Help plz! I’m so confused

Answer:

\(\mathbf{S =6 \sqrt{1 + \dfrac{\pi^2}{9} }+ \dfrac{18}{\pi} In (\dfrac{\pi}{3}+ \sqrt{1+ \dfrac{\pi^2}{9}})}\)

Step-by-step explanation:

Given that

curve \(y = \dfrac{\pi x}{3}, 0 \leq x \leq 3\)

The objective is to find the area of the surface obtained by rotating the above curve about the x-axis.

Suppose f is positive and posses a continuous derivative,

the surface is gotten by the rotating the curve about the x-axis is:

\(S = \int ^b_a 2 \pi f (x) \sqrt {1 + (f' (x))^2 } \ dx\)

The derivative of the function \(y' = \dfrac{\pi}{3} cos \dfrac{\pi x}{3}\)

As such, the surface area is:

\(S = \int ^3_0 2 \pi sin \dfrac{\pi x}{3} \sqrt {1 +(\dfrac{\pi}{3}cos \dfrac{\pi x}{3})^2 } \ dx\)

Suppose ;

\(u = \dfrac{\pi}{3}cos \dfrac{\pi x}{3}\)

\(du = -( \dfrac{\pi}{3})^2 sin \dfrac{\pi x}{3} \ dx\)

If x = 0 , then \(u = \dfrac{\pi}{3}cos \dfrac{\pi (0)}{3} = \dfrac{\pi}{3}\)

If x = 3 , then \(u = \dfrac{\pi}{3}cos \dfrac{\pi (3)}{3}\)

\(u = \dfrac{\pi}{3}(-1)\)

\(u = -\dfrac{\pi}{3}\)

The equation for S can now be rewritten as:

\(S = \int^3_0 2 \pi sin \dfrac{\pi x}{3} \sqrt{1+(\dfrac{\pi}{3} cos \dfrac{\pi x}{3})^2 }\ dx\)

\(S = 2 \pi \int ^{-\frac{\pi}{3} }_{\frac{\pi}{3}}(-\dfrac{9 \ du }{\pi^2} ) \sqrt{1+u^2}\)

\(S = 18 \pi * \dfrac{1}{\pi ^2 } \int ^{-\frac{\pi}{3}}_{\frac{\pi}{3}} \sqrt{1+u^2} \ du\)

\(S = \dfrac{18} {\pi} \int ^{-\frac{\pi}{3}}_{\frac{\pi}{3}} \sqrt{1+u^2} \ du\)

\(S = \dfrac{18} {\pi} (2 \int ^{-\frac{\pi}{3}}_{0} \sqrt{1+u^2} \ du)\)

since \((\int ^a_{-a} fdx = 2\int^a_0 fdx , f= \sqrt{1+u^2} \ is \ even )\)

Applying the formula:

\(\int {\sqrt{1+x^2}} \ d x= \dfrac{x}{2} \sqrt{1+x^2}+ \dfrac{1}{2} In ( x + \sqrt{1+x^2})\)

\(S = \dfrac{36}{x}[ \dfrac{u}{2} \sqrt{1+u^2}+ \dfrac{1}{2} \ In (u+ \sqrt{1+u^2}) ] ^{\frac{\pi}{3}}_{0}\)

\(S = \dfrac{36}{x}[ \dfrac{\dfrac{\pi}{3}}{2} \sqrt{1+\dfrac{\pi^2}{9}}+ \dfrac{1}{2} \ In (\dfrac{\pi}{3}+ \sqrt{1+\dfrac{\pi^2}{9}})-0 ]\)

\(S =6 \sqrt{1 + \dfrac{\pi^2}{9} }+ \dfrac{18}{\pi} In (\dfrac{\pi}{3}+ \sqrt{1+ \dfrac{\pi^2}{9}})\)

Therefore, the exact area of the surface is \(\mathbf{S =6 \sqrt{1 + \dfrac{\pi^2}{9} }+ \dfrac{18}{\pi} In (\dfrac{\pi}{3}+ \sqrt{1+ \dfrac{\pi^2}{9}})}\)

The area of the surface is,\(S = 6\sqrt{1+\dfrac{\pi ^2}{3}} + \dfrac{18}{3}\ ln (\dfrac{\pi }{3}+\sqrt{1+\dfrac{\pi ^2} {9}})\).

