Quadrilateral JKLM is rotated 90° clockwise about the origin to produce Quadrilateral J'K'L'M'. is m 60 80 100 120

The integral can be evaluated by substituting everything you know:

[tex]\displaystyle\int_C\mathbf F\cdot\mathrm d\mathbf r=\int_C\mathbf F(x(t),y(t),z(t))\cdot\dfrac{\mathrm d\mathbf r}{\mathrm dt}\,\mathrm dt[/tex]

[tex]=\displaystyle\int_0^1(t^3\,\mathbf i+t^5\,\mathbf j+t^4\,\mathbf k)\cdot(\mathbf i+2t\,\mathbf j+3t^2\,\mathbf k)\,\mathrm dt[/tex]

[tex]=\displaystyle\int_0^1(t^3+5t^6)\,\mathrm dt[/tex]

[tex]=\dfrac{t^4}4+\dfrac{5t^7}7\bigg|_0^1=\dfrac14+\dfrac57=\boxed{\dfrac{27}{28}}[/tex]

The line integral ∫F · dr along the curve is 9/10.

To evaluate the line integral ∫F · dr along the curve C, where F(x, y, z) = xyi + yzj + zxk and C is the twisted cubic given by x = t, y = t², z = t³ for 0 ≤ t ≤ 1, we need to parameterize the curve C and compute the dot product between F and the tangent vector dr.

The parameterization of C is:

r(t) = ti + t²j + t³k

To compute dr, we take the derivative of r(t) with respect to t:

dr = (dx/dt)i + (dy/dt)j + (dz/dt)k

dr = i + 2tj + 3t²k

Now we can compute the dot product between F and dr:

F · dr = (xy)(dx/dt) + (yz)(dy/dt) + (zx)(dz/dt)

F · dr = (t)(i) + (t²)(2t)(j) + (t)(t³)(3t²)(k)

F · dr = ti + 2t³j + 3t⁴k

To evaluate the line integral, we integrate F · dr with respect to t over the interval [0, 1]:

∫[0,1] F · dr = ∫[0,1] (ti + 2t³j + 3t⁴k) dt

Integrating each component separately:

∫[0,1] ti dt = (1/2)t² ∣[0,1] = (1/2)(1)² - (1/2)(0)² = 1/2

∫[0,1] 2t³j dt = (1/4)t⁴ ∣[0,1] = (1/4)(1)⁴ - (1/4)(0)⁴ = 1/4

∫[0,1] 3t⁴k dt = (1/5)t⁵ ∣[0,1] = (1/5)(1)⁵ - (1/5)(0)⁵ = 1/5

Adding the results together:

∫[0,1] F · dr = (1/2) + (1/4) + (1/5) = 5/10 + 2/10 + 2/10 = 9/10

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Answer:

-19.42

-19.42

-19.42

-19.42

Step-by-step explanation:

It's a charge, so they'll be negative. It's four different charges so they'll stack like this.

Answer:

Step-by-step explanation:

2n + 8.5 = 23

2n = 14.5

2n = 7.25 or 7 1/4 feet

Answer:

1.0

Step-by-step explanation:

The 6 is bigger than 5, so that bups the number up to 1.0.

Answer:

ok put it in a calculator

(12,-12

Answer:

25%

Step-by-step explanation:

There are 6+8+10 = 24 cookies

P ( chocolate chip) = number of chocolate chip/ total

                               = 6/24 = 1/4

Changing to percent

1/4 = 25/100 = 25%

Answer:

Hannah is taller because her z-score is higher than Kylie’s z-score.

Step-by-step explanation:

Answer:

149.40625 approximately

Step-by-step explanation:

There isn't really an explanation, you can just use a calculator ;)

Answer:

Step-by-step explanation:

4781/32

without using calculator you can configure this.

AS

32√4781   ║ 149.40625

    -  32  

        1581

      - 128

          301

        - 288      

             1 30                           (put decimal above to add zero in reminder)

          -  128

                200  (one 0 is from decimal and to add another one add 0 abov)

              -192

                   80

                  -64

                    160

                   - 160

                       X  

Answer:

Step-by-step explanation:

8 inches : 3 feet

12 x 3 = 36 inches

8 inches: 36 inches = 2 inches: 9 inches

The ratio in simplest form to express 8 inches over 3 feet is 2:9.

To express the ratio of 8 inches to 3 feet in simplest form, we need to convert the measurements to a common unit.

Since both measurements involve length, we can convert inches to feet or feet to inches.

We know that 1 foot = 12 inches

So 3 feet = 12×3

=36 inches.

Now the ratio 8 inches over 3 feet is equal to 8 inches over 36 inches.

8/36

Divide numerator and denominator by 4:

2/9

Hence, the ratio in simplest form to express 8 inches over 3 feet is 2:9.

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Answer:

y = 4/5 x - 4

Step-by-step explanation:

Answer is given below

Step-by-step explanation:

given data

average length of all 1015 fishes = 98.06 mm

randomly selects 50 fishes average length = 101.04 mm

solution

Answer: C is the correct answer

Answer:

-18.75 is a rational number. A rational number is any number that has either a repeating decimal or one that ends. It doesn’t no go on, so it is considered rational. Hopefully this helps! Feel free to mark brainliest!

