <A and <D are supplementary angles.

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The skew lines are CG, DH, AD, BC.

The parallel lines are  BC, EH, FG.

Two or more lines which have no intersections but are not parallel.

As, by the definition

The lines skew to EF is CG, DH, AD, BC

The parallel to AD is BC, EH, FG.

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Answer:

[tex]\sf \boxed{\bf y =5\sqrt{22}}[/tex]

Step-by-step explanation:

       The ratio of sides of 45 - 45 - 90 triangle is  a : a : a√2.

a is the side opposite to 45°.

From the figure, a = 5√11

The side opposite to 90° is a√2.

y = a√2

  [tex]\sf = 5\sqrt{11} * \sqrt{2}\\\\ = 5*\sqrt{11*2}\\\\ = 5\sqrt{22}[/tex]

Answer:

Number 1 is 55

Number 2 is 60 :)

Step-by-step explanation:

(115 - 5)/2

110/2

55

Number 1 is 55

Number 2 is 60 :)

60 + 55

110 + 5

115 :)

Have an amazing day!!

Please rate and mark brainliest!!

Answer:

the first number is 55 and the second is 60