Point O is the centroid of triangle ABC. If OD=3x -2 and OC= 5x, find x.

It looks like the integral is

[tex]\displaystyle \int_C (3x+4y)\,\mathrm dx + (2x-3y)\,\mathrm dy[/tex]

where C is the circle of radius 2 centered at the origin.

You can compute the line integral directly by parameterizing C. Let x = 2 cos(t ) and y = 2 sin(t ), with 0 ≤ t ≤ 2π. Then

[tex]\displaystyle \int_C (3x+4y)\,\mathrm dx + (2x-3y)\,\mathrm dy = \int_0^{2\pi} \left((3x(t)+4y(t))\dfrac{\mathrm dx}{\mathrm dt} + (2x(t)-3y(t))\frac{\mathrm dy}{\mathrm dt}\right)\,\mathrm dt \\\\ = \int_0^{2\pi} \big((6\cos(t)+8\sin(t))(-2\sin(t)) + (4\cos(t)-6\sin(t))(2\cos(t))\big)\,\mathrm dt \\\\ = \int_0^{2\pi} (12\cos^2(t)-12\sin^2(t)-24\cos(t)\sin(t)-4)\,\mathrm dt \\\\ = 4 \int_0^{2\pi} (3\cos(2t)-3\sin(2t)-1)\,\mathrm dt = \boxed{-8\pi}[/tex]

Another way to do this is by applying Green's theorem. The integrand doesn't have any singularities on C nor in the region bounded by C, so

[tex]\displaystyle \int_C (3x+4y)\,\mathrm dx + (2x-3y)\,\mathrm dy = \iint_D\frac{\partial(2x-3y)}{\partial x}-\frac{\partial(3x+4y)}{\partial y}\,\mathrm dx\,\mathrm dy = -2\iint_D\mathrm dx\,\mathrm dy[/tex]

where D is the interior of C, i.e. the disk with radius 2 centered at the origin. But this integral is simply -2 times the area of the disk, so we get the same result: [tex]-2\times \pi\times2^2 = -8\pi[/tex].

Answer:

12.6>12.3

Step-by-step explanation:

Answer:

5/26 chance because there is only five vowels in the alphabet

Answer:

Not counting y as a vowel: 5/26  or a  19.23% chance

Step-by-step explanation:

There are a total of 26 letters in the alphabet.

There are 5 vowels (a, e, i, o, u)

Picking a vowel has a 5 in 26 chance of occurring.

Answer:

Option A because functions only point to 1 output.

Answer:

[tex]\boxed {\boxed {\sf ( -9, \frac{11}{2}) }}[/tex]

Step-by-step explanation:

We are asked to find the midpoint of a segment. We essentially calculate the average of the x-coordinates and the y-coordinates using the following formula.

[tex]( \frac {x_1+x_2}{2}, \frac{ y_1 + y_2}{2})[/tex]

In this formula, (x₁ , y₁) and (x₂ , y₂) are the endpoints of the segment. For this problem, the 2 endpoints are (-12, 12) and (-6, -1). If we match the variable and the corresponding value, we see that:

Substitute the values into the formula.

[tex]( \frac{-12 + -6}{2}, \frac{12 + -1} {2} )[/tex]

Solve the numerators.

[tex]( \frac{-18}{2}, \frac{11}{2})[/tex]

Divide.

[tex]( -9, \frac{11}{2} )[/tex]

The midpoint of the segment is [tex]\bold {( -9, \frac{11}{2} )}[/tex].

Answer:

.........................

Step-by-step explanation:

............................................................................

Answer:

Angle ABD = 60

Step-by-step explanation:

Angle ABD = angle ABC + angle CBD

We are given that angle ABC = 25 and angle CBD = 35

So angle ABD = 25 + 35 = 60

Answer:

60

Step-by-step explanation:

to find the length of the entire angle, you will have to add both seperated sides to find it.

<ABC = 25

<CBD = 35

25 + 35 = 60

So, <ABD = 60

Hope this helped.