Given that,

The exact area of the surface obtained by rotating the curve about the x-axis. y = sin πx\3 , 0 ≤ x ≤ 3.

We have to determine,

Area of the surface obtained by rotating the curve.

According to the question,

Suppose f is positive and posses a continuous derivative,

The surface is gotten by the rotating the curve about the x-axis is:

Area of the surface is given by,

\(S = \int\limits^b_a {2\pi f(x) .\sqrt{1+ (f'(x))} } \, dx\)

The given curve is x-axis,

\(y = \dfrac{sin\pi x}{3}\)

The derivative of the function is,

\(\dfrac{dy}{dx} =\dfrac{\pi }{3} \dfrac{ cos\pi x}{3}\)

The surface area is,

\(S = \int\limits^b_a {2\pi f(x) .\sqrt{1+(\dfrac{\pi }{3} \dfrac{ cos\pi x}{3})^2} }}} \, dx\)

Substitute the value of f(x),

\(S = \int\limits^3_0{2\pi\dfrac{sin\pi x}{3} .\sqrt{1+(\dfrac{\pi }{3} \dfrac{ cos\pi x}{3})^2} }}} \, dx\)

Suppose;

\(u = \dfrac{\pi }{3}cos\dfrac{\pi x}{3}dx\\\\\du =( \dfrac{-\pi }{3})^2 sin\dfrac{\pi x}{3}dx\\\\if \ x = 0, \ then \ u = \dfrac{\pi }{3}cos\dfrac{\pi (0)}{3} = \dfrac{\pi }{3}\\\\if \ x = 3, \ then \ u = \dfrac{\pi }{3}cos\dfrac{\pi (3)}{3} = \dfrac{\pi }{3}(-1)= \dfrac{-\pi }{3}\)

Then,

\(S = \int\limits^3_0{2\pi\dfrac{sin\pi x}{3} .\sqrt{1+(\dfrac{\pi }{3} \dfrac{ cos\pi x}{3})^2} }}} \, dx\\\\S = 2\pi \int\limits^{\frac{-\pi}{3}}_ \frac{\pi }{3} (\dfrac{-9du}{\pi ^2})\sqrt{1+u^2} \ du\\\\S = 18\pi \times \dfrac{1}{\pi ^2}\int\limits^{\frac{-\pi}{3}}_ \frac{\pi }{3} \sqrt{1+u^2} \ du\\\\S = \dfrac{18}{\pi}\int\limits^{\frac{-\pi}{3}}_ {0} 2\sqrt{1+u^2} \ du\\\\\\\)

Since,

\((\int\limits^a_{-a}{f} \, dx = 2\int\limits^a_0 {f} \, dx , \ f = \sqrt{1+u^2}\ is \ even)\)

By applying the formula to solve the given integration,

\(\int {\sqrt{1+x^2} } \, dx = \dfrac{x}{2}\sqrt{1+x^2} + \dfrac{1}{2} \ ln(x+\sqrt{1+x^2})\\\\S = \dfrac{36}{2} [ \dfrac{u}{2} \sqrt{1+u^2} + \dfrac{1}{2} \ ln(u+\sqrt{1+u^2})}]^{\frac{\pi }{3}}_0\\\\\)

\(S = \dfrac{36}{2} [ \dfrac{\dfrac{\pi }{3}}{2} \sqrt{1+\dfrac{\pi^2 }{9}} + \dfrac{1}{2} \ ln(\dfrac{\pi }{3}+\sqrt{1+\dfrac{\pi ^2} {9}}-0)]\\\\S = 6\sqrt{1+\dfrac{\pi ^2}{3}} + \dfrac{18}{3}\ ln (\dfrac{\pi }{3}+\sqrt{1+\dfrac{\pi ^2} {9}})\)

Hence, The area of the surface is,\(S = 6\sqrt{1+\dfrac{\pi ^2}{3}} + \dfrac{18}{3}\ ln (\dfrac{\pi }{3}+\sqrt{1+\dfrac{\pi ^2} {9}})\)

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The orthogonal projection of vector v onto vector w in R^3 is (-54/14, -159/70, -159/35).

To find the orthogonal projection of v onto w, we need to calculate the scalar projection of v onto w and multiply it by the unit vector of w. The scalar projection of v onto w is given by the formula:

proj_w(v) = (v⋅w) / (w⋅w) * w

where ⋅ denotes the dot product.

