Problem 4. (10 points) Evaluate the line integral [(32³y + 4y) ds, where C is the portion of the circle x² + y² = 4 that joins the point A = (2,0) to the point B = (-√√2, √2) counterclockwise

here is a link to the aneser hope it helps

The coordinates of the image of the point (4,5) after reflecting over the

the y-axis is (- 4, 5).

Two-dimensional figures can be transformed mathematically in order to travel about a plane or coordinate system.

Dilation: The preimage is scaled up or down to create the image.

Reflection: The picture is a preimage that has been reversed.

Rotation: Around a given point, the preimage is rotated to create the final image.

Translation: The image is translated and moved a fixed amount from the preimage.

Given, A point (4, 5) is reflected over the y-axis.

We know points of coordinated (x, y) reflected over the x-axis becomes

(- x, y).

Therefore, The coordinate points (4, 5) after reflecting over the y-axis would be ( - 4, 5).

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Answer: 4°F

Step-by-step explanation:

8-4=4

Thus, the linear equation for the perimeter if the rectangle is found as:

P = 2(8x + 8y) units.

P = (L + W) 2 is the perimeter rule for a rectangle, where P stands for perimeter, L for length, and W for width.

To find the perimeter of a rectangle with specified dimensions, all you need to do is enter the values of L and W into the formula.

The perimeter calculation can be used, for instance, to calculate how many feet with brick border are required overall if the rectangle  depicts a garden that requires a brick border.

Given data:

Length = x + 7y units

Width = 8x-x+y units

perimeter P = 2(L + W)

P = 2(x + 7y + 8x - x + y)

adding the same variables.

P = 2(8x + 8y)

Thus, the linear equation for the perimeter if the rectangle is found as:

P = 2(8x + 8y) units.

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Complete question:

Find the perimeter

Length = x + 7y units

Width = 8x-x+y units

Answer:

y = -2x.

Step-by-step explanation:

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

y = mx + b

where m is the slope of the line, and b is the y-intercept.

In this case, the slope is -2, and the y-intercept is 0. So we can substitute these values into the slope-intercept form of the equation:

y = (-2)x + 0

Simplifying, we get:

y = -2x

the equation of the line in slope-intercept form is y = -2x.

Answer:

Total surface area=

304+9pi

~= 332.3

Step-by-step explanation:

Surface area is the areas of all the parts/sides/surfaces of the shape all added together.

There is a BOTTOM, 4 SIDES, a flat TOP, and a DOME shape.

The BOTTOM and SIDES are rectangles, so you can get the areas by multiplying length × width (or b•h)

BOTTOM: 8×10 =80

SIDES: There are 4×8 sides. 4×8 = 32. There are two of them 2×32=64.

There are 4×10 sides. 4×10 = 40. There are two of them, 2×40 = 80

For the flat TOP, it is also 8×10=80, but it has a circle cut out of it. Or, well, the circle that's under the dome doesn't count bc of the dome. So we'll take it away.

CIRCLE (under the dome):

Area of a circle is A=pi•r^2= pi•3^2

A = 9pi

So the flat TOP is:

80 - 9pi ~= 51.7

The DOME is a hemisphere (a half ball shape). Surface Area of a sphere is 4pi•r^2 We find that, then take half.

DOME =

4pi•3^2•(1/2)

= 4pi•9•(1/2)

= 18pi

~= 56.5

Now add up all the pieces:

80+64+80+80-9pi+18pi

= 304+9pi

~= 304 +28.3

= 332.3

The fraction of the bag of sugar that Rick's dad pour into the water is 2/3

An equation is an expression that shows the relationship between numbers and variables.

Fractions is a part of a whole number. It is the ratio of two numbers. The top number is the numerator while the bottom number is the denominator. Hence:

Fraction = numerator / denominator

Rick opens a 3-cup bag of sugar. Rick's dad pours 2 cups into the water. Hence:

Fraction of sugar poured into water = amount of sugar poured in water / total amount of sugar

Substituting:

Fraction of sugar poured into water = 2 cups / 3 cups = 2/3

Ricks dad pour 2/3 of the sugar into the water

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Answer:

If you overshare online your talking to strangers who can learn more about you

Step-by-step explanation:

Another danger is that they can find out more about you and try to kidnap you

Answer:

See explanation.

Step-by-step explanation:

1.

Someone can steal your information.

2.

They can pretend to be you, if your info is stolen.

3.

They can pretend to be someone else. They can also get you out of your school or college, and cause you harm.

hope this helps.