-18.75 is a rational number

Rational numbers are numbers that can be expressed as the fractions of two integers

That is, R is a rational number if it can be expression as:

R  =  p/q

where p and q are integers

-18.75 can be expressed as -1875/100 where both -1875 and 1000 are integers.

Since -18.75 can be expressed as the fraction of two integers, it is a rational number.

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X equal to 6 plus 1 by 3 which is 19 by 3 is the answer which is also a improper fraction

Answer:

x=19/3

Step-by-step explanation:

x-1/3 =6 /×3

3x - 1 =18

3x=18 +1

3x =19

x=19/3

Answer:

x = 6

∠B = 126

Step-by-step explanation:

∠A = ∠B

where

∠A = 8x + 78°

∠B = 2x + 114°

8x + 78°  = 2x + 114°    

8x - 2x = 114 - 78

6x = 36

x = 36/6

x = 6

plugin x into  ∠B = 2x + 114°

∠B = 2x + 114°

∠B = 2(6) + 114°

∠B = 126

Answer:

x = 6

∠B = 126

Step-by-step explanation:

i got this correct

Answer:

4+is the absolute value is greater than 3

Answer:

i think x=-1 and y=3. ....

Answer:

x = -1 ,  y = 3

Step-by-step explanation:

2x+5y = 13

-x+4y = 13

Decide whether to add or subtract the two equations by using Different Add Same Subtract (DASS)   or in case below as its SUBTRACT

i apply (SDSS).  

We subtract 5y as this is easier equation either positive prioritises or if both positive then easier number becomes priory.

Results to SDSS  before substituting Y if 5y etc was subtracted

2x+5y = 13             Subtract -5  

2x+5y -5y = 13 -5y  

2x= 13 - 5y             then Divide by 2

2x / 2 = 13/2 - 5y/2          Show then

x = 13 - 5y  / 2  + 4y = 13     Simplify

simplify  13 - 13y  / 2   as   y = 3  

as 13/2 = 6.5 and 2.5 +4 = 6.5

y = 3

Substitute y = 3

13-5y )3) / 2

13-5 (3)  / 2

BODMAS Brackets first Multiplying only for y substitute 5y = 5 x 3

-5 (3) = 15

13-15 = -2

-2/2 = -1

x = -1

Step-by-step explanation:

DG+GM=DM

r+2+2r-13=25

combine like terms

3r-11=25

3r=36

r=12

Answer:

x=6.5

Step-by-step explanation:

2x+3=16

2x=16-3

2x=13

x=13/2

x=6.5

Answer; bonjour , j ai compris que le 2 c est

Step-by-step explanation:

This is 36,96  , and 14,3

The composite function g(f(x)) is equivalent to 10x^2 - 1

This are also referred to as function of a function. Given the following functions;

f(x) = 2x^2 - 5

g(x) = 5x + 7

In order to determine the composite function g(f(x))

g(f(x)) = g(2x^2 - 5)

Replace x with 2x^2 - 5 in g(x) to have;

g(f(x)) = 5(2x^2 - 5) + 7

g(f(x)) = 10x^2 - 18

Hence the composite function g(f(x)) is equivalent to 10x^2 - 1

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Answer:

[tex]\frac{2x+2}{x}\ge \:0[/tex]

Step-by-step explanation:

[tex]3+\frac{4}{x}\ge \frac{x+2}{x}[/tex]

Subtract [tex]\frac{x+2}{x}[/tex] from both sides:

[tex]3+\frac{4}{x}-\frac{x+2}{x}\ge \frac{x+2}{x}-\frac{x+2}{x}[/tex]

[tex]3+\frac{4}{x}-\frac{x+2}{x}\ge \:0[/tex]

[tex]\frac{3x}{x} +\frac{-x+2}{x}[/tex]

[tex]\frac{2x+2}{x}\ge \:0[/tex]

Answer:

C.) 1

Step-by-step explanation: Any number raised to the zeroth power will always be 1.

Answer: 27

Step-by-step explanation:

-21 to 6= 27

The difference between the numbers -21 and 6 is 27.

A number line in elementary mathematics is a representation of a graduated straight line that serves as an abstraction for real numbers, represented by the symbol R." It is assumed that every point on a number line corresponds to a real number and that every real number corresponds to a point.

Given that the two numbers are -21 and 6. The distance between the two numbers will be calculated as,

Distance = 6 - ( -21 )

Distance = 6 + 21

Distance = 27

Hence, the difference is 27.

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Answer:

163

Step-by-step explanation:

10(10)+9(7) Stubstitute the variables for the values given

100+63 Multiply

163 Add

Answer: $0.31

Step-by-step explanation:

A dozen = 12

Cost of 12 daises = 3.75

Cost of one daisy = 3.75/12 = 0.3125

0.3125 to the nearest hundredth = 0.31  

Answer: 6x6 =36

Step-by-step explanation:

Sorry if it's wrong, but should be right cause it makes sense.