Calculating the dot product of v and w:

v⋅w = (-7)(-5) + (6)(-3) + (-6)(-6) = 35 + (-18) + 36 = 53

Calculating the dot product of w with itself:

w⋅w = (-5)(-5) + (-3)(-3) + (-6)(-6) = 25 + 9 + 36 = 70

Now, substituting these values into the formula, we have:

proj_w(v) = (53/70) * (-5,-3,-6) = (-54/14, -159/70, -159/35)

Therefore, the orthogonal projection of v onto w is (-54/14, -159/70, -159/35).

In simpler terms, the orthogonal projection of v onto w can be thought of as the vector that represents the shadow of v when it is cast onto the line defined by w. It is calculated by finding the component of v that aligns with w and multiplying it by the direction of w. The resulting vector (-54/14, -159/70, -159/35) lies on the line defined by w and represents the closest point to v along that line.

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Answer:

The answers are on the sheet, the numbers it says are the percentages. The others you just have to subtract them.

The term that can be added to the list so that the greatest common factor of the three terms  12h3 36h3, 12h6, is 48h5

A group of numbers' greatest common factor (GCF) is the biggest factor that all the numbers have in common. For instance, 12, 20, and 24 all share two characteristics.

The term that  can fit in to the list so the GCF is 12h3 would be 48h5, this is so because 48 is first divisible by 12  without any  fraction, and we can remove upon dividing 3 h's from this term as it contains a total of 5 h's.

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Answer:

Rome, Italy is 1 hour ahead of Casablanca, Morocco.

The Propositions are resulting

(a) ∀x∃y(x = y²) is False

(b) ∀x∃y(x² = y) is True.

(c) ∃x∀y(xy = 0) is True.

(d) ∀x∃y(x + y = 1) is True.

(a) ∀x∃y(x = y²)

This proposition states that for every x, there exists a y such that x is equal to y². To determine the truth value, we need to check if this statement holds true for every value of x.

If we take any positive value for x, we can find a corresponding value of y that satisfies the equation.

For example, if x = 4, then y = 2 satisfies the equation since 4 = 2². Similarly, if x = 9, then y = 3 satisfies the equation since 9 = 3².

Therefore, the proposition (a) is false.

(b) ∀x∃y(x² = y)

For any given positive or negative value of x, we can find a corresponding value of y that satisfies the equation.

For example, if x = 4, then y = 2 satisfies the equation since 4² = 2. Similarly, if x = -4, then y = -2 satisfies the equation since (-4)² = -2.

Therefore, the proposition (b) is true.

(c) ∃x∀y(xy = 0)

The equation xy = 0 can only be satisfied if x = 0, regardless of the value of y. Therefore, there exists an x (x = 0) that makes the equation true for every y.

Therefore, the proposition (c) is true.

(d) ∀x∃y(x + y = 1)

To determine the truth value, we need to check if this statement holds true for every value of x.

If we take any value of x, we can find a corresponding value of y that satisfies the equation.

For example, if x = 2, then y = -1 satisfies the equation since 2 + (-1) = 1. Similarly, if x = 0, then y = 1 satisfies the equation since 0 + 1 = 1.

Therefore, the proposition (d) is true.

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Answer:

280

Step-by-step explanation:

when you get the answer to all of that, you get 280 have a great day :)

the answer is 280.

Division is the process of splitting a number or an amount into equal parts.

here, we have,

given that,

4(950/2-125)/5

=4(475-125)/5

=4(350)/5

=1400/5

=280

hence, the answer is 280.

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Answer:

$ 256

Step-by-step explanation:

square footage of door =   8 x 4 = 32 ft^2

32 ft^2  * 8 dollar /ft^2  = $ 256

Applying the rule of exponent, the equivalent expression is: \(x^{45}y^{5}z^{20}\)

One of the rules of exponents is given as, \((xy)^m=(x^m)(y^m)\).

Therefore, given:

(x9yz4)5

To find the equivalent expression, apply the rule of exponents as shown below:

\((x^9yz^4)^5=(x^{9*5})(y^5)(z^{4*5})\)

\((x^9yz^4)^5=x^{45}y^5z^{20}\)

Therefore, applying the rule of exponent, the equivalent expression is:

\(x^{45}y^{5}z^{20}\)

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Answer:

chromosomes

Step-by-step explanation:

The legs are defined by \(L(x) = 2x\). The Hypotenuse if defined by \(h(x) = L(x)\cdot \sqrt{2}\). The perimeter is defined by:

\(p(x) = h(x)+2\cdot L(x) \\~\\p(x) = L(x)\cdot\sqrt{2} +2\cdot L(x) \\~\\p(x) = L(x)\cdot\left(\sqrt{2}+2\right) \\~\\p(x) = 2x\cdot\left(\sqrt{2}+2\right) \\~\\p(x)= 2\sqrt{2}x+4x\)

D. P(x) = 2x √2 + 4x

The perimeter of the isosceles right triangle will be P(x) = x√2 + 2x. Then the correct option is B.