Answer:

64

Step-by-step explanation:

Use  \((x^a)^b=x^{ab}\)

So \(512^{\frac{2}{3}}=(512^\frac{1}{3})^2 =8^2=64\)

Answer:

(0, 3 )

Step-by-step explanation:

Given the 2 equations

16x - 2y = - 6 → (1)

8x - 8y = - 24 → (2)

Multiplying (2) by - 2 and adding to (1) will eliminate the x- term

- 16x + 16y = 48 → (3)

Add (1) and (3) term by term to eliminate x, that is

0 + 14y = 42

14y = 42 ( divide both sides by 14 )

y = 3

Substitute y = 3 into either of the 2 equations and solve for y

Substituting into (1)

16x - 2(3) = - 6

16x - 6 = - 6 ( add 6 to both sides )

16x = 0 , thus

x = 0

solution is (0, 3 )

The angles in the figure are:

∠PQR = 45°

∠POR = 90°

Given : O is the centre of circle, ∠OPQ = 25° and ∠ ORQ = 20°

To Find : ​values of ∠ POR and ∠ PQR.

OP = OQ  = Radius

⇒ ∠OPQ = ∠OQP  

⇒ ∠OQP = 25°

OR = OQ  = Radius

⇒ ∠OQR = ∠ORQ

⇒ ∠OQR = 20°

∠PQR = ∠OQP + ∠OQR

⇒ ∠PQR =   25° + 20°

⇒ ∠PQR =   45°

∠POR = 2∠PQR

⇒ ∠POR = 2*45°

⇒  ∠POR = 90°

Hence we get the two angles as 45° and 90° respectively.

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See picture for math work and answer.

Answer:

the right answer is the last one

<5 and <13

Continuous compounding is the process of calculating interest and reinvesting it into an account's balance over an infinite number of periods.

For continuously compounded interest: FV = PV x e (i x t), where e is the mathematical constant approximated as 2.7183.

What is meant by process?

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5. The value of x in the figure is

7. Length of arc AD is 125 degrees

8. Angle ROT is 36.87 degrees

The length of chord x is solved using Pythagoras theorem as follows

5.

let x/2 = y then we have

y² = 12² - 9 ² = 144 - 81 = 63

y = √63 = 3√7

and x/2 = y = 3√7. so x = 6√7

7. BD is the diameter hence arc BAD = 180 degrees

if arc ABC is 110 then arc BA = 110 /2 = 55

Arc AD = arc BAD - arc BA

Arc AD = 180 - 55

Arc AD = 125 degrees

8. Angle ROT = arc sin (3/5)

Angle ROT = 36.87 degrees

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Step-by-step explanation:

x -y = 92     x = 92+y

xy = minumum

(92+y)  * y  = minumum

y^2 + 92y  = minumum      this quadratic has a minimum at

                                               y = -b/2a =  - 92/(2*1) = - 46

x -  -46 = 92   shows x = +46         minimum is then - 2116  

Answer:

18 tons

Step-by-step explanation:

1 pound = 0.0005 ton

Therefore,

36,000 pounds

= 36000*0.0005

= 18 tons

The area of the wall is 96 square feet.

To find the area of the wall, we multiply the length and width of the wall. In this case, the length of the wall is given as 8ft, and the height or width of the wall is given as 12ft.

Using the formula for the area of a rectangle (A = length × width), we can calculate the area of the wall:

Area = 8ft × 12ft = 96 square feet.

Therefore, the area of the wall is 96 square feet.

It's important to note that the area represents the two-dimensional space covered by the wall.

The given dimensions of 8ft and 12ft refer to the length and width (or height) of the wall, respectively.

By multiplying these two values, we obtain the total area of the wall in square feet.

Knowing the area of the wall is useful for various purposes, such as calculating the amount of paint needed or determining the cost of materials for the painting project.

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Answer:

{3, 4, 5}

Step-by-step explanation:

Domain is all the x's

Answer:

B. {3, 4, 5}

Step-by-step explanation: got it right on edge

Answer:

WY = 24

Step-by-step explanation:

from the diagram WZ and WY are congruent , denoted by the stroke on each segment, then

WY = WZ = 24

Answer: Slope: 16

Step-by-step explanation:

Slope Formula:

(y2-y1)/(x2-x1)=m

(8-(-8))/9-8=

(8+8)/1=16

The price to rent a bike for 2 hours is $25.

The given formula for the price, p, in dollars, to rent a bike for h hours is p = 5h + 15.

We are to find the price to rent a bike for 2 hours.

Substitute h = 2 into the formula p = 5h + 15 to find the price to rent a bike for 2 hours.

p = 5(2) + 15p

= 10 + 15p

= 25

Therefore, the price to rent a bike for 2 hours is $25.

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The can's minimum surface area should have a height of 8 cm and a radius of 4 cm.

Given:

The volume of closed right circular cylindrical cans = 128π cm³

As we know the volume of a cylinder = πr²h

By equating;

πr²h = 128π

h = 128/r²

To get the dimensions of a can with minimum surface area;

S = 2πrh + 2πr

Put h = 128/r²;

Therefore, S(r) = 256π/r + 2πr²

                 S'(r) =  -256π/r² + 4πr

                S''(r) = -(2*256π)/r³ + 4π

Now, for S(r) = 0;

               r = 4cm

         for S''(4) > 0 at r = 4 is minimum point.

Hence,

h = 128π/(π*4*4)

h = 8cm

Therefore, the minimum surface area of the can should have a radius of 4 cm and a height of 8 cm.