Answer:

twice the

Step-by-step explanation:

hope it helps you

Answer:

the value of x = 40

I hope it's helps you

Answer:

[tex]x = 40 \\ \\ [/tex]

it's vertical angel they are equal each other ( = )

Answer:

$15,500

Step-by-step explanation:

It would help if you put the actual question in place

    10³ CDs = 1000 at $12 each    = $12000

+ 10² Players = 100 at $35 each = $  3500

Total                                                 $15500

103(12) + 102(35) = $4806

Answer:

4x-3 16t-4

Step-by-step explanation:

Answer:

1. 8x-4x=4x

5-2=3

so the answer will be

4x+3

2.9t-7t+12-8=2t+4.

3.i have no idea

4. 18x^2+12x^2+16x-11x-17+19=30x^2+5x-36.

Answer:

420 even numbers

Step-by-step explanation:

Answer

Total 4 digit even numbers = (Total even numbers) - (Total 3 digit even numbers)

Total even numbers: 4⋅6⋅5⋅4=480

Total 3-digit even numbers: 3⋅5⋅4⋅1=60

Total 4-digit even numbers: 480−60=420 ??

Step-by-step explanation:

Answer:

D

Step-by-step explanation:

standard form would be 3x^2-12x+12

vertex form y=3(x-2)^2

Answer:

y = 3(x + 2)2

Step-by-step explanation:

Answer:

2√10 + 2√10 + 3√10 =7√10

Step-by-step explanation:

√40=√10×4 =√10×√4 = 2√10

√90= √10×9 = √10×√9 =3√10

Answer:

y=3x-3

Step-by-step explanation:

slope intercept form is y=mx+b

you are given m as 3 and b as -3

so substitute

y=3x-3

Answer:

15 degree = 54,000 seconds

Step-by-step explanation:

15*60*60

Answer:

She bought more polka dot fabric

Step-by-step explanation:

you can cross multiply so 9x11=99 and 12x7=84. Since 99>84, 11/12>7/9

Answer:

join me on no comments yet the story is about to the turf and a bagane and pinni geting step by step explanation friendship is not working properly and the story of a y I have a mantra and sister about your self and the story of the story is a bagane unda and the story and the portion of the story of the story of the story is about the event of a y you know if

3(4x+3)=12x+9

i don't know what do you need,

if roots, let 12x+9=0

the root is x=-3/4

Answer:

102=2*3*17

68=2*2*17

136=2*2*2*2*17

The common prime factors are 2 and 17

Highest common factor (HCF)=2*17=34

Answer:

120 customers on the 2nd day

Step-by-step explanation:

100/1ST DAY

120/2nd day

140/3rd day

160/ 4TH DAY

Answer:

Step-by-step explanation:

Distance between two points P(x1,y1) and Q(x2,y2) is given by: d(P, Q) = √ (x2 − x1)2 + (y2 − y1)2 {Distance formula} 2. Distance of a point P(x, y) from the origin is given by d(0,P) = √ x2 + y2.

Answer:

use phythagoras formula of calculating right angles

a^2=b^2+c^2

42^2=b^2+78^2 (substitution + transposement)

b^2=72^2-42^2

b^2=3420 (introduce a square root both sides)

what you do on the left .you also do it on the right

b is the unknown side of the triangle

b=58.48 inched

The lengths of the legs of the right angle triangle is 30 inches and 72 inches.

A triangle is a closed plane figure formed by joining three noncolinear points.

We know Pythagoras's theorem which states the sum of the squares of the smaller two sides of a right-angle triangle is equal to the square of the largest side.

Given one leg of a right-angle triangle is 42 inches longer than the other leg.

Assuming the smallest leg to be x inches.

∴ The other leg is (x + 42) inches also given hypotenuse is 78 inches.

∴ (x + 42)² + x² = 78².

x² + 84x + 1764 + x² = 6084.

2x² + 84x - 4320 = 0.

x² + 42x - 2160 = 0.

As length can not be negative value of x = 30 inches.

∴ The smaller leg is 30 inches and the larger leg is (30 + 42) = 72 inches.

learn more about triangles here :

https://brainly.com/question/2773823

#SPJ2

Answer:

X=6

Step-by-step explanation:

20 × 1 or y = 20

5 × 1 or y = 5

20 - 5 = 15

1 or y + 5 = 6

Answer: The antonym of multiply is divide.