A triangle is a three-sided polygon with three angles. The angles of the triangle add up to 180 degrees.

The sum of all the sides of the triangle will be known as the perimeter of the triangle.

In an isosceles triangle, the two legs of the triangle are congruent and their opposite angles too.

An isosceles right triangle has a hypotenuse length that can be modeled with the function h(x) = x√2.

The combined length of the legs can be modeled with the function L(x) = 2x.

Then the perimeter of the isosceles right triangle will be

P(x) = h(x) + L(x)

P(x) = x√2 + 2x

Thus, the perimeter of the isosceles right triangle will be P(x) = x√2 + 2x.

Then the correct option is B.

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The property illustrated in equation 4(-8+5) = -32 + 20 is the Distributive Property.

The Distributive Property states that when a number is multiplied by a sum or difference in parentheses, it can be distributed or multiplied by each term inside the parentheses separately, and then the results can be added or subtracted.

In this case, the number 4 is multiplied by the sum (-8 + 5). By applying the Distributive Property, we distribute the 4 to each term inside the parentheses:

4(-8 + 5) = (4 * -8) + (4 * 5)

This simplifies to:

4(-8 + 5) = -32 + 20

Finally, we can perform the addition:

-32 + 20 = -12

Therefore, the equation demonstrates the application of the Distributive Property.

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2x+3y-12=0

Step-by-step explanation:

Thats. That. boi. byś.

Answer:

4

Step-by-step explanation:

2(0) + 3y = 12

3y = 12

  4

Hopefully this helps you!!!

Answer:

4005

Step-by-step explanation:

3,998 - (-7) = ?

Two negative signs will make a positive sign.

3,998 - (-7) = 3998 + 7 = 4005

So, the answer is 4005

This is how to solve it, I believe this is correct. If you need a better understanding, let me know.

Answer:

The area of the garden is 12.

Step-by-step explanation:

All you have to do is multiple the width time the length and you will get 12.

Answer:

(0,0) (1,-12)

:)

The value of x is 17

Define Angle

An angle is the figure formed by two rays, called the sides of the angle, sharing a common endpoint, called the vertex of the angle.

Define Mid-line in Triangle

In a triangle, a midline (or a midsegment) is any of the three lines joining the midpoints of any pair of the sides of the triangle.

We know, the x+6 is mid-line of 46.

So, according to that make it a half of 46 is 23

Now, equate the value and find x

23 = x + 6

23 - 6 = x

17 = x

swap the sides

x = 17

Hence, the value of x is 17

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Answer:

Step-by-step explanation:

Scholarship and grants are money given to the candidates to support his financial needs in school. It will serves as the means of revenue for the student.

Revenue generated = Grant + Scholarship amount

Revenue generated = $350 + $400

Revenue generated= $750

Total money needed to be spent in school = Tuition + fees

If tuition is $113.67 per credit hour and I used 15 credit hours, total amount of tuition paid = 15* $113.67 =  $1705.05

Total fees =  $660

Total money needed to be spent in school = $1705.05 + $660

Total money needed to be spent in school =  $2365.05

Amount I will need to pay for classes next semester = Total money that will be spent - (grant+scholarship)

=  $2365.05 - $750

= $1615.05

Hence, the amount I will need to pay for classes next semester is  $1615.05

The composition (f o g)(x) = 10/(x+10) and its domain is all real numbers except x = -10.

a) To find (f o g) (x), we need to substitute g(x) into f(x) wherever we see x. That is,

(f o g) (x) = f(g(x)) = f(10/x) = (10/x) / (10/x + 1)

b) To find the domain of (f o g) (x), we need to look for any values of x that make the denominator of the expression equal to zero, since division by zero is undefined. Thus, we solve the equation:

10/x + 1 = 0

10/x = -1

x = -10

Therefore, the domain of (f o g) (x) is all real numbers except x = -10, since that value makes the denominator equal to zero. In interval notation, the domain is:

(-∞, -10) U (-10, ∞)

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Answer:

2.005 x 10^2

Step-by-step explanation:

Answer:2661615

Step-by-step explanation:

29573.5 is how many millimeters are in an ounce multiply that by 90 and you get 2661615

hope this helps

Answer:

you used two different types of things ounces measure mass and millimeters measure length

but I used google and it said 2.662e+6

Answer:

y = -8/3x + 8

Step-by-step explanation:

Step 1:  Identify which values we have and need to find in the slope-intercept form:

The general equation of the slope-intercept form of a line is given by:

y = mx + b, where

Since we're told that the y-intercept is 8, this is our b value in the slope-intercept form.

Step 2:  Find m, the slope of the line:

Thus, we can find m, the slope of the line by plugging in (3, 0) for (x, y) and 8 for b:

0 = m(3) + 8

0 = 3m + 8

-8 = 3m

-8/3 = m

Thus, the slope is -8/3.

Therefore, the the equation of the line in slope-intercept form whose x-intercept is 3 and whose y-intercept is 8 is y = -8/3x + 8.

Optional Step 3:  Check the validity of the answer:

Thus, we can check that we've found the correct equation in slope-intercept form by plugging in (3, 0) and (0, 8) for (x, y), -8/3 for m, and 8 for b and seeing if we get the same answer on both sides of the equation when simplifying:

Plugging in (3, 0) for (x, y) along with -8/3 for m and 8 for b:

0 = -8/3(3) + 8

0 = -24/3 + 8

0 = -8 = 8

0 = 0

Plugging in (0, 8) for (x, y) along with -8/3 for m and 8 for b;

8 = -8/3(0) + 8

8 = 0 + 8

8 = 8

Thus, the equation we've found is correct as it contains the points (3, 0) and (0, 8), which are the x and y intercepts.

Answer:

-6m² - 16mw + 5w²

General Formulas and Concepts:

Pre-Algebra

Algebra I

Step-by-step explanation:

Step 1: Define

(-10m² - 11mw - 7w²) - (-4m² + 5mw - 12w²)

Step 2: Simplify

Answer:

-6m² - 16mw + 5w²

Step-by-step explanation:

(−10m2−11mw−7w2)−(−4m2+5mw−12w2)=−10m2−11mw−7w2+4m2−5mw+12w2

Use the commutative property to bring the like terms together and simplify.

−10m2−11mw−7w2+4m2−5mw+12w2=−10m2+4m2−11mw−5mw−7w2+12w2=−6m2−16mw+5w2

Answer:

vfvgyfygj

Step-by-step explanation:

gvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvdyu so yeah

Answer:

(0, -8)

General Formulas and Concepts:

Pre-Algebra

Order of Operations: BPEMDAS

Equality Properties

Algebra I

Step-by-step explanation:

Step 1: Define Systems

y = 4x - 8

x - 2y = 16

Step 2: Solve for x

Substitution

Step 3: Solve for y

Answer:

C

Step-by-step explanation:

Zscore = - 0.18 ; Z = 1.23

To find the percentage :

P(Z< 1.23) - P(Z < - 0.18)

Using the Z probability calculator :

P(Z < - 0.18) = 0.42858

P(Z < 1.23) = 0.89065

0.89065 - 0.42858

= 0.46207

= 46.2%

Answer:

x=5

Step-by-step explanation:

i think you posted this question twice, but here it is:

in order for this figure to truly be a kite, AD and AB have to be equal.

So:

4x=x+15

now we must solve the equation:

3x=15

x=5

The point estimate for the population proportion of adults in the country who believe that televisions are a luxury they could do without is 0.5069.

A population is described as a collection of people who belong to the same species and cohabit in a certain region. In order to survive throughout time, individuals of a population frequently rely on the same resources, are susceptible to the same environmental restrictions, and depend on the availability of other members.

A sample is a more limited representation of the population as a whole. It serves as a good sample for a study's population. The people who are invited to participate in surveys are considered the sample while conducting them.

Let assume,

x be the population who believe that televisions are a luxury

n is the random sample of adults.

So, x = 511, n = 1008

Thus, population, p = x/n

or, p = 511 /1008

or, p = 0.5069

Thus, The point estimate for the population proportion of adults in the country who believe that televisions are a luxury they could do without is 0.5069.

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