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The solution set to the given system of equations using Gauss-Jordan elimination is  x1 = -2, x2 = 0, x3 = -2, x4 = -2.

To solve this system, we can represent the equations in matrix form as follows:

\(\begin{bmatrix}1 &1 & 1 &-1 &| &4 \\1 &-1 &-1 &-1 & | &2 \\ 1&1 &-1 &1 & | &-2 \\1 &-1 &1 & 1 &| &-8 \\\end{bmatrix}\)

We can perform elementary row operations to transform the augmented matrix into reduced row-echelon form. The goal is to create zeros below and above the leading 1's in each row.

Starting with the first row, we can subtract the first equation from all other equations to eliminate x1 from their coefficients. After performing the necessary row operations, the matrix becomes:

\(\begin{bmatrix}1 &1 & 1 &-1 &| &4 \\0&-2 &-2 &0 & | &-2 \\ 0&0 &-2 &2 & | &-6 \\0 &-2 &2& 2 &| &-12 \\\end{bmatrix}\)

Next, we can divide the second row by -2 to create a leading 1. We can continue the process by adding the second row to the third row. And subtracting the second row from the fourth row:Now, we can subtract the third row from the second row:And subtract twice the third row from the fourth row: Finally, we can divide the fourth row by -2 to obtain the reduced row-echelon form:

\(\begin{bmatrix}1 &1 & 1 &-1 &| &4 \\0&0 &-2 &0 & | &6 \\ 0&1 &-1 &2 & | &-5 \\0 &0 &0& 1 &| &-1/2 \\\end{bmatrix}\)

From this form, we can directly read off the solution set: x1 = -2, x2 = 0, x3 = -2, x4 = -2.

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Answer:

true sorry if wrong im not the best at this type of math but im average

Step-by-step explanation:

Answer:

It will take Ernie 6 hours to do the job by himself

Step-by-step explanation:

Rate x time = job

Burt's rate x time + Ernie's rate x time = 1 job getting completed.

\(\frac{1}{3}\)(2) + x(2) = 1  To clear the fraction multiply everything by 3

2 + 6x = 3  Subtract 2 from both sides

6x = 1  Divide both sides by 6

x = \(\frac{1}6}\)  This is Ernie's rate

The rate is the number of jobs 1 over the number of hours 6, so it will take Ernie 6 hours to do this job by himself

Breakdown of clearing the fraction:

(\(\frac{1}{3}\))(2) + x2 = 1  Multiply everything by 3 to clear the fraction.

(\(\frac{3}{1}\))(\(\frac{1}{3}\)((\(\frac{2}{1}\)) + (3)(x2) =  (3) (1)

\(\frac{6}{3}\) + 6x = 6

2 + 6x = 6

Answer:

\(\dfrac{7}{3}\pi \text{ ft.}\)

Step-by-step explanation:

The distance traveled is just the circumference of the wheel

Circumference of a circle of radius r = 2πr

Here
\(r= 1 \dfrac{1}{6}\)

Convert this mixed fraction to an improper fraction:
\(1\dfrac{1}{6}=\dfrac{1\cdot 6+1}{6} = \dfrac{7}{6}\)

Therefore circumference of the wheel:
\(2\pi\cdot \dfrac{7}{6} = \dfrac{7\pi}{3}\)

Answer: Last choice: \(\dfrac{7}{3}\pi\) ft

The distance travelled by the wheel in one rotation is  7π/3 ft.

The circumference of a circle is the distance around the circle.

It is expressed as;

C = 2πr

Where r is the radius

Given that;

First, convert the radius from mixed to improper fraction.

Radius r = 1 1/6

Radius r = ( 1 × 6 + 1 )/6

Radius r = ( 6 + 1 )/6

Radius r = 7/6

Now, plug r = 7/6 into the above formula and simplify.

C = 2πr

C = 2π × 7/6

C = 14π/6

Cancel out the common factor of 14 and 6 which is 2

C = 7π/3 ft

Therefore, the distance is 7π/3 feet.

Option D) 7π/3 ft is the correct answer.

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Step-by-step explanation:

to find the missing side length we need to use the invisible triangle that is kind of cut off in the top left corner.

it is a right-angled triangle, and the missing side is the Hypotenuse (baseline). therefore, we use Pythagoras.

now, can we get the invisible side lengths of this triangle ?

yes, because the complete figure including the invisible triangle is s perfect rectangle with 2 equal lengths and 2 equal widths.

so, the complete rectangle side on the left would also be 5. but we see only 2. so the invisible part is 5-2=3.

and the complete rectangle side in the top would also be 8. but we see only 4. so the invisible part is 8-4=4.

so, with Pythagoras,

unknown side² = 3² + 4² = 9 + 16 = 25.

unknown side = 5

and now the perimeter is

P = 2 + 8 + 5 + 4 + 5 = 24

Answer:

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Answer:

Either 4/9 as a fraction or 0.44444444447