Answer:

Divide

Step-by-step explanation:

Antonym simply means the opposite of the given word.

So the opposite of multiplication is division thus division is the answer.

HOPE THIS HELPED

Answer:

[tex]\sf 2(3\sqrt{8}+4\sqrt{20}+2\sqrt{24})[/tex]

[tex]\sf 2(3\sqrt{8})+2(4\sqrt{20}+2\sqrt{24})[/tex]

[tex]\sf 12 \sqrt{2}+16 \sqrt{5}+8 \sqrt{6}[/tex]

[tex]\sf 6 \cdot 8^{\frac{1}{2}}+8 \cdot 20^{\frac{1}{2}}+4 \cdot 24^{\frac{1}{2}}[/tex]

[tex]\sf 12 \cdot 2^{\frac{1}{2}}+16 \cdot 5^{\frac{1}{2}}+8 \cdot 6^{\frac{1}{2}}[/tex]

Step-by-step explanation:

Perimeter of a rectangle

Perimeter = 2(width + length)

Given information:

  [tex]\textsf{width} = 3\sqrt{8}[/tex]

  [tex]\textsf{length} = 4\sqrt{20}+2\sqrt{24}[/tex]

Equivalent Expression 1

Substitute the given information into the formula:

[tex]\sf Perimeter = 2(3\sqrt{8}+4\sqrt{20}+2\sqrt{24})[/tex]

Equivalent Expression 2

Using the distributive property law, this can also be written as:

[tex]\sf Perimeter = 2(3\sqrt{8})+2(4\sqrt{20}+2\sqrt{24})[/tex]

Equivalent Expression 3

Distribute the parentheses and simplify the radicals:

[tex]\begin{aligned}\sf Perimeter & = \sf 2(3\sqrt{8}+4\sqrt{20}+2\sqrt{24})\\& = \sf 6\sqrt{8}+8\sqrt{20}+4\sqrt{24}\\& = \sf 6\sqrt{4 \cdot 2}+8\sqrt{4 \cdot 5}+4\sqrt{4 \cdot 6}\\& = \sf 6\sqrt{4}\sqrt{2}+8\sqrt{4}\sqrt{5}+4\sqrt{4}\sqrt{6}\\& = \sf 6 \cdot 2 \sqrt{2}+8 \cdot 2 \sqrt{5}+4 \cdot 2 \sqrt{6}\\& = \sf 12 \sqrt{2}+16 \sqrt{5}+8 \sqrt{6}\end{aligned}[/tex]

Equivalent Expression 4

Distribute the parentheses and rewrite the square roots as [tex]\sf \sqrt{a}=a^{\frac{1}{2}}[/tex] :

[tex]\begin{aligned}\sf Perimeter & = \sf 2(3\sqrt{8}+4\sqrt{20}+2\sqrt{24})\\& = \sf 6\sqrt{8}+8\sqrt{20}+4\sqrt{24}\\ & = \sf 6 \cdot 8^{\frac{1}{2}}+8 \cdot 20^{\frac{1}{2}}+4 \cdot 24^{\frac{1}{2}}\end{aligned}[/tex]

Equivalent Expression 5

Rewrite the square roots as [tex]\sf \sqrt{a}=a^{\frac{1}{2}}[/tex] :

[tex]\sf Perimeter=12 \cdot 2^{\frac{1}{2}}+16 \cdot 5^{\frac{1}{2}}+8 \cdot 6^{\frac{1}{2}}[/tex]

Sorry I'm not sure if I'm right just my thinking...

set the number to be x so that (5x+2)(3x-4)??

Step-by-step explanation:

The domain of a function is the range of x such that the function is defined.

Now we know the function

[tex]f(x) = \frac{1}{ {x}^{2} + 3x - 4 }[/tex]

is only defined when the denominator is not zero, in other words, when

[tex] {x}^{2} +3x - 4 \neq \: 0[/tex]

or

[tex](x + 4)(x - 1) \neq0[/tex]

[tex]x \ne-4 [/tex]

and

[tex]x \neq +1[/tex]

Answer:

this is unclear

Step-by-step explanation:

yoy miss typed